About Electrical & Systems Engineering
The mission of our undergraduate programs is to instill in students the knowledge and perspective, appropriate both for a professional career and for the pursuit of advanced degrees, in fields that rely on key electrical engineering and systems principles and practices. Such principles and practices include rigorous quantitative reasoning and robust engineering design. This mission is accomplished by ensuring that students achieve both depth and breadth of knowledge in their studies and by maintaining a high degree of flexibility in the curriculum. Our programs also seek to provide good preparation for life, including the ability to communicate in written and oral forms and a desire to continue learning throughout life. In addition, they aim to provide the opportunity and training for students to acquire the skills and attitudes to become leaders.
The department offers courses of study leading to degrees in both electrical engineering and systems science and engineering. Opportunities for study and research currently available in the department include semiconductor theory and devices, optoelectronics, nanophotonics, communication theory and systems, information theory, signal and image processing, tomographic imaging, linear and nonlinear dynamics and control, robotics, identification and estimation, multisensor fusion and navigation, computational mathematics, optimization, optimal control, autonomous systems, operations research, and financial engineering. Students are encouraged to participate in research activities as soon as they have received training in the fundamentals appropriate for a given research area.
Electrical engineering is the profession for those intrigued with electrical phenomena and eager to contribute their skills to a society increasingly dependent on electricity and sophisticated electronic devices. It is a profession of broad scope with many specialty careers designed for engineers who seek an endless diversity of career paths on the cutting edge of technology. The Institute of Electrical and Electronics Engineers publishes transactions on about 60 different topics, from aerospace and electronic systems to visualization and computer graphics. This is a breadth so great that no single electrical engineering department can hope to span it. Moreover, those fields themselves encompass still more fascinating specialties. We give the basics; the future is yours to shape.
Systems science and engineering is based on an approach that views an entire system of components as an entity rather than simply as an assembly of individual parts; each component is designed to fit properly with the other components rather than to function by itself. The engineering and mathematics of systems is a rapidly developing field. It is one of the most modern segments of applied mathematics, as well as an engineering discipline. It is concerned with the identification, modeling, analysis, design and control of systems that are potentially as large and complex as the U.S. economy or as precise and vital as a space voyage. Its interests run from fundamental theoretical questions to the implementation of operational systems. It draws on the most modern and advanced areas of mathematics. A very important characteristic of the systems field is that its practitioners must, of necessity, interact within a wide interdisciplinary environment, not only with various engineers and scientists but also with economists, biologists or sociologists. Such interaction is both emphasized and practiced in the programs.
Our Department of Electrical & Systems Engineering offers a challenging basic curriculum, a broadly qualified faculty, and modern facilities so that students can receive a contemporary preparation for a career in electrical or systems engineering.
Undergraduate Degree Programs
The Department of Electrical & Systems Engineering (ESE) offers four undergraduate degree programs: two professional degrees and two applied science degrees. The two professional degrees are the Bachelor of Science in Electrical Engineering (BSEE) and the Bachelor of Science in Systems Science & Engineering (BSSSE). These two programs are accredited by the Engineering Accreditation Commission of ABET. The two applied science degrees are the Bachelor of Science in Applied Science (Electrical Engineering) and the Bachelor of Science in Applied Science (Systems Science & Engineering). All programs have flexible curricula as well as specific requirements, and students may elect programs of study tailored to individual interests and professional goals.
In the professional BSEE curriculum, there are required courses in electrical circuits, signals and systems, digital systems and electromagnetic fields, along with laboratory and design courses, which provide students with a common core of experience. Subsequently, one may orient the program toward breadth, so that many disciplines within the profession are spanned or toward a specialty with more emphasis on depth in one or more disciplines. Areas of specialization include modern electronics, applied physics, telecommunications, control systems, and signal and image processing.
Students in the professional BSSSE degree program take required courses in engineering mathematics, signals and systems, operations research, and automatic control systems, along with laboratory and design courses. This program emphasizes the importance of realworld applications of systems theory, and accordingly students are required to take a concentration of courses in one of the traditional areas of engineering or science. There are numerous elective courses in control theory and systems, signal processing, optimization, robotics, probability and stochastic processes, and applied mathematics.
Students enrolled in any of the ESE undergraduate degree programs have a variety of opportunities to augment their educational experience at Washington University. Students may participate in the PreMedical Engineering program or in the Cooperative Education program. Some students pursue double majors, in which two sets of degree requirements, either within or outside the ESE department, are satisfied concurrently. The Process Control Systems program is one such doubledegree program, involving the degrees Bachelor of Science in Systems Science & Engineering (BSSSE) and Bachelor of Science in Chemical Engineering (BSChE). Finally, students may earn both an undergraduate and a graduate degree through the school's fiveyear BS–Master's program.
Students who seek a broad undergraduate education in electrical engineering or systems science and engineering but plan on careers outside of engineering may pursue the applied science degrees: Bachelor of Science in Applied Science (Electrical Engineering) and Bachelor of Science in Applied Science (Systems Science & Engineering). These programs of study are appropriate for students planning to enter medical, law or business school, who desire a more technical undergraduate experience than what otherwise may be available to them.
The ESE department also offers a variety of educational opportunities for students enrolled in other departments. These include the second major in systems science and the second major in electrical engineering science, which are open to students inside as well as outside of the School of Engineering & Applied Science, such as the College of Arts & Sciences and the School of Business. They also include the minor in applied physics & electrical engineering, the minor in electrical engineering, the minor in energy engineering, the minor in mechatronics, the minor in robotics, and the minor in systems science & engineering.
BS–Master's Programs in Electrical & Systems Engineering
Students enrolled in any of the undergraduate degree programs in the School of Engineering & Applied Science may choose to extend their educational experience by enrolling in a fiveyear BS–Master's program. The Master of Science in Electrical Engineering (MSEE), Master of Science in Systems Science and Mathematics (MSSSM), Master of Control Engineering (MCE), Master of Engineering in Robotics (MER), and Master of Science in Engineering Data Analytics and Statistics (MSDAS) degrees are participating graduate degrees, and these may be combined with any undergraduate degree that provides the appropriate background.
General requirements for the BS–Master's programs include the residency and other applicable requirements of the university and the School of Engineering & Applied Science, which are found elsewhere in this catalog. In summary, students must complete all the degree requirements for both the undergraduate and graduate degrees (at least 120 units plus 30 units; 150 units) but are not required to complete all the undergraduate degree requirements first.
Phone:  3149355565 

Website:  http://ese.wustl.edu 
Chair
R. Martin Arthur
Newton R. and Sarah Louisa Glasgow Wilson Professor of Engineering
PhD, University of Pennsylvania
Ultrasonic imaging, electrocardiography
Endowed Professors
Arye Nehorai
Eugene and Martha Lohman Professor of Electrical Engineering
PhD, Stanford University
Signal processing, imaging, biomedicine, communications
Joseph A. O'Sullivan
Samuel C. Sachs Professor of Electrical Engineering
Dean, UMSL/WUSTL Joint Undergraduate Engineering Program
PhD, Notre Dame University
Information theory, statistical signal processing, imaging science with applications in medicine and security, and recognition theory and systems
Lan Yang
Edward H. & Florence G. Skinner Professor of Engineering
PhD, California Institute of Technology
Nano/micro photonics, ultra highquality optical microcavities, ultralowthreshold microlasers, nano/micro fabrication, optical sensing, single nanoparticle detection, photonic molecules, photonic materials
Professors
Shantanu Chakrabartty
PhD, Johns Hopkins University
New frontiers in unconventional analog computing techniques using silicon and hybrid substrates, fundamental limits of energy efficiency, sensing and resolution by exploiting computational and adaptation primitives inherent in the physics of devices
Hiroaki Mukai
Professor
PhD, University of California, Berkeley
Theory and computational methods for optimization, optimal control, systems theory, electric power system operations, differential games
Heinz Schaettler
PhD, Rutgers University
Optimal control, nonlinear systems, mathematical models in biomedicine
Associate Professors
JrShin Li
Das Family Distinguished Career Development Associate Professor
PhD, Harvard University
Mathematical control theory, optimization, quantum control, biomedical applications
Robert E. Morley Jr.
DSc, Washington University
Computer and communication systems, VLSI design, digital signal processing
Assistant Professors
ShiNung Ching
Das Family Distinguished Career Development Assistant Professor
PhD, University of Michigan
Systems and control in neural medicine, nonlinear and constrained control, physiologic network dynamics, stochastic control
Zachary Feinstein
PhD, Princeton University
Financial engineering, operations research, variational analysis
Ulugbek Kamilov
PhD, École Polytechnique Fédérale de Lausanne, Switzerland
Computational imaging, signal processing, biomedical imaging
Matthew D. Lew
PhD, Stanford University
Microscopy, biophotonics, computational imaging, nanooptics
JungTsung Shen
Das Family Distinguished Career Development Assistant Professor
PhD, Massachusetts Institute of Technology
Theoretical and numerical investigations on nanophotonics, optoelectronics, plasmonics, metamaterials
Chuan Wang
PhD, University of Southern California
Flexible electronics, stretchable electronics, printed electronics, nanomaterials, nanoelectronics, optoelectronics
Shen Zeng
PhD, University of Stuttgart
Systems and control theory, databased analysis and control of complex dynamical systems, inverse problems, biomedical applications
Xuan "Silvia" Zhang
PhD, Cornell University
Robotics, cyberphysical systems, hardware security, ubiquitous computing, embedded systems, computer architecture, VLSI, electronic design automation, control optimization, and biomedical devices and instrumentation
Senior Professors
I. Norman Katz
PhD, Massachusetts Institute of Technology
Numerical analysis, differential equations, finite element methods, locational equilibrium problems, algorithms for parallel computations
Paul S. Min
PhD, University of Michigan
Routing and control of telecommunication networks, fault tolerance and reliability, software systems, network management
William F. Pickard
PhD, Harvard University
Biological transport, electrobiology, energy engineering
Daniel L. Rode
PhD, Case Western Reserve University
Optoelectronics and fiber optics, semiconductor materials, lightemitting diodes (LEDs) and lasers, semiconductor processing, electronics
Ervin Y. Rodin
PhD, University of Texas at Austin
Optimization, differential games, artificial intelligence, mathematical modeling
Barbara A. Shrauner
PhD, Harvard University (Radcliffe)
Plasma processing, semiconductor transport, symmetries of nonlinear differential equations
Donald L. Snyder
PhD, Massachusetts Institute of Technology
Communication theory, random process theory, signal processing, biomedical engineering, image processing, radar
Barry E. Spielman
PhD, Syracuse University
Highfrequency/highspeed devices, RF & MW integrated circuits, computational electromagnetics
Tzyh Jong Tarn
DSc, Washington University
Quantum mechanical systems, bilinear and nonlinear systems, robotics and automation, life science automation
Professors of Practice
Dedric Carter
PhD, Nova Southeastern University
MBA, MIT Sloan School of Management
Dennis Mell
MS, University of MissouriRolla
Ed Richter
MS, Washington University
Jason Trobaugh
DSc, Washington University
Senior Lecturer
Martha Hasting
PhD, Saint Louis University
Lecturers
Randall Brown
PhD, Washington University
Randall Hoven
MS, Johns Hopkins University
Vladimir Kurenok
PhD, Belarus State University (Minsk, Belarus)
Tsitsi MadziwaNussinov
PhD, University of California, Los Angeles
Jinsong Zhang
PhD, University of Miami
Research Assistant Professors
Scott Marrus
MD, PhD, Washington University School of Medicine
Cardiac electrophysiology
Professors Emeriti
William M. Boothby
PhD, University of Michigan
Differential geometry and Lie groups, mathematical system theory
Lloyd R. Brown
DSc, Washington University
Automatic control, electronic instrumentation
David L. Elliott
PhD, University of California, Los Angeles
Mathematical theory of systems, nonlinear difference, differential equations
Robert O. Gregory
DSc, Washington University
Electronic instrumentation, microwave theory, circuit design
Please refer to the sections below for information about the BS in Electrical Engineering, BS in Systems Science & Engineering, BS in Applied Science (Electrical Engineering), BS in Applied Science (Systems Science & Engineering), the Second Major in Electrical Engineering Science, Second Major in Systems Science and the Second Major in Financial Engineering.
Bachelor of Science in Electrical Engineering
This professional degree program is accredited by the Engineering Accreditation Commission of ABET.
Educational Objectives of the BSEE Degree Program
A. Our graduates will be engaged as practicing professionals in a broad range of careers in industry or government or be pursuing advanced degrees in academic graduate education in engineering or a related field.
B. Our graduates will function effectively as members of teams demonstrating sensitivity to professional and societal contexts, integrity and versatility.
Student Outcomes
Graduates of the BSEE program are expected to know or have:
(a) An ability to apply knowledge of mathematics, science and engineering
(b) An ability to design and conduct experiments, as well as to analyze and interpret data
(c) An ability to design a system, component or process to meet desired needs
(d) An ability to function on multidisciplinary teams
(e) An ability to identify, formulate and solve engineering problems
(f) An understanding of professional and ethical responsibility
(g) An ability to communicate effectively
(h) The broad education necessary to understand the impact of engineering solutions in a global and societal context
(i) A recognition of the need for, and an ability to engage in, lifelong learning
(j) A knowledge of contemporary issues
(k) An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
BSEE Degree Requirements
To obtain the degree Bachelor of Science in Electrical Engineering, students must complete a minimum of 120 units consistent with the residency and other applicable requirements of Washington University and the School of Engineering, and subject to the following program requirements.
 Common Studies program of the School of Engineering: This includes courses in engineering, mathematics, chemistry, humanities, social sciences and technical writing. The required chemistry sequence is Chem 111A–Chem 151, although Chem 111A–Chem 112A–Chem 151–Chem 152 is recommended.
 Engr 4501 Engineering Ethics and Sustainability (1 unit).
 Two of the following three computer science courses: CSE 131 Computer Science I (3 units); CSE 132 Computer Science II (3 units); or CSE 247 Data Structures and Algorithms (3 units).
 Engineering and science breadth requirements: 9 units in engineering or science outside of electrical engineering. These units must be taken in the following areas: biomedical engineering; chemical engineering; computer science and engineering; mechanical engineering; systems science and engineering; economics; mathematics; physics; biology; chemistry; earth and planetary sciences; and premedicine. These units must be at the 200 level or higher and shall not be used to satisfy the Common Studies requirements (item 1 above) or the CS requirement (item 3). Courses in other fields can be arranged with special departmental approval.
Examples of engineering and science courses are MEMS 255 Engineering Mechanics II, EECE 210 Introduction to Environmental Engineering, EECE 203 Thermodynamics I in EECE, EECE 201 Engineering Analysis of Chemical Systems, CSE 247 Data Structures and Algorithms, Engr 324 From Concept to Market: The Business of Engineering, BME 240 Biomechanics, Physics 217 Introduction to Quantum Physics, Physics 318 Introduction to Quantum Physics II, MEMS 253 Engineering Mechanics I, Biol 2960 Principles of Biology I, Biol 2970 Principles of Biology II, Chem 261 Organic Chemistry I with Lab, Chem 262 Organic Chemistry II with Lab.  28 units of required ESE courses:
Course List Code Title Units ESE 230 Introduction to Electrical and Electronic Circuits 4 ESE 232 Introduction to Electronic Circuits 3 ESE 260 Introduction to Digital Logic and Computer Design 3 ESE 318 Engineering Mathematics A 3 ESE 319 Engineering Mathematics B 3 ESE 326 Probability and Statistics for Engineering 3 ESE 330 Engineering Electromagnetics Principles 3 ESE 351 Signals and Systems 3 ESE 498 Electrical Engineering Capstone Design Projects 3 Total Units 28  Two upperlevel laboratory courses (6 units) from the following list: ESE 331, ESE 435, ESE 447, ESE 448, ESE 465, ESE 488. The selection must contain at least one course from ESE 331, ESE 435, ESE 465, ESE 488.
 15 units of elective ESE courses in electrical engineering subjects, from the following list: ESE 330–399, ESE 400, ESE 405, ESE 407, ESE 415, ESE 425, ESE 429–499, ESE 503–589.
 The entire course sequence for the BSEE containing engineering topics of at least 45 units. The numbers of engineering topic units assigned to undergraduate courses in the School of Engineering & Applied Science vary from none (0) to the number of credits given to the course. For the precise number for each course, please refer to the table of Topics Units — Engineering Courses provided by Engineering Student Services.
 Limitations. No more than 3 credits of 500level courses may be applied toward the EE elective requirement (item 7).
 Limitations. No more than 6 units of the combined units of ESE 400 Independent Study and ESE 497 Undergraduate Research (including ESE 497A and ESE 497B) may be applied toward the EE elective requirement (Item 7) of the BSEE degree. The balance of combined units, if there are any left, are allowed as free electives to satisfy the requirement on the total number of units.
 The courses taken to satisfy the following BSEE degree requirements must be taken for a letter grade and not on a pass/fail basis: Item 5 (required ESE courses), Item 6 (upperlevel laboratory courses) and Item 7 (elective ESE courses).
Most students acquire more than 120 credit units. For a typical sequence of subjects for the Bachelor of Science in Electrical Engineering degree, please refer to the following tables:
For more information on BS in Electrical Engineering curriculums, please visit the ESE website.
Bachelor of Science in Systems Science & Engineering
This professional degree program is accredited by the Engineering Accreditation Commission of ABET.
Objectives and Requirements
Key points:
 Systems Engineering: how to integrate different components in engineering systems
 Operations Research: mathematical solutions to business problems
 PreFinancial Engineering: the best preparation for the MS in Financial Engineering
 Applied Mathematics
 Control Engineering: how to control jet airplanes, electric power grids, and the nation's economy
 Ideal for students strong in math and physics
 Ideal for students interested in engineering and business
 Ideal for students interested in a second degree
 The most mathematical program in the School of Engineering & Applied Science
 The most flexible professional program in the School of Engineering & Applied Science
This program educates students in the engineering and science of systems. Graduates are expected to have mathematical competence and knowledge of systems analysis, control, design methods, numerical methods, differential equations, dynamic systems theory, automatic control theory, system stability, estimation, optimization, modeling, identification, simulation and basic computer programming. Graduates will have an engineering outlook and engineer's competence of their own and be able to interact fully with other engineers. They also will possess sufficient proficiency in computer use to design algorithms for simulation, estimation, control and optimization.
The engineering departments of hightechnology industries are staffed by large numbers of engineers with this type of expertise. However, graduates are by no means restricted to careers in traditional industry or in hightechnology industries. Within the outlined framework, a salient feature of the program is its flexibility and interdisciplinary nature. It is possible for students to orient study toward preparation for systems science and engineering work in large complex systems such as transportation or power or communications networks or in societal systems such as the economy, ecology, the cities or biological systems. Students may wish to prepare for work along theoretical or professional lines. There is ample room in the program structure to accommodate all these interests and to make preparation at the BS level ideally suited for a student's future plans and interests.
Educational Objectives of the BSSSE Degree Program
A. Our graduates will be engaged as practicing professionals in a broad range of careers in industry or government or be pursuing advanced degrees in academic graduate education in engineering or a related field.
B. Our graduates will function effectively as members of teams demonstrating sensitivity to professional and societal contexts, integrity and versatility.
Student Outcomes
Graduates of the BSSSE program are expected to know or have:
(a) An ability to apply knowledge of mathematics, science and engineering
(b) An ability to design and conduct experiments, as well as to analyze and interpret data
(c) An ability to design a system, component, or process to meet desired needs
(d) An ability to function on multidisciplinary teams
(e) An ability to identify, formulate and solve engineering problems
(f) An understanding of professional and ethical responsibility
(g) An ability to communicate effectively
(h) The broad education necessary to understand the impact of engineering solutions in a global and societal context
(i) A recognition of the need for, and an ability to engage in, lifelong learning
(j) A knowledge of contemporary issues
(k) An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
BSSSE Degree Requirements
The course sequence designed to achieve the type of education outlined above requires at least 120 units, satisfies the residency and other applicable requirements of Washington University and the School of Engineering & Applied Science, and meets the following program requirements:
 Common Studies program of the School of Engineering & Applied Science. This includes courses in engineering, mathematics, physics, chemistry, humanities, social sciences and technical writing. The required chemistry sequence is Chem 111A–Chem 151.
 Engr 4501 Engineering Ethics and Sustainability (1 unit).
 Required courses in systems science and engineering: ESE 205 Introduction to Engineering Design (3 units); Math 309 Matrix Algebra (3 units); ESE 318 Engineering Mathematics A (3 units) and ESE 319 Engineering Mathematics B (3 units); ESE 326 Probability and Statistics for Engineering (3 units); ESE 351 Signals and Systems (3 units); ESE 403 Operations Research (3 units); ESE 441 Control Systems (3 units); ESE 448 Systems Engineering Laboratory (3 units); and ESE 499 Systems Science and Engineering Capstone Design Project (3 units).

Two of the following three computer science courses: CSE 131 Computer Science I (3 units); CSE 247 Data Structures and Algorithms (3 units); and CSE 132 Computer Science II (3 units). Students are encouraged to take CSE 131 Computer Science I and CSE 247 Data Structures and Algorithms. The other possible sequence is CSE 131 and CSE 132.
 One of the following three laboratory courses: ESE 447 Robotics Laboratory (3 units), ESE 449 Digital Process Control Laboratory (3 units), ESE 488 Signals and Communication Laboratory (3 units). ESE 449 is only recommended to students with a chemical engineering background.
 12 units in elective courses in systems science and engineering: ESE 400 through 428; ESE 437; ESE 440 through 459; ESE 470 through 489; ESE 497; ESE 500 through 529; ESE 540 through 559. Up to 3 units of the following business courses may be part of the 12 units of SSE electives: OSCM 356 Operations Management, OSCM 458 Operations Planning and Control, OMM 576 Foundations of Supply Chain Management, OMM 577 Information Technology and Supply Chain Management.
 12 units in engineering concentration outside of systems science and engineering. These units must all be taken in one of the following engineering areas: Biomedical Engineering, Chemical Engineering, Computer Science & Engineering, Electrical Engineering (ESE 102; ESE 230 through 239; ESE 260 through 290; ESE 330 through 339; ESE 360 through 390; ESE 429 through 439; ESE 460 through 469; 490 through 496; ESE 498; ESE 530 through 539; ESE 560 through 589), or Mechanical Engineering & Materials Science. Of the 12 units, 9 units must be at the 200 level or higher. Sequences for concentrations in economics, mathematics, physics, premedicine and other fields can be arranged with special departmental approval to meet a student's specific needs. When a nonengineering discipline is chosen as the outside concentration, the student needs to pay special attention to the next requirement, which is required of all students, and make sure that enough engineering contents are obtained from the other courses. The use of basic required courses to fulfill the requirement for an outside concentration is not permitted.
 The entire course sequence for the BSSSE, containing engineering topics of at least 45 units. The numbers of engineering topic units assigned to undergraduate courses in the School of Engineering & Applied Science vary from none (0) to the number of credits given to the course. For the precise number for each course, please refer to the table of Topics Units — Engineering Courses provided by Engineering Student Services.
 Limitations. No more than 6 units of the combined units of ESE 400 Independent Study and ESE 497 Undergraduate Research (including 497A and 497B) may be applied toward the SSE elective requirement (item 6) of the BSSSE degree. Any remaining combined units are allowed as free electives to satisfy the requirement on the total number of units.
 The courses taken to satisfy the following BSSSE degree requirements must be taken for a letter grade and not on a pass/fail basis: item 3 (required ESE courses), item 5 (elective laboratory course) and item 6 (elective ESE courses).
The program requirements for the BS in Systems Science & Engineering allow a double major with another department. Changes in the program to accommodate such double majors may be made with departmental approval. For a sample program for the BS in Systems Science & Engineering, please refer to the following tables:
 Sample Systems Science & Engineering Curriculum
 Sample PreMed Systems Science & Engineering Curriculum
For more information on BS in Systems Science & Engineering curriculums, please visit the ESE website.
Bachelor of Science in Applied Science (Electrical Engineering)
Students who do not plan to pursue a career in electrical engineering but seek a strong foundation in the principles of electrical engineering may choose the Bachelor of Science in Applied Science (Electrical Engineering). The program ensures that the student learns the foundations of electrical engineering through breadth requirements. In addition, there is flexibility in selecting upperlevel courses to meet the student's individual objectives. This program also may be attractive for students interested in obtaining multiple degrees because the requirements are less strict than for the BSEE degree. Historically students have matched a degree in electrical engineering with degrees in other engineering disciplines, in the natural sciences, in music, in history and in business; other combinations are possible. This also may be an attractive option for students planning graduate studies in a variety of disciplines including medicine, law or business. This applied science degree is not accredited by the Engineering Accreditation Commission of ABET.
The degree requirements include the residency and general requirements of the university and the School of Engineering & Applied Science and:
Courses  Units 

Humanities and social sciences electives  18 
Mathematics, science and engineering electives  24 
Required courses in electrical engineering (ESE 230, ESE 232, ESE 330 and ESE 351)  13 
Computer Science requirement (CSE 131)  3 
Upperlevel elective courses in electrical engineering (ESE 260, ESE 326, ESE 330–399, ESE 400, ESE 405, ESE 407, ESE 415, ESE 425, ESE 429–499, ESE 503–589)  21 
Free electives  41 
Total  120 
The program must include at least 48 units at the 300 level or higher.
Bachelor of Science in Applied Science (Systems Science & Engineering)
This program provides a student with the opportunity to prepare their academic career with maximum flexibility, but with enough organization to assure substantive, consistent training in systems science methodology and outlook. This program is recommended if students wish to pursue a program that does not follow conventional lines. It is an especially advantageous degree for a double major in association with mathematics, physics, economics or another engineering discipline. The program can be planned to provide a desirable background for graduate work in biological, medical or management fields. This applied science degree is not accredited by the Engineering Accreditation Commission of ABET.
The degree requirements include the residency and general requirements of the university and the School of Engineering and:
Courses  Units 

Humanities and social sciences electives  18 
Mathematics, science and engineering electives  24 
Required courses: ESE 205, ESE 351, ESE 403, and ESE 441  12 
Computer Science requirement (CSE 131)  3 
Systems science and engineering electives (ESE 400–428, ESE 437, ESE 440–459, ESE 470–489, ESE 500–529, ESE 540–559)  15 
Free electives  48 
Total  120 
The program must include at least 48 units at the 300 level or higher.
The Second Major in Electrical Engineering Science
A second major in electrical engineering science is ideal for students majoring in many areas, such as mathematics, physics, chemistry and biology. Students in the School of Engineering & Applied Science as well as the other undergraduate divisions at Washington University now have the opportunity to pursue a second major in electrical engineering science. Students are not allowed to add this second major to either the BS in Electrical Engineering or the BS in Applied Science (Electrical Engineering).
The requirements for a second major in electrical engineering science are:
Code  Title  Units 

ESE 230  Introduction to Electrical and Electronic Circuits  4 
ESE 260  Introduction to Digital Logic and Computer Design  3 
ESE 351  Signals and Systems  3 
And one of the following:
Code  Title  Units 

ESE 232  Introduction to Electronic Circuits  3 
ESE 318  Engineering Mathematics A  3 
ESE 319  Engineering Mathematics B  3 
ESE 326  Probability and Statistics for Engineering  3 
ESE 330  Engineering Electromagnetics Principles  3 
And seven 3unit ESE courses in the Electrical Engineering area chosen from:
Code  Title  Units 

ESE 330–399  
ESE 400  Independent Study  13 
ESE 405  Reliability and Quality Control  3 
ESE 407  Analysis and Simulation of Discrete Event Systems  3 
ESE 425  Random Processes and Kalman Filtering  3 
ESE 429–499  
ESE 503–589 
The above program assumes the completion of the following courses:
Code  Title  Units 

Math 132 & Math 233  Calculus II and Calculus III  6 
Math 217  Differential Equations  3 
CSE 131  Computer Science I  3 
Physics 117A  General Physics I  4 
Physics 118A  General Physics II  4 
Students may petition to substitute electrical scienceoriented courses from other disciplines in Arts & Sciences for up to two of the above 11 courses (for example, certain courses in physics or applied mathematics). When such substitutions are employed, the total number of units for nonArts & Sciences courses is 31 or 32 units. Within this second major in electrical engineering science, areas of concentration are possible in: applied physics, signal processing, and control systems. The second major in the electrical engineering science program comprises a total of 34 or 35 units. To design a customized program, contact the director of the program Professor R. Martin Arthur.
The Second Major in Systems Science
A second major in systems science is ideal for study in many areas such as physics, chemistry, economics, finance, supply chain management, and computational biology. Students in the School of Engineering as well as the other undergraduate divisions at Washington University have the opportunity to pursue a second major in systems science in the Preston M. Green Department of Electrical & Systems Engineering in the School of Engineering & Applied Science. Students are not allowed to add this second major to either the BS in SSE or the BS in Applied Science (SSE).
The requirements for a second major in systems science are:
Code  Title  Units 

ESE 205  Introduction to Engineering Design  3 
Math 309  Matrix Algebra  3 
ESE 351  Signals and Systems  3 
ESE 403  Operations Research  3 
One of the following:
Code  Title  Units 

ESE 318  Engineering Mathematics A  3 
ESE 319  Engineering Mathematics B  3 
ESE 326  Probability and Statistics for Engineering  3 
ESE 441  Control Systems  3 
Eight 3unit ESE courses in the Systems area chosen from:
 ESE 318 through 326
 ESE 400 through 428
 ESE 437
 ESE 440 through 459
 ESE 470 through 489
 ESE 500 through 529
 ESE 540 through 559
Students may petition to substitute systemsoriented courses from other disciplines in Arts & Sciences for two of these eight courses (for example, courses in computational physics, econometrics or computational mathematics). When such substitutions are employed, the total number of units for nonArts & Sciences courses will be 30 units.
Within this second major in systems science, areas of concentration are possible in: robotics, control systems, and operations research.
This totals 34 to 40 units of systems science, depending on student's use of the substitution option for upperlevel electives. To design a customized program, contact the departmental associate chair Professor Hiro Mukai or the director of the program Professor Heinz Schaettler.
The Second Major in Financial Engineering
A second major in financial engineering is ideal for students who are interested in careers or graduate school in financial engineering, quantitative finance, or related fields. This program covers classes in engineering, computer science and business.
Background Course Work: 18 units
Code  Title  Units 

CSE 131  Computer Science I  3 
ESE 326  Probability and Statistics for Engineering  3 
or QBA 121  Managerial Statistics II  
or Econ 413  Introduction to Econometrics  
or Math 439  Linear Statistical Models  
Math 217  Differential Equations  3 
Math 233  Calculus III  3 
Math 309  Matrix Algebra  3 
MEC 290  Microeconomics  3 
or Econ 4011  Intermediate Microeconomic Theory 
Engineering Professional Core Requirements: 15 units
Code  Title  Units 

CSE 240  Logic and Discrete Mathematics  3 
CSE 247  Data Structures and Algorithms  3 
CSE 417T  Introduction to Machine Learning  3 
or CSE 427S  Cloud Computing with Big Data Applications  
ESE 403  Operations Research  3 
or ESE 415  Optimization  
ESE 427  Financial Mathematics  3 
Olin Professional Core Requirements: 9 units
Code  Title  Units 

ACCT 2610  Principles of Financial Accounting  3 
FIN 340  Capital Markets and Financial Management  3 
FIN 441  Investments  3 
Olin Elective Courses: 6 units minimum
Code  Title  Units 

FIN 500Q  Quantitative Risk Management  3 
FIN 537  Advanced Derivative Securities  3 
FIN 539  Mathematical Finance  1.5 
FIN 551  Advanced Fixed Income and Credit Risk Modeling  2 
FIN 552  Fixed Income Derivatives  1.5 
Financial Mathematics (ESE 427) is to be taken after Capital Markets and Financial Management (FIN 340) and to be taken before the 6 credit hours of FIN 500+.
Students must have a 3.0 or higher GPA to pursue this second major, which includes the cumulative GPA, business GPA, and engineering GPA.
For students earning School of Engineering & Applied Science undergraduate degrees:
 A maximum of 12 units may be doublecounted for this second major and an engineering or computer science undergraduate degree (this does not include the background course work).
To design a customized program, contact the director of the program Professor Zachary Feinstein.
Please refer to the sections below for information about the minors in applied physics & electrical engineering, electrical engineering, energy engineering (ESE), mechatronics (ESE), robotics, and systems science & engineering.
The Minor in Applied Physics & Electrical Engineering
(Program Director: Dr. JungTsung Shen)
Units required: 19
The minor in applied physics & electrical engineering provides students with course work that will enhance their background, knowledge and skills in the topical area of applied physics and electrical engineering. This program covers classes in several fields of science and engineering, encompassing electronics, solidstate devices, applied electromagnetics, RF and microwave technology, fiberoptic communication, applied optics, nanophotonics, sensors, and medical and biological imaging technology.
This program consists of six courses total: one required course, two core courses and three electives. At least three courses among the six courses must be ESE courses taught by the ESE department and not taught by other departments by means of crosslisting. Students who complete the following requirements in Applied Physics & Electrical Engineering subjects at Washington University as specified below may be awarded a minor in applied physics & engineering.
Target students: Students who are interested in applied physics and electrical engineering applications.
Prerequisite: ESE 318 Engineering Mathematics A, or equivalent, is recommended.
Course requirements:
 Required course:
ESE 230 Introduction to Electrical and Electronic Circuits  One core lab course from the following list:
ESE 331 Electronics Laboratory; or Physics 321 Electronics Laboratory
ESE 435 Electrical Energy Laboratory  One core course from the following list:
ESE 232 Introduction to Electronic Circuits
ESE 330 Engineering Electromagnetics Principles; or Physics 421 Electricity and Magnetism
ESE 337 Electronic Devices and Circuits
ESE 444 Sensors and Actuators
Physics 471 Quantum Mechanics  Three electives from the following list. These three courses (i) must exclude the course selected in the requirement (3) above, and (ii) must include at least one Physics course:
Code  Title  Units 

ESE 232  Introduction to Electronic Circuits  3 
ESE 330  Engineering Electromagnetics Principles  3 
ESE 332  Power, Energy and Polyphase Circuits  3 
ESE 337  Electronic Devices and Circuits  3 
ESE 433  Radio Frequency and Microwave Technology for Wireless Systems  3 
ESE 434  SolidState Power Circuits and Applications  3 
ESE 438  Applied Optics  3 
ESE 444  Sensors and Actuators  3 
ESE 531  Nano and Micro Photonics  3 
ESE 532  Introduction to NanoPhotonic Devices  3 
ESE 534  Special Topics in Advanced Electrodynamics  3 
ESE 575  FiberOptic Communications  3 
Physics 463  Statistical Mechanics and Thermodynamics  3 
Physics 471  Quantum Mechanics  3 
Physics 472  Solid State Physics  3 
Physics 537  Kinetics of Materials  3 
The Minor in Electrical Engineering
Units required: 16
Required courses:
Code  Title  Units 

ESE 230  Introduction to Electrical and Electronic Circuits  4 
ESE 330  Engineering Electromagnetics Principles  3 
ESE 351  Signals and Systems  3 
Electives: Students must select two electrical engineering elective courses from the following list:
Code  Title  Units 

ESE 232  Introduction to Electronic Circuits  3 
ESE 260  Introduction to Digital Logic and Computer Design  3 
ESE 330–399  
ESE 429–499 with the exception of ESE 431 
For more information, contact the director for the minor (Professor R. Martin Arthur) or visit the ESE website.
The Minor in Energy Engineering (ESE)
This minor will provide students with course work that will enhance their background, knowledge and skills in the topical area of energy engineering. The minor covers classes in several fields of science and engineering, encompassing the Department of Energy, Environmental & Chemical Engineering; the Department of Electrical & Systems Engineering; and the Department of Mechanical Engineering & Materials Science. A minor in energy engineering requires the completion of 18 units. It is open to undergraduate students pursuing an engineering major, students from the sciences (biology, chemistry, physics) in Arts & Sciences, and students pursuing the environmental studies major. The detailed requirements for the minor can be found on the Energy, Environmental & Chemical Engineering Minors page. Questions regarding the minor should be directed to a member of the committee for the energy engineering minor: Professor Pratim Biswas (EECE), Professor Hiro Mukai (ESE) or Professor David Peters (MEMS).
Committee to Oversee Energy Engineering Minor
Pratim Biswas (EECE, Coordinator)
Hiro Mukai (ESE)
David Peters (MEMS)
The committee ensures that any course added to the above lists contains a significant amount of energy topics and that the entire program be cohesive.
Visit the ESE website for more information.
The Minor in Mechatronics (ESE)
(Program Director: Heinz Schaettler)
Advancements in power electronics, electronic sensors, and computer hardware and software have led to an expanding role for "smart" systems, which combine electronic and mechanical components. Automotive examples illustrate this point. The replacement of carburetors by fuel injection systems is almost universal, and hybrid/electric cars are replacing traditional automobiles. Not only are auxiliary devices such as fuel pumps, air bags and airconditioner compressors driven by electric motors controlled by microprocessors, but fundamental components such as intake and outtake valves soon will be driven in this way. The internal combustion engine itself may be replaced by fuel cells and motors. Medical devices, microelectromechanical systems, robots, flybywire aircraft and wind turbines also all rely on electronic sensing of mechanical parameters and actuation of motion. These examples suggest strongly that engineers who are adept in the design, analysis and simulation of electromechanical systems will be in demand. The minor in mechatronics is created to encourage our students to study this important subject and provide recognition to those who do so.
This program is primarily designed for students in the ESE and MEMS departments and has been approved by the two departments. It is available for others as well.
The proposed minor program consists of four required courses, two electives and one prerequisite:
Four required courses:
Code  Title  Units 

MEMS 255  Engineering Mechanics II (Dynamics)  3 
MEMS 411  Mechanical Engineering Design Project (Mechatronics project)  3 
ESE 444  Sensors and Actuators  3 
ESE 446  Robotics: Dynamics and Control  3 
Total Units  12 
Two electives from the following:
Code  Title  Units 

MEMS 4301  Modeling, Simulation and Control  3 
or ESE 441  Control Systems  
MEMS 4310  Dynamics and Vibrations  3 
MEMS 5101  Analysis and Design of FluidPower Systems  3 
ESE 337  Electronic Devices and Circuits  3 
ESE 482  Digital Signal Processing  3 
CSE 467S  Embedded Computing Systems  3 
Prerequisite:
Basic programming course: CSE 131 Computer Science I
Visit the ESE website for more information.
The Minor in Robotics
Robotic systems have wide applications in modern technology and manufacturing. Robots can vary in complexity and use, from microrobots for surgical procedures to moderatesize robots common in manufacturing and undersea exploration to macrorobots used for disposal of nuclear wastes and as arms on spacestation modules. The program designed for a minor in robotics provides a fundamental understanding of robotic operation and preliminary training in design and use of robots.
Units required: 18
Prerequisites:
Code  Title  Units 

Math 217  Differential Equations  3 
Physics 117A  General Physics I  4 
or Physics 197  Physics I  
Physics 118A  General Physics II  4 
or Physics 198  Physics II  
CSE 131  Computer Science I  3 
Required courses:
Code  Title  Units 

MEMS 255  Engineering Mechanics II  3 
ESE 351  Signals and Systems  3 
or MEMS 4310  Dynamics and Vibrations  
ESE 446  Robotics: Dynamics and Control  3 
ESE 447  Robotics Laboratory  3 
Total Units  12 
Plus two courses chosen with the approval of the director of the program for a minor in robotics. Suggested courses are:
Code  Title  Units 

CSE 417T  Introduction to Machine Learning  3 
CSE 452A  Computer Graphics  3 
CSE 546T  Computational Geometry  3 
ESE 407  Analysis and Simulation of Discrete Event Systems  3 
ESE 435  Electrical Energy Laboratory  3 
ESE 441  Control Systems  3 
or MEMS 4301  Modeling, Simulation and Control  
MEMS 3110  Machine Elements  3 
To find out more about this minor, contact the director (Heinz Schaettler) of the program.
The Minor in Systems Science & Engineering
This minor consists of fundamental courses in control systems and operations research. In the area of control systems, students will be introduced to design techniques for controlling engineering and socioeconomic systems such as airplanes, automobiles, nuclear reactors, ecological systems, communication networks, the nation's economy, and biological systems. In the area of operations research, students are introduced to techniques for optimally managing business resources and controlling business networks such as supply chains.
Requirements:
Students who complete 15 units of course work in Systems Science & Engineering at Washington University as specified below may be awarded a minor in systems science & engineering.
The required courses for the minor are:
Code  Title  Units 

ESE 151  Introduction to Systems Science and Engineering  2 
ESE 351  Signals and Systems  3 
ESE 403  Operations Research  3 
or ESE 404  Applied Operations Research  
ESE 441  Control Systems  3 
Students must select one Systems Science & Engineering elective course from the following list: ESE 400 through 425 except 409; ESE 437; ESE 440 through 459 except 449; ESE 470 through 489.
Prerequisites:
A student who has finished engineering common studies courses needs to take only ESE 318 in addition to the above five courses. The student may start taking ESE 151 before taking Math 217 or Math 233.
For more information, contact the director (Heinz Schaettler) for the minor.
Visit online course listings to view semester offerings for E35 ESE.
E35 ESE 101 Introduction to Engineering Tools: MATLAB and Simulink
MATLAB and Simulink are important tools in quickly analyzing different designs in many engineering disciplines and are also perhaps the most used software in many engineering schools. Gain skills in the basics of the arraybased language MATLAB to write programs, including scripts and functions, to calculate and display variables and images. Learn the basics of Simulink to build and simulate models from standard blocks. Discover both MATLAB and Simulink in an environment with supervised practice and handson experience. Practice problems are chosen from different engineering fields as well as from a few socioeconomic fields so that students can see the software being exploited in real life applications. This is a pass/fail course. Prerequisite: freshman standing.
Credit 1 unit. EN: TU
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E35 ESE 103 Introduction to Electrical Engineering
A handson introduction to electrical engineering to put the fun into the electrical engineering fundamentals. Experiments are designed to be easy to conduct and understand. Some of the technologies explored are used in a variety of applications including ultrasound imaging, computed tomography, DC motors, analog to digital converters and credit card readers. Students work in groups of two in the newly renovated Urbauer 115 laboratory. Each station is equipped with modern electronic test equipment and a computer with an integrated Data Acquisition system. Using this lab equipment, students design and build solutions to the exercises. The students also learn to program in LabVIEW to control the Data Acquisition system and process the acquired signals. Also, throughout the semester, presentations are given by the ESE faculty about their research.
Credit 1 unit. EN: TU
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E35 ESE 141 Introductory Robotics
A handson introduction to robotics. Projectoriented course where students build and program a robot guided by upperdivision students. Friendly competition at the end of semester. Students gain electrical lab experience, programming experience, and a guided introduction into the field of robotics. Recommended to freshmen and sophomores. This is a pass/fail course.
Credit 1 unit. EN: TU
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E35 ESE 151 Introduction to Systems Science and Engineering
Systems Science and Engineering (SSE) has grown in applicability to many industries. This course will provide an overview of the broad applicability of the analytical methods studied in SSE, as well as introduce many of these analytical methods. Each module of the course will present a domain area (e.g., energy, health care, etc.) with examples of how one of the SSE analytical methods (e.g., optimization, discrete event systems, etc.) is used with assistance of one of the many computing tools available for SSEstyle projects (e.g., MATLAB, SIMUL8, etc.). The course will close with a final, exploratory project and presentation of an analytical method of the students' choosing and how this is applied to an industry of their choosing. (Not open to seniors or graduate students.) Corequisite: Math 132, Physics 117A or 197.
Credit 2 units. EN: TU
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E35 ESE 205 Introduction to Engineering Design
A handson course where students, divided in groups of two or three, will creatively solve one problem throughout the semester using tools from electrical and systems engineering. The groups choose their own schedule and work under the supervision of an academic team consisting of faculty and higherlevel students. The evaluation considers the completion of objectives set by the students with help of the academic team, as well as the originality, innovation, and impact of the project. Prerequisites: CSE 131, Physics 117A or equivalent.
Credit 3 units. EN: TU
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E35 ESE 230 Introduction to Electrical and Electronic Circuits
Electrical energy, current, voltage, and circuit elements. Resistors, Ohm's Law, power and energy, magnetic fields and DC motors. Circuit analysis and Kirchhoff's voltage and current laws. Thevenin and Norton transformations and the superposition theorem. Measuring current, voltage and power using ammeters and voltmeters. Energy and maximum electrical power transfer. Computer simulations of circuits. Reactive circuits, inductors, capacitors, mutual inductance, electrical transformers, energy storage, and energy conservation. RL, RC and RLC circuit transient responses, biological cell action potentials due to Na and K ions. AC circuits, complex impedance, RMS current and voltage. Electrical signal amplifiers and basic operational amplifier circuits. Inverting, noninverting, and difference amplifiers. Voltage gain, current gain, input impedance, and output impedance. Weekly laboratory exercises related to the lectures are an essential part of the course. Prerequisite: Physics 118A. Corequisite: Math 217.
Credit 4 units. EN: TU
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E35 ESE 232 Introduction to Electronic Circuits
Analysis and design of linear electronic circuits. Terminal characteristics of active semiconductor devices. Incremental and DC models for diodes, metaloxidesemiconductor field effect transistors (MOSFETs) and bipolar junction transistors (BJTs). Design and analysis of single and multistage amplifiers. Volatile and nonvolatile memories. Understanding of common application circuits (e.g., operational amplifier, memories) in integrated circuit chips. Semesterlong design project. Prerequisite: ESE 230.
Credit 3 units. EN: TU
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E35 ESE 260 Introduction to Digital Logic and Computer Design
Introduction to design methods for digital logic and fundamentals of computer architecture. Boolean algebra and logic minimization techniques; sources of delay in combinational circuits and effect on circuit performance; survey of common combinational circuit components; sequential circuit design and analysis; timing analysis of sequential circuits; use of computeraided design tools for digital logic design (schematic capture, hardware description languages, simulation); design of simple processors and memory subsystems; program execution in simple processors; basic techniques for enhancing processor performance; configurable logic devices. Prerequisite: CSE 131.
Same as E81 CSE 260M
Credit 3 units. EN: TU
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E35 ESE 297 Introduction to ESE Undergraduate Research Projects
This course is offered to students at all levels from all departments. The course is designed to give students some handson experience by implementing projects that use the lab PCs, the sbRIO robots from National Instruments, acoustic sensors, biomedical sensors and 3D cameras. These projects are implemented in LabVIEW and Matlab and should prepare the students to work on topics that include the Robotic Sensing Undergraduate Research Projects in subsequent semesters. Note that under ESE 497 Undergraduate Research, students may select the Robotic Sensing Projects as well as other projects. Working in groups, students implement algorithms that run on PCs and our wireless robotic platforms to track a moving audio source. Also, they use an EEG system to implement a Brain Computer Interface (BCI) project and work with the new Kinect camera from Microsoft. Corequisite: CSE 131 or equivalent.
Credit 3 units.
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E35 ESE 318 Engineering Mathematics A
Laplace transforms; matrix algebra; vector spaces; eigenvalues and eigenvectors; vector differential calculus and vector integral calculus in three dimensions. Prerequisites: Math 233 and Math 217 or their equivalents.
Credit 3 units.
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E35 ESE 319 Engineering Mathematics B
Power series and Frobenius series solutions of differential equations; Legendre's equation; Bessel's equation; Fourier series and Fourier transforms; SturmLiouville theory; solutions of partial differential equations; wave and heat equations. Prerequisites: Math 233 and Math 217 or their equivalents.
Credit 3 units.
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E35 ESE 326 Probability and Statistics for Engineering
Study of probability and statistics together with engineering applications. Probability and statistics: random variables, distribution functions, density functions, expectations, means, variances, combinatorial probability, geometric probability, normal random variables, joint distribution, independence, correlation, conditional probability, Bayes theorem, the law of large numbers, the central limit theorem. Applications: reliability, quality control, acceptance sampling, linear regression, design and analysis of experiments, estimation, hypothesis testing. Examples are taken from engineering applications. Prerequisites: Math 233 or equivalent.
Credit 3 units. EN: TU
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E35 ESE 330 Engineering Electromagnetics Principles
Electromagnetic theory as applied to electrical engineering: vector calculus; electrostatics and magnetostatics; Maxwell's equations, including Poynting's theorem and boundary conditions; uniform planewave propagation; transmission lines, TEM modes, including treatment of general lossless lines, and pulse propagation; introduction to guided waves; introduction to radiation and scattering concepts. Prerequisites: Physics 118A and ESE 318 En Math A. Corequisite: ESE 319 En Math B.
Credit 3 units. EN: TU
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E35 ESE 331 Electronics Laboratory
Laboratory exercises provide students with a combination of handson experience in working with a variety of real instruments and in working in a simulated "virtual" laboratory setting. A sequence of lab experiments provide handson experience with grounding and shielding techniques, signal analysis, realistic operation amplifier (op amp) characterization, op amp based active filters characterization, MOSFET chopper/amplifier behavior, measurement of pulses propagating on a transmission line with various terminations, experience with both AM and FM modulation. Students will gain experience in working with: sampling oscilloscopes, various signal generators, frequency counters, digital multimeters, spectrum analyzers, and contemporary connection boards. The course concludes with a handson project to design and demonstrate an electronic component. Prerequisites: ESE 230, ESE 232; Corequisite: ESE 330.
Credit 3 units. EN: TU
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E35 ESE 332 Power, Energy and Polyphase Circuits
Fundamental concepts of power and energy; electrical measurements; physical and electrical arrangement of electrical power systems; polyphase circuit theory and calculations; principal elements of electrical systems such as transformers, rotating machines, control and protective devices, their description and characteristics; elements of industrial power system design. Prerequisite: ESE 230.
Credit 3 units. EN: TU
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E35 ESE 337 Electronic Devices and Circuits
Introduction to semiconductor electronic devices: transistors and diodes. Device electrical DC and highfrequency characteristics. Bipolar transistors and MOSFET transistors for analog electronics applications. Transistor fabrication as integratedcircuit chips and fundamentals of very large scale integration (VLSI). Largesignal and smallsignal analysis of transistor amplifiers: voltage gain, input resistance and output resistance. Analysis of multitransistor amplifiers: cascoded amplifiers and differential amplifiers. Analysis of feedback circuits, operational amplifiers, stability, frequency compensation. Fundamentals of Analog VLSI Layout and postlayout simulation of operational amplifiers. Prerequisite: ESE 232.
Credit 3 units. EN: TU
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E35 ESE 351 Signals and Systems
Introduction to concepts and methodology of linear dynamic systems in relation to discrete and continuoustime signals. Mathematical modeling. Representation of systems and signals. Fourier, Laplace, and Ztransforms and convolution. Inputoutput description of linear systems: impulse response, transfer function.Timedomain and frequencydomain system analysis: transient and steadystate responses, system modes, stability, frequency spectra and frequency responses. System design: filter, modulation, sampling theorem. Continuity is emphasized from analysis to synthesis. Use of Matlab. Prerequisites: Physics 117A118A, Math 217, CSE 131, matrix addition and multiplication; Corequisite: ESE 318.
Credit 3 units. EN: TU
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E35 ESE 362 Computer Architecture
This course explores the interaction and design philosophy of hardware and software for digital computer systems. Topics include: Processor architecture, Instruction Set Architecture, Assembly Language, memory hierarchy design, I/O considerations, and a comparison of computer architectures. Prerequisite: CSE 260M.
Same as E81 CSE 362M
Credit 3 units. EN: TU
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E35 ESE 400 Independent Study
Opportunities to acquire experience outside the classroom setting and to work closely with individual members of the faculty. A final report must be submitted to the department. Not open to firstyear or graduate students. Consult adviser. Hours and credit to be arranged.
Credit variable, maximum 3 units.
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E35 ESE 401 Fundamentals of Engineering Review
A review and preparation of the most recent NCEES Fundamentals of Engineering (FE) Exam specifications is offered in a classroom setting. Exam strategies will be illustrated using examples. The main topics for the review include: engineering mathematics, statics, dynamics, thermodynamics, heat transfer, mechanical design and analysis, material science and engineering economics. A discussion of the importance and responsibilities of professional engineering licensure along with ethics will be included.
Same as E37 MEMS 4001
Credit 1 unit.
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E35 ESE 403 Operations Research
Introduction to the mathematical aspects of various areas of operations research, with additional emphasis on problem formulation. This is a course of broad scope, emphasizing both the fundamental mathematical concepts involved, and also aspects of the translation of realworld problems to an appropriate mathematical model. Subjects to be covered include linear and integer programming, network problems, and dynamic programming. Prerequisites: CSE 131, Math 309, and ESE 326, or permission of instructor.
Credit 3 units. EN: TU
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E35 ESE 404 Applied Operations Research
Application of operations research techniques to realworld problems. Emphasis is given to integer linear programming and computational methods. Realworld examples of integer programs will be studied in areas such as network flow, facility location, partitioning, matching, and transportation. Special emphasis will be placed on techniques used to solve integer programs. Prerequisites: ESE 403 and CSE 131.
Credit 3 units. EN: TU
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E35 ESE 405 Reliability and Quality Control
An integrated analysis of reliability and quality control function in manufacturing. Statistical process control, acceptance sampling, process capability analysis, reliability prediction, design, testing, failure analysis and prevention, maintainability, availability, and safety are discussed and related. Qualitative and quantitative aspects of statistical quality control and reliability are introduced in the context of manufacturing. Prerequisite: ESE 326 or equivalent.
Credit 3 units. EN: TU
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E35 ESE 407 Analysis and Simulation of Discrete Event Systems
Study of the dynamic behavior of discrete event systems and techniques for analyzing and optimizing the performance of such systems. Covers both classical and recent approaches. Classical topics include Markov chains, queueing theory, networks of queues, related algorithms and simulation methods. Recent approaches include decomposition and aggregation, approximation, and perturbation analysis of nonclassical systems. Applications are drawn from various areas, including production systems. Prerequisites: Math 217, ESE 326 or equivalent, programming experience such as CSE 131 or CSE 200.
Credit 3 units. EN: TU
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E35 ESE 408 A System Dynamics Approach to Designing Sustainable Policies and Programs
Principles and practice of modeling dynamic systems in the sciences, engineering, social sciences and business. Model structure and its relationships to prior knowledge and assumptions, measurable quantities and ultimate use in solving problems in application areas. Problems considered are in the areas of intervention, policy making, business and engineering systems. Model verification. The basic theory and practice of system dynamics. Quantitative methods are emphasized. Senior or graduate standing.
Credit 3 units. EN: TU
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E35 ESE 415 Optimization
Optimization problems with and without constraints. The projection theorem. Convexity, separating hyperplane theorems; Lagrange multipliers, KuhnTuckertype conditions, duality; computational procedures. Use of optimization techniques in engineering design. Prerequisites: CSE 131, Math 309 and ESE 318 or permission of instructor.
Credit 3 units. EN: TU
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E35 ESE 425 Random Processes and Kalman Filtering
Probability and random variables; random processes; linear dynamic systems and random inputs; autocorrelation; spectral density; the discrete Kalman filter; applications; the extended Kalman filter for nonlinear dynamic systems. Kalman filter design using a computer package, mean square estimation; maximum likelihood; Wiener filtering and special factorization, LQG/LTR control. Prerequisite: ESE 326 and ESE 351 or equivalent.
Credit 3 units. EN: TU
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E35 ESE 427 Financial Mathematics
This course is a selfcontained introduction to financial mathematics at the undergraduate level. Topics to be covered include pricing of the financial instruments such as options, forwards, futures and their derivatives along with basic hedging techniques and portfolio optimization strategies. The emphasis is put on using of discrete, mostly binary models. The general, continuous case including the concepts of Brownian motion, stochastic integral, and stochastic differential equations, is explained from intuitive and practical point of view. Among major results discussed are the Arbitrage Theorem and BlackScholes differential equations and their solutions. Prerequisites: ESE 318 and ESE 326 or the consent of the instructor.
Credit 3 units. EN: TU
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E35 ESE 429 Basic Principles of Quantum Optics and Quantum Information
This course provides an accessible introduction to quantum optics and quantum engineering for undergraduate students. This course covers the following topics: concept of photons, quantum mechanics for quantum optics, radiative transitions in atoms, lasers, photon statistics (photon counting, Sub/SuperPoissionian photon statistics, bunching, antibunching, theory of photodetection, shot noise), entanglement, squeezed light, atomphoton interactions, cold atoms, atoms in cavities. The course will also provide an overview for quantum information processing: quantum computing, quantum cryptography, and teleportation. Prerequisite: Engineering Mathematics 318 or equivalent.
Credit 3 units. EN: TU
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E35 ESE 433 Radio Frequency and Microwave Technology for Wireless Systems
Focus is on the components and associated techniques employed to implement analog and digital radio frequency (RF) and microwave (MW) transceivers for wireless applications, including: cell phones; pagers; wireless local area networks; global positioning satellitebased devices; and RF identification systems. A brief overview of systemlevel considerations is provided, including modulation and detection approaches for analog and digital systems; multipleaccess techniques and wireless standards; and transceiver architectures. Focus is on RF and MW: transmission lines; filter design; active component modeling; matching and biasing networks; amplifier design; and mixer design. Prerequisite: ESE 330.
Credit 3 units. EN: TU
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E35 ESE 434 SolidState Power Circuits and Applications
Study of the strategies and applications power control using solidstate semiconductor devices. Survey of generic power electronic converters. Applications to power supplies, motor drives and consumer electronics. Introduction to power diodes, thyristors and MOSFETs. Prerequisites: ESE 232, ESE 351.
Credit 3 units. EN: TU
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E35 ESE 435 Electrical Energy Laboratory
Experimental studies of principles important in modern electrical energy systems. Topics include: AC power measurements, electric lighting, photovoltaic cells and arrays, batteries, DCDC and DCAC converters, and threephase circuits. Each experiment requires analysis, simulation with MultiSim, and measurement via LabView and the Elvis II platform. Prerequisites: ESE 230 and ESE 351.
Credit 3 units. EN: TU
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E35 ESE 436 Advanced Electronic Devices
The physics of stateoftheart electronic devices. Devices studied include novel diode structures (lightemitting diodes, semiconductor laser diodes), highpower devices (SCRs, TRIACs and power transistors), and highspeed devices. Highspeed devices include heterojunction bipolar (HBT), heterojunction fieldeffect (HFET) and high electron mobility (HEMT) transistors used in very highspeed systems (up to 100 GHz). Advanced bipolar transistors (polySi), used in highspeed microprocessors, examined; also materials properties, transport mechanisms, band structure and physics of these devices. Prerequisite: ESE 336.
Credit 3 units. EN: TU
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E35 ESE 437 Sustainable Energy Systems
We will survey the field of sustainable energy and explore contributions within electrical and systems engineering. Topics include introductory electric power systems, smart grids, and the roles of heat engines, photovoltaics, wind power, and energy storage, as well as analysis and optimization of energy systems. The course will include review and discussion of literature, problem sets, exams, and student projects. Prerequisites: ESE 318 or 319 and ESE 230 or ESE 351 or permission of instructor.
Credit 3 units. EN: TU
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E35 ESE 438 Applied Optics
Topics relevant to the engineering and physics of conventional as well as experimental optical systems and applications explored. Items addressed include geometrical optics, Fourier optics such as diffraction and holography, polarization and optical birefringence such as liquid crystals, and nonlinear optical phenomena and devices. Prerequisite: ESE 330 or equivalent.
Credit 3 units. EN: TU
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E35 ESE 439 Introduction to Quantum Communications
This course covers the following topics: quantum optics, singlemode and twomode quantum systems, nonlinear optics, and quantum systems theory. Specific topics include the following: Dirac notation quantum mechanics; harmonic oscillator quantization; number states, coherent states, and squeezed states; direct, homodyne, and heterodyne detection; linear propagation loss; phase insensitive and phase sensitive amplifiers; entanglement and teleportation; field quantization; quantum photodetection; phasematched interactions; optical parametric amplifiers; generation of squeezed states, photontwin beams, nonclassical fourthorder interference, and polarization entanglement; optimum binary detection; quantum precision measurements; and quantum cryptography. Prerequisites: ESE 330 or Physics 421; Physics 217 or equivalent.
Credit 3 units. EN: TU
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E35 ESE 441 Control Systems
Introduction to the theory and practice of automatic control for dynamical systems. Dynamical systems as models for physical and observed phenomena. Mathematical representation of dynamical systems, such as statespace differential and difference equations, transfer functions, and block diagrams. Analysis of the time evolution of a system in response to control inputs, steadystate and transient responses, equilibrium points and their stability. Control via linear state feedback, and estimation using Leunberger observers. Relating the time response of a system to its frequency response, including Bode and Nyquist plots. Inputoutput stability and its relation to the stability of equilibrium points. Simple frequencybased controllers, such as PID and leadlag compensators. Exercise involving the use of MATLAB/Simulink (or equivalent) to simulate and analyze systems. Prerequisites: CSE 131, and either ESE 351 or MEMS 431.
Credit 3 units. EN: TU
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E35 ESE 444 Sensors and Actuators
The course provide engineering students with basic understanding of two of the main components of any modern electrical or electromechanical system; sensors as inputs and actuators as outputs. The covered topics include transfer functions, frequency responses and feedback control. Component matching and bandwidth issues. Performance specification and analysis, Sensors: analog and digital motion sensors, optical sensors, temperature sensors, magnetic and electromagnetic sensors, acoustic sensors, chemical sensors, radiation sensors, torque, force and tactile sensors. Actuators: stepper motors, DC and AC motors, hydraulic actuators, magnet and electromagnetic actuators, acoustic actuators. Introduction to interfacing methods: bridge circuits, A/D and D/A converters, microcontrollers. This course is useful for those students interested in control engineering, robotics and systems engineering. Prerequisites: one of the following 4 conditions: (1) prerequisite of ESE 230 and corequisite of ESE 351; (2) prerequisites of ESE 230, ESE 318 and MEMS 255 (Mechanics II); (3) prerequisites of ESE 151 and ESE 351; (4) permission of instructor.
Credit 3 units. EN: TU
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E35 ESE 446 Robotics: Dynamics and Control
Homogeneous coordinates and transformation matrices. Kinematic equations and the inverse kinematic solutions for manipulators, the manipulator Jacobian and the inverse Jacobian. General model for robot arm dynamics, complete dynamic coefficients for sixlink manipulator. Synthesis of manipulation control, motion trajectories, control of single and multiplelink manipulators, linear optimal regulator. Model reference adaptive control, feedback control law for the perturbation equations along a desired motion trajectory. Design of the control system for robotics. Prerequisites: ESE 351, knowledge of a programming language, and ESE 318; Corequisite: ESE 441.
Credit 3 units. EN: TU
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E35 ESE 447 Robotics Laboratory
Introduces the students to various concepts such as modeling, identification, model validation and control of robotic systems. The course focuses on the implementation of identification and control algorithms on a twolink robotic manipulator (the socalled pendubot) that will be used as an experimental testbed. Topics include: introduction to the mathematical modeling of robotic systems; nonlinear model, linearized model; identification of the linearized model: inputoutput and statespace techniques; introduction to the identification of the nonlinear model: energybased techniques; model validation and simulation; stabilization using linear control techniques; a closer look at the dynamics; stabilization using nonlinear control techniques. Prerequisite: ESE 351 or MEMS 431. Corequisites or Prerequisites: ESE 441 and 446.
Credit 3 units. EN: TU
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E35 ESE 448 Systems Engineering Laboratory
Experimental study of real and simulated systems and their control. Identification, inputoutput analysis, design and implementation of control systems. Noise effects. Design and implementation of control laws for specific engineering problems. Corequisites: ESE 441 and knowledge of a programming language.
Credit 3 units. EN: TU
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E35 ESE 449 Digital Process Control Laboratory
Applications of digital control principles to laboratory experiments supported by a networked distributed control system. Lecture material reviews background of realtime programming, data acquisition, process dynamics, and process control. Exercises in data acquisition and feedback control design using simple and advanced control strategies. Experiments in flow, liquid level, temperature, and pressure control. Term project. Prerequisite: ESE 441 or EECE 401 or equivalent. (Prior to FL2015, this course was numbered: E63 433.)
Same as E44 EECE 424
Credit 3 units. EN: TU
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E35 ESE 455 Quantitative Methods for Systems Biology
Application of computational mathematical techniques to problems in contemporary biology. Systems of linear ordinary differential equations in reactiondiffusion systems, hidden Markov models applied to gene discovery in DNA sequence, ordinary differential equation and stochastic models applied to gene regulation networks, negative feedback in transcription and metabolic pathway regulation. Prerequisites: (1) Math 217 Differential Equations and (2) a programming course and familiarity with MATLAB.
Credit 3 units. EN: TU
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E35 ESE 460 Switching Theory
Advanced topics in switching theory as employed in the synthesis, analysis, and design of information processing systems. Combinational techniques: minimization, multiple output networks, state identification and fault detection, hazards, testability and design for test are examined. Sequential techniques: synchronous circuits, machine minimization, optimal state assignment, asynchronous circuits, and builtin selftest techniques. Prerequisite: CSE 260M.
Same as E81 CSE 460T
Credit 3 units. EN: TU
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E35 ESE 461 Design Automation for Integrated Circuit Systems
Integrated circuit systems provide the core technology that power today's most advanced devices and electronics: smart phones, wearable devices, autonomous robots, and cars, aerospace or medical electronics. These systems often consist of silicon microchips made up by billions of transistors and contain various components such as microprocessors, DSPs, hardware accelerators, memories, and I/O interfaces; therefore, design automation is critical to tackle the design complexity at the system level. The objectives of this course are to 1) introduce transistorlevel analysis of basic digital logic circuits; 2) provide a general understanding of hardware description language (HDL) and design automation tools for very large scale integrated (VLSI) systems; 3) expose students to the design automation techniques used in the bestknown academic and commercial systems. Topics covered include device and circuits for digital logic circuits, digital IC design flow, logic synthesis, physical design, circuit simulation and optimization, timing analysis, power delivery network analysis. Assignments include homework, miniprojects, term paper and group project. Prerequisites: ESE 232; ESE 260.
Credit 3 units. EN: TU
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E35 ESE 462 Computer Systems Design
Introduction to modern design practices, including the use of FPGA design methodologies. Students use a commercial CAE/CAD system for VHDLbased design and simulation while designing a selected computation system. Prerequisites: CSE 361S and 362M.
Same as E81 CSE 462M
Credit 3 units. EN: TU
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E35 ESE 465 Digital Systems Laboratory
Hardware/software codesign; processor interfacing; procedures for reliable digital design, both combinational and sequential; understanding manufacturers' specifications; use of test equipment. Several singleperiod laboratory exercises, several design projects, and application of microprocessors in digital design. One lecture and one laboratory period a week. Prerequisites: CSE 260M and CSE 361S.
Credit 3 units. EN: TU
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E35 ESE 467 Embedded Computing Systems
Introduces the issues, challenges and methods for designing embedded computing systems — systems designed to serve a particular application, which incorporate the use of digital processing devices. Examples of embedded systems include PDAs, cellular phones, appliances, game consoles, automobiles and iPod. Emphasis is given to aspects of design that are distinct to embedded systems. The course examines hardware, software and systemlevel design. Hardware topics include microcontrollers, digital signal processors, memory hierarchy and I/O. Software issues include languages, runtime environments and program analysis. Systemlevel topics include realtime operating systems, scheduling, power management and wireless sensor networks. Students perform a course project on a real wireless sensor network testbed. Prerequisite: CSE 361S.
Same as E81 CSE 467S
Credit 3 units. EN: TU
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E35 ESE 471 Communications Theory and Systems
Introduction to the concepts of transmission of information via communication channels. Amplitude and angle modulation for the transmission of continuoustime signals. Analogtodigital conversion and pulse code modulation. Transmission of digital data. Introduction to random signals and noise and their effects on communication. Optimum detection systems in the presence of noise. Elementary information theory. Overview of various communication technologies such as radio, television, telephone networks, data communication, satellites, optical fiber and cellular radio. Prerequisites: ESE 351 and ESE 326.
Credit 3 units. EN: TU
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E35 ESE 474 Introduction to Wireless Sensor Networks
This is an introductory course on wireless sensor networks for senior undergraduate students. The course uses a combination of lecturing, reading, and discussion of research papers to help each student to understand the characteristics and operations of various wireless sensor networks. Topics covered include sensor network architecture, communication protocols on Medium Access Control and Routing, sensor network operation systems, sensor data aggregation and dissemination, localization and time synchronization, energy management, and target detection and tracking using acoustic sensor networks. Prerequisite: ESE 351 (Signals and Systems).
Credit 3 units. EN: TU
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E35 ESE 482 Digital Signal Processing
Introduction to analysis and synthesis of discretetime linear timeinvariant (LTI) systems. Discretetime convolution, discretetime Fourier transform, ztransform, rational function descriptions of discretetime LTI systems. Sampling, analogtodigital conversion and digital processing of analog signals. Techniques for the design of finite impulse response (FIR) and infinite impulse response (IIR) digital filters. Hardware implementation of digital filters and finiteregister effects. The Discrete Fourier Transform and the Fast Fourier Transform (FFT) algorithms. Prerequisite: ESE 351.
Credit 3 units. EN: TU
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E35 ESE 488 Signals and Communication Laboratory
A laboratory course designed to complement the traditional EE course offerings in signal processing and communication theory. Signals and systems fundamentals: continuoustime and discretetime linear timeinvariant systems, impulse and step response, frequency response, A/D and D/A conversion. Digital signal processing: FIR and IIR digital filter design, implementation and application of the Fast Fourier Transform. Communication theory: baseband, digital communication, amplitude modulation, frequency modulation, bandpass digital communication. Laboratory experiments involve analog and digital electronics. Computer workstations and modern computational software used extensively for system simulation and realtime signal processing. Prerequisite: ESE 351.
Credit 3 units. EN: TU
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E35 ESE 497 Undergraduate Research
Undergraduate research under the supervision of a faculty member. The scope and depth of the research must be approved by the faculty member prior to enrollment. A written final report and a webpage describing the research are required.
Credit variable, maximum 3 units.
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E35 ESE 498 Electrical Engineering Capstone Design Projects
Capstone design project supervised by the course instructor. The project must use the theory, techniques, and concepts of the student's major: electrical engineering or systems science & engineering. The solution of a real technological or societal problem is carried through completely, starting from the stage of initial specification, proceeding with the application of engineering methods, and terminating with an actual solution. Collaboration with a client, typically either an engineer or supervisor from local industry or a professor or researcher in university laboratories, is encouraged. A proposal, an interim progress update, and a final report are required, each in the forms of a written document and oral presentation, as well as a webpage on the project. Weekly progress reports and meetings with the instructor are also required. Prerequisite: ESE senior standing and instructor's consent. Note: This course will meet at the scheduled time only during select weeks. If you cannot attend at that time, you may still register for the course.
Credit 3 units. EN: TU
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E35 ESE 499 Systems Science and Engineering Capstone Design Project
Capstone design project supervised by the course instructor. The project must use the theory, techniques, and concepts of the student's major: electrical engineering or systems science & engineering. The solution of a real technological or societal problem is carried through completely, starting from the stage of initial specification, proceeding with the application of engineering methods, and terminating with an actual solution. Collaboration with a client, typically either an engineer or supervisor from local industry or a professor or researcher in university laboratories, is encouraged. A proposal, an interim progress update, and a final report are required, each in the forms of a written document and oral presentation, as well as a webpage on the project. Weekly progress reports and meetings with the instructor are also required. Prerequisite: ESE senior standing and instructor's consent. Note: This course will meet at the scheduled time only during select weeks. If you cannot attend at that time, you may still register for the course.
Credit 3 units. EN: TU
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E35 ESE 500 Independent Study
Opportunities to acquire experience outside the classroom setting and to work closely with individual members of the faculty. A final report must be submitted to the department. Prerequisite: Students must have the ESE Research/Independent Study Registration Form (PDF) approved by the department.
Credit variable, maximum 3 units.
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E35 ESE 501 Mathematics of Modern Engineering I
Matrix algebra: systems of linear equations, vector spaces, linear independence and orthogonality in vector spaces, eigenvectors and eigenvalues; vector calculus: gradient, divergence, curl, line and surface integrals, theorems of Green, Stokes, and Gauss; Elements of Fourier analysis and its applications to solving some classical partial differential equations, heat, wave, and Laplace equation. Prerequisites: ESE 318 and ESE 319 or equivalent or consent of instructor. This course will not count toward the ESE doctoral program.
Credit 3 units. EN: TU
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E35 ESE 502 Mathematics of Modern Engineering II
Fourier series and Fourier integral transforms and their applications to solving some partial differential equations, heat and wave equations; complex analysis and its applications to solving realvalued problems: analytic functions and their role, Laurent series representation, complexvalued line integrals and their evaluation including the residual integration theory, conformal mappings and their applications. Prerequisites: ESE 318 and ESE 319 or ESE 317 or equivalent, or consent of instructor. This course will not count toward the ESE doctoral program.
Credit 3 units. EN: TU
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E35 ESE 512 Advanced Numerical Analysis
Special topics chosen from numerical solution of partial differential equations, uniform and leastsquares approximation spline approximation, Galerkin methods and finite element approximation, functional analysis applied to numerical mathematics, and other topics of interest. Prerequisite: ESE 511 or consent of instructor.
Credit 3 units. EN: TU
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E35 ESE 513 Convex Optimization and Duality Theory
Graduate introduction to convex optimization with emphasis on convex analysis and duality theory. Topics include: convex sets, convex functions, convex cones, convex conjugates, FenchelMoreau theorem, convex duality and biconjugation, directional derivatives, subgradients and subdifferentials, optimality conditions, ordered vector spaces, HahnBanach theorem, extension and separation theorems, minimax theorems, and vector and set optimization. Prerequisites: ESE 415, Math 4111.
Credit 3 units.
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E35 ESE 514 Calculus of Variations
Introduction to the theory and applications of the calculus of variations. Theory of functionals; variational problems for an unknown function; Euler's equation; variable endpoint problems; variational problems with subsidiary conditions; sufficient conditions for extrema: applications to optimum control and/or to other fields. A term project is required. Prerequisites: ESE 318 and 319 or ESE 317 or equivalent.
Credit 3 units.
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E35 ESE 516 Optimization in Function Space
Linear vector spaces, normed linear spaces, Lebesque integrals, the Lp spaces, linear operators, dual space, Hilbert spaces. Projection theorem, HahnBanach theorem. Hyperplanes and convex sets, Gateaux and Frächet differentials, unconstrained minima, adjoint operators, inverse function theorem. Constrained minima, equality constraints, Lagrange multipliers, calculus of variations, EulerLagrange equations, positive cones, inequality constraints. KuhnTucker theorem, optimal control theory, Pontryagin's maximum principle, successive approximation methods, Newton's methods, steepest descent methods, primaldual methods, penalty function methods, multiplier methods. Prerequisite: Math 4111.
Credit 3 units.
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E35 ESE 517 Partial Differential Equations
Linear and nonlinear first order equations. Characteristics. Classification of equations. Theory of the potential linear and nonlinear diffusion theory. Linear and nonlinear wave equations. Initial and boundary value problems. Transform methods. Integral equations in boundary value problems. Prerequisites: ESE 318 and 319 or equivalent or consent of instructor.
Credit 3 units. EN: TU
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E35 ESE 518 Optimization Methods in Control
The course is divided in two parts: convex optimization and optimal control. In the first part we cover applications of Linear Matrix Inequalities and SemiDefinite Programming to control and estimation problems. We also cover Multiparametric Linear Programming and its application to the Model Predictive Control and Estimation of linear systems. In the second part we cover numerical methods to solve optimal control and estimation problems. We cover techniques to discretize optimal control problems, numerical methods to solve them, and their optimality conditions. We apply these results to the Model Predictive Control and Estimation of nonlinear systems. Prerequisites: ESE 551, and ESE 415 or equivalent.
Credit 3 units. EN: TU
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E35 ESE 519 Convex Optimization
Concentrates on recognizing and solving convex optimization problems that arise in applications. Convex sets, functions, and optimization problems. Basics of convex analysis. Leastsquares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal processing, statistics and machine learning, control and mechanical engineering, digital and analog circuit design, and finance. Prerequisites: Math 309 and ESE 415.
Credit 3 units.
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E35 ESE 520 Probability and Stochastic Processes
Review of probability theory; models for random signals and noise; calculus of random processes; noise in linear and nonlinear systems; representation of random signals by sampling and orthonormal expansions. Poisson, Gaussian and Markov processes as models for engineering problems. Prerequisite: ESE 326.
Credit 3 units. EN: TU
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E35 ESE 521 Random Variables and Stochastic Processes I
Mathematical foundations of probability theory, including constructions of measures, Lebesquemeasure, Lebesqueintegral, Banach space property of Lp, basic Hilbertspace theory, conditional expectation. Kolmogorov's theorems on existence and samplepath continuity of stochastic processes. An indepth look at the Wiener process. Filtrations and stopping times. Markov processes and diffusions, including semigroup properties and the Kolmogorov forward and backward equations. Prerequisites: ESE 520 or equivalent, Math 411.
Credit 3 units.
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E35 ESE 523 Information Theory
Discrete source and channel model, definition of information rate and channel capacity, coding theorems for sources and channels, encoding and decoding of data for transmission over noisy channels. Corequisite: ESE 520.
Credit 3 units. EN: TU
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E35 ESE 524 Detection and Estimation Theory
Study of detection and estimation of signals in noise. Linear algebra, vector spaces, independence, projections. Data independence, factorization theorem and sufficient statistics. NeymanPearson and Bayes detection. Least squares, maximumlikelihood and maximum a posteriori estimation of signal parameters. Conjugate priors, recursive estimation, Wiener and Kalman filters. Prerequisite: ESE 520.
Credit 3 units. EN: TU
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E35 ESE 529 Special Topics in Information Theory and Applied Probability
Credit 3 units.
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E35 ESE 531 Nano and Micro Photonics
This course focuses on fundamental theory, design, and applications of photonic materials and micro/nano photonic devices. It includes review and discussion of lightmatter interactions in nano and micro scales, propagation of light in waveguides, nonlinear optical effect and optical properties of nano/micro structures, the device principles of waveguides, filters, photodetectors, modulators and lasers. Prerequisite: ESE 330.
Credit 3 units. EN: TU
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E35 ESE 532 Introduction to NanoPhotonic Devices
Introduction to photon transport in nanophotonic devices. This course focuses on the following topics: light and photons, statistical properties of photon sources, temporal and spatial correlations, lightmatter interactions, optical nonlinearity, atoms and quantum dots, single and twophoton devices, optical devices, and applications of nanophotonic devices in quantum and classical computing and communication. Prerequisites: ESE 330 and Physics 217, or permission of instructor.
Credit 3 units. EN: TU
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E35 ESE 534 Special Topics in Advanced Electrodynamics
This course covers advanced topics in electrodynamics. Topics include electromagnetic wave propagation (in free space, confined waveguides, or along engineered surfaces); electromagnetic wave scattering (off nanoparticles or molecules); electromagnetic wave generation and detection (antenna and nanoantenna); inverse scattering problems; and numerical and approximate methods. Prerequisites: ESE 330, or Physics 421 and Physics 422.
Credit 3 units. EN: TU
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E35 ESE 536 Introduction to Quantum Optics
This course covers the following topics: quantum mechanics for quantum optics, radiative transitions in atoms, lasers, photon statistics (photon counting, Sub/SuperPoissionian photon statistics, bunching, antibunching, theory of photodetection, shot noise), entanglement, squeezed light, atomphoton interactions, cold atoms, atoms in cavities. If time permits, the following topics are selectively covered: quantum computing, quantum cryptography, and teleportation. Prerequisites: ESE 330 and Physics 217 or Physics 421.
Credit 3 units. EN: TU
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E35 ESE 538 Advanced Electromagnetic Engineering
The course builds on undergraduate electromagnetics to systematically develop advanced concepts in electromagnetic theory for engineering applications. The following topics are covered: Maxwell's equations; fields and waves in materials; electromagnetic potentials and topics for circuits and systems; transmissionline essentials for digital electronics and for communications; guided wave principles for electronics and optoelectronics; principles of radiation and antennas; and numerical methods for computational electromagnetics.
Credit 3 units.
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E35 ESE 543 Control Systems Design by State Space Methods
Advanced design and analysis of control systems by statespace methods: classical control review, Laplace transforms, review of linear algebra (vector space, change of basis, diagonal and Jordan forms), linear dynamic systems (modes, stability, controllability, state feedback, observability, observers, canonical forms, output feedback, separation principle and decoupling), nonlinear dynamic systems (stability, Lyapunov methods). Frequency domain analysis of multivariable control systems. State space control system design methods: state feedback, observer feedback, pole placement, linear optimal control. Design exercises with CAD (computeraided design) packages for engineering problems. Prerequisite: ESE 351 and ESE 441, or permission of instructor.
Credit 3 units. EN: TU
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E35 ESE 544 Optimization and Optimal Control
Constrained and unconstrained optimization theory. Continuous time as well as discretetime optimal control theory. Timeoptimal control, bangbang controls and the structure of the reachable set for linear problems. Dynamic programming, the Pontryagin maximum principle, the HamiltonianJacobiBellman equation and the Riccati partial differential equation. Existence of classical and viscosity solutions. Application to time optimal control, regulator problems, calculus of variations, optimal filtering and specific problems of engineering interest. Prerequisites: ESE 551, ESE 552.
Credit 3 units. EN: TU
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E35 ESE 545 Stochastic Control
Introduction to the theory of stochastic differential equations based on Wiener processes and Poisson counters, and an introduction to random fields. The formulation and solution of problems in nonlinear estimation theory. The KalmanBucy filter and nonlinear analogues. Identification theory. Adaptive systems. Applications. Prerequisites: ESE 520 and ESE 551.
Credit 3 units. EN: TU
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E35 ESE 546 Dynamics & Control in Neuroscience & Brain Medicine
This course provides an introduction to systems engineering approaches to modeling, analysis and control of neuronal dynamics at multiple scales. A central motivation is the manipulation of neuronal activity for both scientific and medical applications using emerging neurotechnology and pharmacology. Emphasis is placed on dynamical systems and control theory, including bifurcation and stability analysis of single neuron models and population meanfield models. Synchronization properties of neuronal networks are covered and methods for control of neuronal activity in both oscillatory and nonoscillatory dynamical regimes are developed. Statistical models for neuronal activity are also discussed. An overview of signal processing and data analysis methods for neuronal recording modalities is provided, toward the development of closedloop neuronal control paradigms. The final evaluation is based on a project or research survey. Prerequisite(s): ESE 553 (or equivalent); ESE 520 (or equivalent); ESE 351 (or equivalent).
Credit 3 units. EN: TU
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E35 ESE 547 Robust and Adaptive Control
Graduatelevel control system design methods for multiinput multioutput systems. Linear optimalbased methods in robust control, nonlinear model reference adaptive control. These design methods are currently used in most industry control system design problems. These methods are designed, analyzed and simulated using MATLAB. Linear control theory (review), robustness theory (Mu Analysis), optimal control and the robust servomechanism, Hinfinity optimal control, robust output feedback controls, Kalman filter theory and design, linear quadratic gaussian with loop transfer recovery, the Loop Transfer Recovery method of Lavretsky, Mu synthesis, Lyapunov theory (review), LaSalle extensions, Barbalat's Lemma, model reference adaptive control, artificial neural networks, online parameter estimation, convergence and persistence of excitation. Prerequisite: ESE 543 or ESE 551 or equivalent.
Credit 3 units. EN: TU
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E35 ESE 551 Linear Dynamic Systems I
Inputoutput and statespace description of linear dynamic systems. Solution of the state equations and the transition matrix. Controllability, observability, realizations, poleassignment, observers and decoupling of linear dynamic systems. Prerequisite: ESE 351.
Credit 3 units. EN: TU
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E35 ESE 552 Linear Dynamic Systems II
Least squares optimization problems. Riccati equation, terminal regulator and steadystate regulator. Introduction to filtering and stochastic control. Advanced theory of linear dynamic systems. Geometric approach to the structural synthesis of linear multivariable control systems. Disturbance decoupling, system invertibility and decoupling, extended decoupling and the internal model principle. Prerequisite: ESE 551.
Credit 3 units. EN: TU
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E35 ESE 553 Nonlinear Dynamic Systems
State space and functional analysis approaches to nonlinear systems. Questions of existence, uniqueness and stability; Lyapunov and frequencydomain criteria; wlimits and invariance, center manifold theory and applications to stability, steadystate response and singular perturbations. PoincareBendixson theory, the van der Pol oscillator, and the Hopf Bifurcation theorem. Prerequisite: ESE 551.
Credit 3 units. EN: TU
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E35 ESE 554 Advanced Nonlinear Dynamic Systems
Differentiable manifolds, vector fields, distributions on a manifold, Frobenius' theorem, Lie algebras. Controllability, observability of nonlinear systems, examined from the viewpoint of differential geometry. Transformation to normal forms. Exact linearization via feedback. Zero dynamics and related properties. Noninteracting control and disturbance decoupling. Controlled invariant distributions. Noninteracting control with internal stability. Prerequisites: ESE 553 and ESE 551.
Credit 3 units.
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E35 ESE 557 Hybrid Dynamic Systems
Theory and analysis of hybrid dynamic systems, which is the class of systems whose state is composed by continuousvalued and discretevalued variables. Discreteevent systems models and language descriptions. Models for hybrid systems. Conditions for existence and uniqueness. Stability and verification of hybrid systems. Optimal control of hybrid systems. Applications to cyberphysical systems and robotics. Prerequisite: ESE 551.
Credit 3 units. EN: TU
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E35 ESE 560 Computer Systems Architecture I
An exploration of the central issues in computer architecture: instruction set design, addressing and register set design, control unit design, microprogramming, memory hierarchies (cache and main memories, mass storage, virtual memory), pipelining, and bus organization. The course emphasizes understanding the performance implications of design choices, using architecture modeling and evaluation using VHDL and/or instruction set simulation. Prerequisites: CSE 361S and CSE 260M.
Same as E81 CSE 560M
Credit 3 units. EN: TU
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E35 ESE 561 Computer Systems Architecture II
Advanced techniques in computer system design. Selected topics from: processor design (multithreading, VLIW, data flow, chipmultiprocessors, application specific processors, vector units, large MIMD machines), memory systems (topics in locality, prefetching, reconfigurable and specialpurpose memories), system specification and validation, and interconnection networks. Prerequisites: CSE 560M or permission of instructor.
Same as E81 CSE 561M
Credit 3 units. EN: TU
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E35 ESE 562 Analog Integrated Circuits
This course focuses on fundamental and advanced topics in analog and mixedsignal VLSI techniques. The first part of the course covers graduatelevel materials in the area of analog circuit synthesis and analysis. The second part of the course covers applications of the fundamental techniques for designing analog signal processors and data converters. Several practical aspects of mixedsignal design, simulation and testing are covered in this course. This is a projectoriented course, and it is expected that the students apply the concepts learned in the course to design, simulate and explore different circuit topologies. Prerequisites: CSE 260 and ESE 232.
Credit 3 units.
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E35 ESE 565 Acceleration of Algorithms in Reconfigurable Logic
Reconfigurable logic, in the form of FieldProgrammable Gate Arrays (FPGAs), enables the deployment of custom hardware for individual applications. To exploit this capability, the application developer is required to specify the design at the registertransfer level. This course explores techniques for designing algorithms that are amenable to hardware acceleration as well as provides experience in actual implementation. Example applications are drawn from a variety of fields, such as networking, computational biology, etc. Prerequisites: basic digital logic (CSE 260M) and some experience with a hardware description language (e.g., VHDL or Verilog).
Same as E81 CSE 565M
Credit 3 units. EN: TU
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E35 ESE 566A Modern SystemonChip Design
The SystemonChip (SoCs) technology is at the core of most electronic systems: smart phones, wearable devices, autonomous robots, and cars, aerospace or medical electronics. In these SoCs, billions of transistors can be integrated on a single silicon chip, containing various components such as microprocessors, DSPs, hardware accelerators, memories, and I/O interfaces. Topics include SoC architectures, design tools and methods, as well as systemlevel tradeoffs between performance, power consumption, energy efficiency, reliability and programmability. Students gain an insight into the early stage of the SoC design process performing the tasks of developing functional specification, partition and map functions onto hardware and/or software, and evaluating and validating system performance. Assignments include handson design projects. Open to both graduate and senior undergraduate students. Prerequisite: ESE 461.
Credit 3 units. EN: TU
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E35 ESE 567 Computer Systems Analysis
A comprehensive course on performance analysis techniques. The topics include common mistakes, selection of techniques and metrics, summarizing measured data, comparing systems using random data, simple linear regression models, other regression models, experimental designs, 2**k experimental designs, factorial designs with replication, fractional factorial designs, one factor experiments, two factor full factorial design w/o replications, two factor full factorial designs with replications, general full factorial designs, introduction to queueing theory, analysis of single queues, queueing networks, operational laws, meanvalue analysis, time series analysis, heavy tailed distributions, selfsimilar processes, longrange dependence, random number generation, analysis of simulation results, and art of data presentation. Prerequisites: CSE 131 and CSE 260M.
Same as E81 CSE 567M
Credit 3 units. EN: TU
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E35 ESE 569 Parallel Architectures and Algorithms
Several contemporary parallel computer architectures are reviewed and compared. The problems of process synchronization and load balancing in parallel systems are studied. Several selected applications problems are investigated and parallel algorithms for their solution are considered. Selected parallel algorithms are implemented in both a shared memory and distributed memory parallel programming environment. Prerequisites: graduate standing and knowledge of the C programming language.
Same as E81 CSE 569M
Credit 3 units. EN: TU
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E35 ESE 570 Coding Theory
Introduction to the algebra of finite fields. Linear block codes, cyclic codes, BCH and related codes for error detection and correction. Encoder and decoder circuits and algorithms. Spectral descriptions of codes and decoding algorithms. Code performances.
Credit 3 units. EN: TU
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E35 ESE 571 Transmission Systems and Multiplexing
Transmission and multiplexing systems are essential to providing efficient pointtopoint communication over distance. This course introduces the principles underlying modern analog and digital transmission and multiplexing systems and covers a variety of system examples.
Credit 3 units. EN: TU
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E35 ESE 572 Signaling and Control in Communication Networks
The operation of modern communications networks is highly dependent on sophisticated control mechanisms that direct the flow of information through the network and oversee the allocation of resources to meet the communication demands of end users. This course covers the structure and operation of modern signaling systems and addresses the major design tradeoffs that center on the competing demands of performance and service flexibility. Specific topics covered include protocols and algorithms for connection establishment and transformation, routing algorithms, overload and failure recovery and networking dimensioning. Case studies provide concrete examples and reveal the key design issues. Prerequisites: graduate standing and permission of instructor.
Credit 3 units. EN: TU
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E35 ESE 575 FiberOptic Communications
Introduction to optical communications via glassfiber media. Pulsecode modulation and digital transmission methods, coding laws, receivers, biterror rates. Types and properties of optical fibers; attenuation, dispersion, modes, numerical aperture. Lightemitting diodes and semiconductor laser sources; device structure, speed, brightness, modes, electrical properties, optical and spectral characteristics. Prerequisites: ESE 330, ESE 336.
Credit 3 units. EN: TU
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E35 ESE 581 Radar Systems
An introduction to the selection and processing of radar signals. Signal design for improving range and Doppler resolution, ambiguity functions, chirp and steppedfrequency waveforms, pulsecompression codes. Statistical models for radar data: rangespread, Dopplerspread, doubly spread reflectors. Matchedfilter and estimatorcorrelator receivers for range and Doppler estimation. Tracking. Multiantenna radar receivers: interference rejection, adaptive canceling. DelayDoppler radarimaging using syntheticaperture processing. Prerequisite: ESE 524.
Credit 3 units. EN: TU
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E35 ESE 582 Fundamentals and Applications of Modern Optical Imaging
Analysis, design and application of modern optical imaging systems with emphasis on biological imaging. First part of the course focuses on the physical principles underlying the operation of imaging systems and their mathematical models. Topics include ray optics (speed of light, refractive index, laws of reflection and refraction, plane surfaces, mirrors, lenses, aberrations), wave optics (amplitude and intensity, frequency and wavelength, superposition and interference, interferometry), Fourier optics (spaceinvariant linear systems, HuygensFresnel principle, angular spectrum, Fresnel diffraction, Fraunhofer diffraction, frequency analysis of imaging systems), and lightmatter interaction (absorption, scattering, dispersion, fluorescence). Second part of the course compares modern quantitative imaging technologies including, but not limited to, digital holography, computational imaging, and superresolution microscopy. Students evaluate and critique recent optical imaging literature. Prerequisites: ESE 318 and ESE 319 or their equivalents; ESE 330 or Physics 421 or equivalent.
Credit 3 units. EN: TU
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E35 ESE 584 Statistical Signal Processing for Sensor Arrays
Methods for signal processing and statistical inference for data acquired by an array of sensors, such as those found in radar, sonar and wireless communications systems. Multivariate statistical theory with emphasis on the complex multivariate normal distribution. Signal estimation and detection in noise with known statistics, signal estimation and detection in noise with unknown statistics, direction finding, spatial spectrum estimation, beam forming, parametric maximumlikelihood techniques. Subspace techniques, including MUSIC and ESPRIT. Performance analysis of various algorithms. Advanced topics may include structured covariance estimation, wideband array processing, array calibration, array processing with polarization diversity, and spacetime adaptive processing (STAP). Prerequisites: ESE 520, ESE 524, linear algebra, computer programming.
Credit 3 units. EN: TU
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E35 ESE 588 Quantitative Image Processing
Introduction to modeling, processing, manipulation and display of images. Application of twodimensional linear systems to image processing. Twodimensional sampling and transform methods. The eye and perception. Image restoration and reconstruction. Multiresolution processing, noise reduction and compression. Boundary detection and image segmentation. Case studies in image processing (examples: computer tomography and ultrasonic imaging). Prerequisites: ESE 326, ESE 482.
Credit 3 units. EN: TU
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E35 ESE 589 Biological Imaging Technology
This class develops a fundamental understanding of the physics and mathematical methods that underlie biological imaging and critically examine case studies of seminal biological imaging technology literature. The physics section examines how electromagnetic and acoustic waves interact with tissues and cells, how waves can be used to image the biological structure and function, image formation methods, and diffraction limited imaging. The math section examines image decomposition using basis functions (e.g., Fourier transforms), synthesis of measurement data, image analysis for feature extraction, reduction of multidimensional imaging datasets, multivariate regression, and statistical image analysis. Original literature on electron, confocal and two photon microscopy, ultrasound, computed tomography, functional and structural magnetic resonance imaging and other emerging imaging technology are critiqued.
Credit 3 units. EN: TU
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E35 ESE 590 Electrical & Systems Engineering Graduate Seminar
This pass/fail course is required for the MS, DSc and PhD degrees in Electrical & Systems Engineering. A passing grade is required for each semester of enrollment and is received by attendance at regularly scheduled ESE seminars. MS students must attend at least three seminars per semester. DSc and PhD students must attend at least five seminars per semester. Parttime students are exempt except during their year of residency. Any student under continuing status is also exempt. Seminars missed in a given semester may be made up during the subsequent semester.
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E35 ESE 596 Seminar in Imaging Science and Engineering
This seminar course consists of a series of tutorial lectures on Imaging Science and Engineering with emphasis on applications of imaging technology. Students are exposed to a variety of imaging applications that vary depending on the semester, but may include multispectral remote sensing, astronomical imaging, microscopic imaging, ultrasound imaging and tomographic imaging. Guest lecturers come from several parts of the university. This course is required of all students in the Imaging Science and Engineering program; the only requirement is attendance. This course is graded pass/fail. Prerequisite: admission to Imaging Science and Engineering program. Same as CSE 596 (when offered) and BME 506.
Credit 1 unit.
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E35 ESE 599 Master's Research
Prerequisite: Students must have the ESE Research/Independent Study Registration Form (PDF) approved by the department.
Credit variable, maximum 3 units.
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