Washington University, St. LouisEngineering
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Dept # Course Name :  [Course Description On]  Credits
ESE 500 Independent Study 3
  Opportunities for graduate students to explore possible areas of interest with individual faculty members. Coordinated study programs dealing with areas not covered by formal course work are possible. Independent study credit can be changed to research credit (EE 599) any time during the semester if enrollment is appropriate. A final report is required to be submitted to the Department. 
ESE 501 Mathematics of Modern Engineering I 3
  Vectors and vector spaces, Matrix operations, System of linear equations, Eigenvalues and eigenvectors, Vector fields, Line and surface integrals, Solutions to ordinary and partial differential equations, Series expansions, Fourier Series. Prerequisite: ESE 318 and ESE 319 or ESE 317 or equivalent or consent of instructor. ESE Ph.D. students will not recieve credit for this course. 
ESE 502 Mathematics of Modern Engineering II 3
  Techniques of solving ordinary differential equations with constant coefficients, Laplace's Transform, solutions for the heat and wave equations, Laplace's Equation, Legendre and Bessel Function, Introduction to function of a complex variable, conformal mapping, contour integrals. Prerequisite: ESE 317 or equivalent, or consent of instructor. 
ESE 513 Convex Optimization and Duality Theory 3
  Graduate introduction to convex optimization with emphasis on convex analysis and duality theory. Topics include: convex sets, convex functions, convex cones, convex conjugates, Fenchel-Moreau theorem, convex duality and biconjugation, directional derivatives, subgradients and subdifferentials, optimality conditions, ordered vector spaces, Hahn-Banach theorem, extension and separation theorems, minimax theorems, and vector and set optimization. Prerequisites: ESE 415; Math 4111 
ESE 516 Optimization in Function Space 3
  Linear vector spaces. Normed linear spaces. Lebesque integrals. The Lp spaces. Linear operators. Dual spaces. Hilbert spaces. Projection theorem. Hahn-Banach theorem. Hyperplanes and convex sets. Gateaux and FrĊ½chet differentials. Unconstrained minima. Adjoint operators. Inverse function theorem. Constrained minima. Equality constraints. Lagrange multipliers. Calculus of variations. Euler-Lagrange equations. Positive cones. Inequality constraints. Kuhn-Tucker theorem. Optimal control theory. Pontryagin's maximum principle. Successive approximation methods. Newton's methods. Steepest descent methods. Primal-dual methods. Penalty function methods. Multiplyer methods. Prerequisite: Math 4111. 
ESE 517 Partial Differential Equations 3
  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. Prerequisite: ESE 318 and 319 or equivalent or consent of instructor. 
ESE 518 Optimization Methods in Control 3
  The course will be divided in two parts: convex optimization and optimal control. In the first part we will cover applications of Linear Matrix Inequalities and Semi-Definite Programming to control and estimation problems. We will also cover Multiparametric Linear Programming and its application to the Model Predictive Control and Estimation of linear systems. In the second part we will cover numerical methods to solve optimal control and estimation problems. We will cover techniques to discretize optimal control problems, numerical methods to solve them, and their optimality conditions. We will apply these results to the Model Predictive Control and Estimation of nonlinear systems. Prerequisites: ESE 551, and ESE 415 or equivalent. 
ESE 520 Probability and Stochastic Processes 3
  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. Prereq: ESE 326. 
ESE 523 Information Theory 3
  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. 
ESE 524 Detection and Estimation Theory 3
  Study of detection, estimation and modulation theory, detection of signals in noise, estimation of signal parameters, linear estimation theory. Kalman-Bucy and Wiener filters, nonlinear modulation theory, optimum angle modulation. Prerequisite: ESE 520. 
ESE 531 Nano and Micro Photonics 3
  This course focuses on theory, design, fabrication and application of photonic materials and micro/nano photonic devices. Interaction of light and matter, propagation of light in waveguide, nonlinear optical effect and optical properties of nano/micro structure, the device principles of silicon-based waveguide, filter, photodetector, modulator and laser devices. Prerequisite: ESE 330. 
ESE 532 Introduction to Nano-Photonic Devices 3
  Introduction to photon transport in nano-photonic devices. This course focuses on the following topics: light and photons, statistical properties of photon sources, temporal and spatial correlations, light-matter interactions, optical nonlinearity, atoms and quantum dots, single- and two-photon devices, optical devices, and applications of nano-photonic devices in quantum and classical computing and communication. Prerequisite: ESE 330 and Physics 217, or permission of instructor.  
ESE 534 Special Topics in Advanced Electrodynamics 3
  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 nano-particles or molecules); electromagnetic wave generation and detection (antenna and nano-antenna); inverse scattering problems; and numerical and approximate methods. Prerequisite: ESE 330, or Physics 421 and 422 
ESE 536 Introduction to Quantum Optics 3
  This course covers the following topics: quantum mechanics for quantum optics, radiative transitions in atoms, lasers, photon statistics (photon counting, Sub-/Super-Poissionian photon statistics, bunching, anti-bunching, theory of photodetection, shot noise), entanglement, squeezed light, atom-photon interactions, cold atoms, atoms in cavities. If time permits, the following topics will be selectively covered: quantum computing, quantum cryptography, and teleportation. Pre-requisites: ESE 330 and Physics 217 or Physics 421 
ESE 543 Control Systems Design by State Space Methods 3
  Advanced design and analysis of control systems by state-space methods: review of linear algebra (vector space, change of basis, diagonal and Jordan forms), linear dynamic systems (modes, stability, controllability, observability, canonical forms), nonlinear dynamic systems and their linearization (stability, Lyapunov methods), servomechanism design, state feedback and output feedback control design, observers and state estimation, introduction to optimal control, state feedback optimal control design and analysis, multivariable frequency response methods, robustness theory. Design exercises with CAD (computer-aided design) packages for engineering problems. Prerequisite: ESE 441 or equivalent, or permission of instructor. 
ESE 544 Optimization and Optimal Control 3
  Constrained and unconstrained optimization theory. Continuous time as well as discrete-time optimal control theory. Time-optimal control, bang-bang controls and the structure of the reachable set for linear problems. Dynamic programming, the Pontryagin maximum principle, the Hamiltonian-Jacobi-Bellman 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. 
ESE 545 Stochastic Control 3
  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 Kalman-Bucy filter and nonlinear analogues. Identification theory. Adaptive systems. Applications. Prerequisites: ESE 520 and ESE 551 
ESE 546 Dynamics & Control in Neuroscience & Brain Medicine 3
  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 mean-field models. Synchronization properties of neuronal networks are covered and methods for control of neuronal activity in both oscillatory and non-oscillatory 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 closed-loop 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) 
ESE 547 Robust and Adaptive Control 3
  This course is a graduate level course taught in two parts. Part 1 covers frequency domain analysis of multivariable systems, robustness theory and structured singular value mu analysis, linear quadratic optimal control system design using state and output feedback architectures, H-infinity optimal control, LQG/LTR, and output feedback projective controls. Part 2 covers the design of direct model reference adaptive controllers for uncertain nonlinear systems, Lyapunov stability theory, Barbalat lemma, neural networks, state feedback model reference adaptive control, and adaptive observer-based loop transfer recovery output feedback. Homework and computer design projects use aerospace examples. The adaptive controllers are developed to be an increment added to the robust control baseline architecture (covered in part 1).Prerequisite: ESE 543 Control Systems Design by State Space Methods or ESE 551 Linear Dynamic Systems or equivalent. 
ESE 551 Linear Dynamic Systems I 3
  Input-output and state-space description of linear dynamic systems. Solution of the state equations and the transition matrix. Controllability, observability, realizations, pole-assignment, observers and decoupling of linear dynamic systems. Prereq: ESE 351. 
ESE 553 Nonlinear Dynamic Systems 3
  State space and functional analysis approaches to nonlinear systems. Questions of existence, uniqueness, and stability; Lyapunov and frequency-domain criteria; w-limits and invariance, center manifold theory and applications to stability, steady state response and singular perturbations. Poincare-Bendixson theory, the van der Pol oscillator and the Hopf Bifurcation theorem. Prerequisite: ESE 551. 
ESE 557 Hybrid Dynamic Systems 3
  Theory and analysis of hybrid dynamic systems, which is the class of systems whose state is composed by continuous-valued and discrete-valued variables. Discrete-event 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 Cyber-Physical systems and robotics. Prerequisite: ESE 551. 
ESE 560 Computer Systems Architecture I 3
ESE 562 Digital System Verification, Testing, and Reliability 3
  This course will focus on fundamental and advanced topics in analog and mixed-signal VLSI techniques. The first part of the course will cover graduate level materials in the area of analog circuit synthesis and analysis. The second part of the course will cover applications of the fundamental techniques for designing filters and sigma-delta modulators. Several practical aspects of mixed-signal design, simulation, layout and testing will be covered in this course and will be used for implementing a VLSI prototype. It is expected that the students complete the design and simulation of a prototype by the end of the course. Prerequisite: ESE 232 
ESE 566A Modern System-on-Chip Design 3
  The System-on-Chip (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 system-level tradeoffs between performance, power consumption, energy efficiency, reliability, and programmability. Students will 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 hands-on design projects. Open to both graduate and senior undergraduate students. Pre-requisites: ESE 260 
ESE 567 Computer Systems Analysis 3
  Comparing systems using measurement, simulation, and queueing models. Common mistakes and how to avoid them, selection of techniques and metrics, art of data presentation, summarizing measured data, comparing systems using sample data, introduction to experimental design, fractional factorial designs, introduction to simulation, common mistakes in simulations, analysis of simulation results, random number generation, random variate generation, commonly used distributions, introduction to queueing theory, single queues, and queueing networks. The techniques of the course can be used to analyze and compare any type of systems including algorithms, protocols, network, or database systems. Students do a project involving application of these techniques to a problem of their interest. Prerequisites: CSE 131 and CSE 260M. 
ESE 568 Imaging Sensors 3
ESE 569 Parallel Architectures and Algorithms 3
ESE 570 Coding Theory 3
  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. 
ESE 571 Transmission Systems and Multiplexing 3
  Transmission and multiplexing systems are essential to providing efficient point-to-point communication over distance. This course introduces the principles underlying modern analog and digital transmission and multiplexing systems and covers a variety of system examples. 
ESE 572 Signaling and Control in Communication Networks 3
  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 trade-offs which 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. 
ESE 575 Fiber-Optic Communications 3
  Introduction to optical communications via glass-fiber media. Pulse-code modulation and digital transmission methods, coding laws, receivers, bit-error rates. Types and properties of optical fibers; attenuation, dispersion, modes, numerical aperture. Light-emitting diodes and semiconductor laser sources; device structure, speed, brightness, modes, electrical properties, optical and spectral characteristics. Prerequisites: ESE 330, 336. 
ESE 582 Fundamentals and Applications of Modern Optical Imaging 3
  Analysis, design, and application of modern optical imaging systems with emphasis on biological imaging. First part of course will focus 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 (space-invariant linear systems, Huygens-Fresnel principle, angular spectrum, Fresnel diffraction, Fraunhofer diffraction, frequency analysis of imaging systems), and light-matter interaction (absorption, scattering, dispersion, fluorescence). Second part of course will compare modern quantitative imaging technologies including, but not limited to, digital holography, computational imaging, and super-resolution microscopy. Students will evaluate and critique recent optical imaging literature.Pre-requisites: ESE 318 and ESE 319 or their equivalents; ESE 330 or PHY 421 or equivalent.  
ESE 588 Quantitative Image Processing 3
  Introduction to the modeling processing and display of images. Two-dimensional linear systems and linear processing of images. Two-dimensional transform methods. Image acquisition and display technology. Psychophysical aspects of vision. Case studies in image processing (examples: tomography, radiology, ultrasonic imaging). Special algorithms for image processing (examples: boundary detection, segmentation, compression, interactive processing and display). Prerequisites: ESE 326, ESE 482. 
ESE 589 Biological Imaging Technology 3
  This class will develop 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 will examine 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 will examine image decomposition using basis functions (e.g. fourier transforms), synthesis of measurement data, image analysis for feature extraction, reduction of multi-dimensional 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 will be critiqued. 
ESE 590 Electrical & Systems Engineering Graduate Seminar 0
  This satisfactory/unsatisfactory course is required for the M.Sc., D.Sc. and Ph.D. degrees in Electrical and Systems Engineering. A passing grade is required for each semester of enrollment and is received by attendance at regularly scheduled ESE seminars. M.Sc. students must attend at least 4 seminars per semester. D.Sc. and Ph.D. students must attend at least 7 seminars per semester. Part-time 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. 
ESE 591 Special Topics: Biomedical Optics I: Principles 3
ESE 591 Biomedical Optics I: Principles 3
  This course covers the principles of optical photon transport in biological tissue. Topics include a brief introduction to biomedical optics, single-scatterer theories, Monte Carlo modeling of photon transport, convolution for broad-beam responses, radiative transfer equation and diffusion theory, hybrid Monte Carlo method and diffusion theory, and sensing of optical properties and spectroscopy. Prerequisite: Differential equations 
ESE 592 Special Topics: Biomedical Optics II: Imaging 3
  This course covers optical imaging technologies. Topics include ballistic imaging, optical coherence tomography, Mueller optical coherence tomography, diffuse optical tomography, photoacoustic tomography, and ultrasound-modulated optical tomography. Pre-reqs: Differential equations; Biomedical Optics I: Principles. 
ESE 596 Seminar in Imaging Science and Engineering 1
  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.  
ESE 599 Masters Research 3
ESE 600 Doctoral Research 9
ESE 883 Masters Continuing Student Status 0
ESE 884 Doctoral Continuing Student Status 0
ESE 885 Masters Nonresident 0
ESE 886 Doctoral Nonresident 0

Washington University in St. Louis School of Engineering & Applied Science, Department of Electrical & Systems Engineering

Green Hall, CB 1042, 1 Brookings Drive, Saint Louis, MO, USA 63130
Phone: (314) 935-5565, Fax: (314) 935-7500

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