## CME 263: Introduction to Linear Dynamical Systems (EE 263)

Applied linear algebra and linear dynamical systems with applications to circuits, signal processing, communications, and control systems. Topics: least-squares approximations of over-determined equations, and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm, and singular-value decomposition. Eigenvalues, left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input/multi-output systems, impulse and step matrices; convolution and transfer-matrix descriptions. Control, reachability, and state transfer; observability and least-squares state estimation. Prerequisites: Linear algebra and matrices as in
ENGR 108 or
MATH 104; ordinary differential equations and Laplace transforms as in
EE 102B or
CME 102.

Terms: Aut
| Units: 3

Instructors:
Lall, S. (PI)
;
Bartan, B. (TA)
;
Lacotte, J. (TA)
;
Lee, C. (TA)
;
Mottaghi, A. (TA)
;
Sinha, R. (TA)
;
Tragus, N. (TA)

## CME 279: Computational Biology: Structure and Organization of Biomolecules and Cells (BIOE 279, BIOMEDIN 279, BIOPHYS 279, CS 279)

Computational techniques for investigating and designing the three-dimensional structure and dynamics of biomolecules and cells. These computational methods play an increasingly important role in drug discovery, medicine, bioengineering, and molecular biology. Course topics include protein structure prediction, protein design, drug screening, molecular simulation, cellular-level simulation, image analysis for microscopy, and methods for solving structures from crystallography and electron microscopy data. Prerequisites: elementary programming background (
CS 106A or equivalent) and an introductory course in biology or biochemistry.

Terms: Aut
| Units: 3

## CME 285: Computational Modeling in the Cardiovascular System (BIOE 285, ME 285)

This course introduces computational modeling methods for cardiovascular blood flow and physiology. Topics in this course include analytical and computational methods for solutions of flow in deformable vessels, one-dimensional equations of blood flow, cardiovascular anatomy, lumped parameter models, vascular trees, scaling laws, biomechanics of the circulatory system, and 3D patient specific modeling with finite elements; course will provide an overview of the diagnosis and treatment of adult and congenital cardiovascular diseases and review recent research in the literature in a journal club format. Students will use SimVascular software to do clinically-oriented projects in patient specific blood flow simulations. Pre-requisites:
CME102, ME133 and
CME192.

Terms: Spr
| Units: 3

Instructors:
Marsden, A. (PI)
;
Schwarz, E. (TA)

## CME 291: Master's Research

Students require faculty sponsor. (Staff)

Terms: Aut, Win, Spr, Sum
| Units: 1-6
| Repeatable
for credit

Instructors:
Begenau, J. (PI)
;
Biondi, B. (PI)
;
Brunskill, E. (PI)
...
more instructors for CME 291 »

Instructors:
Begenau, J. (PI)
;
Biondi, B. (PI)
;
Brunskill, E. (PI)
;
Bustamante, C. (PI)
;
Darve, E. (PI)
;
Dunham, E. (PI)
;
Fedkiw, R. (PI)
;
Gerritsen, M. (PI)
;
Gevaert, O. (PI)
;
Giesecke, K. (PI)
;
Glynn, P. (PI)
;
Goel, A. (PI)
;
Gous, A. (PI)
;
Grundfest, J. (PI)
;
Hanson, K. (PI)
;
Iaccarino, G. (PI)
;
Ioannidis, A. (PI)
;
Lai, T. (PI)
;
Leskovec, J. (PI)
;
Marsden, A. (PI)
;
Osgood, B. (PI)
;
Papanicolaou, G. (PI)
;
Paredes Castro, P. (PI)
;
Pavone, M. (PI)
;
Pelger, M. (PI)
;
Pohl, K. (PI)
;
Rao, A. (PI)
;
Re, C. (PI)
;
Rivas, M. (PI)
;
Rosenberg, N. (PI)
;
Rusu, M. (PI)
;
Santucci, A. (PI)
;
Suckale, J. (PI)
;
Tchelepi, H. (PI)
;
Wheeler, M. (PI)
;
Wootters, M. (PI)
;
Xing, L. (PI)
;
Ying, L. (PI)

## CME 292: Advanced MATLAB for Scientific Computing

Short course running first four weeks of the quarter (8 lectures) with interactive online lectures and application based assignment. Students will access the lectures and assignments on
https://suclass.stanford.edu. Students will be introduced to advanced MATLAB features, syntaxes, and toolboxes not traditionally found in introductory courses. Material will be reinforced with in-class examples, demos, and homework assignment involving topics from scientific computing. MATLAB topics will be drawn from: advanced graphics (2D/3D plotting, graphics handles, publication quality graphics, animation), MATLAB tools (debugger, profiler), code optimization (vectorization, memory management), object-oriented programming, compiled MATLAB (MEX files and MATLAB coder), interfacing with external programs, toolboxes (optimization, parallel computing, symbolic math, PDEs). Scientific computing topics will include: numerical linear algebra, numerical optimization, ODEs, and PDEs.

Last offered: Spring 2020

## CME 298: Basic Probability and Stochastic Processes with Engineering Applications (MATH 158)

Calculus of random variables and their distributions with applications. Review of limit theorems of probability and their application to statistical estimation and basic Monte Carlo methods. Introduction to Markov chains, random walks, Brownian motion and basic stochastic differential equations with emphasis on applications from economics, physics and engineering, such as filtering and control. Prerequisites: exposure to basic probability.

Terms: Spr
| Units: 3

## CME 300: First Year Seminar Series

Required for first-year ICME Ph.D. students; recommended for first-year ICME M.S. students. Presentations about research at Stanford by faculty and researchers from Engineering, H&S, and organizations external to Stanford. May be repeated for credit.

Terms: Aut, Win, Spr
| Units: 1
| Repeatable
for credit

Instructors:
Iaccarino, G. (PI)

## CME 302: Numerical Linear Algebra

Solution of linear systems, accuracy, stability, LU, Cholesky, QR, least squares problems, singular value decomposition, eigenvalue computation, iterative methods, Krylov subspace, Lanczos and Arnoldi processes, conjugate gradient, GMRES, direct methods for sparse matrices. Prerequisites:
CME 108,
MATH 114,
MATH 104.

Terms: Aut
| Units: 3

Instructors:
Darve, E. (PI)
;
Cambier, L. (TA)
;
Cote de Soux, P. (TA)
...
more instructors for CME 302 »

Instructors:
Darve, E. (PI)
;
Cambier, L. (TA)
;
Cote de Soux, P. (TA)
;
Gnanasekaran, A. (TA)
;
Lerner, S. (TA)

## CME 303: Partial Differential Equations of Applied Mathematics (MATH 220)

First-order partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems. Prerequisite: Basic coursework in multivariable calculus and ordinary differential equations, and some prior experience with a proof-based treatment of the material as in
Math 171 or
Math 61CM.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.

Terms: Aut
| Units: 3

Instructors:
Ryzhik, L. (PI)
;
Jia, Q. (TA)

## CME 305: Discrete Mathematics and Algorithms (MS&E 316)

Topics: Basic Algebraic Graph Theory, Matroids and Minimum Spanning Trees, Submodularity and Maximum Flow, NP-Hardness, Approximation Algorithms, Randomized Algorithms, The Probabilistic Method, and Spectral Sparsification using Effective Resistances. Topics will be illustrated with applications from Distributed Computing, Machine Learning, and large-scale Optimization. Prerequisites:
CS 261 is highly recommended, although not required.

Terms: Win
| Units: 3

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