CME 102: Ordinary Differential Equations for Engineers (ENGR 155A)
Analytical and numerical methods for solving ordinary differential equations arising in engineering applications: Solution of initial and boundary value problems, series solutions, Laplace transforms, and nonlinear equations; numerical methods for solving ordinary differential equations, accuracy of numerical methods, linear stability theory, finite differences. Introduction to MATLAB programming as a basic tool kit for computations. Problems from various engineering fields.Prerequisites: knowledge of singlevariable calculus equivalent to the content of
Math 1921 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math21). Placement diagnostic (recommendation non binding) at:(
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext). Recommended:
CME100.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Cameron, M. (PI)
;
Le, H. (PI)
;
Aboumrad, G. (TA)
;
BougdalLambert, I. (TA)
;
Chiu, D. (TA)
;
Goc, K. (TA)
;
Harris, S. (TA)
;
Planeix, P. (TA)
;
Romain, M. (TA)
;
Schleede, P. (TA)
;
Zhang, V. (TA)
CME 103: Introduction to Matrix Methods (EE 103)
Introduction to applied linear algebra with emphasis on applications. Vectors, norm, and angle; linear independence and orthonormal sets; applications to document analysis. Clustering and the kmeans algorithm. Matrices, left and right inverses, QR factorization. Leastsquares and model fitting, regularization and crossvalidation. Constrained and nonlinear leastsquares. Applications include timeseries prediction, tomography, optimal control, and portfolio optimization. Undergraduate students should enroll for 5 units, and graduate students should enroll for 3 units. Prerequisites:
MATH 51 or
CME 100, and basic knowledge of computing (
CS 106A is more than enough, and can be taken concurrently).
EE103/CME103 and
Math 104 cover complementary topics in applied linear algebra. The focus of EE103 is on a few linear algebra concepts, and many applications; the focus of
Math 104 is on algorithms and concepts.
Terms: Aut, Sum

Units: 35

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Osgood, B. (PI)
;
Degleris, A. (TA)
;
Harvey, B. (TA)
...
more instructors for CME 103 »
Instructors:
Osgood, B. (PI)
;
Degleris, A. (TA)
;
Harvey, B. (TA)
;
Jani, T. (TA)
;
Landy, N. (TA)
;
Muppidi, S. (TA)
;
Shen, H. (TA)
;
Sowell, S. (TA)
CME 106: Introduction to Probability and Statistics for Engineers (ENGR 155C)
Probability: random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, nonparametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields. Prerequisite:
CME 100/ENGR154 or
MATH 51 or 52.
Terms: Win, Sum

Units: 4

UG Reqs: GER:DBMath, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Khayms, V. (PI)
;
Earley, E. (TA)
;
Gong, E. (TA)
;
Mantravadi, S. (TA)
;
Trean, M. (TA)
;
Wang, A. (TA)
;
Zhang, V. (TA)
CME 108: Introduction to Scientific Computing (MATH 114)
Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floatingpoint arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).
Terms: Win, Sum

Units: 3

UG Reqs: GER:DBEngrAppSci, WAYAQR, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Marsden, A. (PI)
;
Aboumrad, G. (TA)
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: leastsquares approximations of overdetermined equations, and leastnorm solutions of underdetermined equations. Symmetric matrices, matrix norm, and singularvalue decomposition. Eigenvalues, left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multiinput/multioutput systems, impulse and step matrices; convolution and transfermatrix descriptions. Control, reachability, and state transfer; observability and leastsquares state estimation. Prerequisites: Linear algebra and matrices as in
EE 103 or
MATH 104; ordinary differential equations and Laplace transforms as in
EE 102B or
CME 102.
Terms: Aut, Sum

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Nasiri Mahalati, R. (PI)
;
Bian, A. (TA)
;
Bindhi, M. (TA)
...
more instructors for CME 263 »
Instructors:
Nasiri Mahalati, R. (PI)
;
Bian, A. (TA)
;
Bindhi, M. (TA)
;
Diamandis, T. (TA)
;
Gotlin, A. (TA)
;
Kossyrev, M. (TA)
;
Murray, G. (TA)
CME 291: Master's Research
Students require faculty sponsor. (Staff)
Terms: Aut, Win, Spr, Sum

Units: 16

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Begenau, J. (PI)
;
Biondi, B. (PI)
;
Darve, E. (PI)
;
Gerritsen, M. (PI)
;
Gevaert, O. (PI)
;
Giesecke, K. (PI)
;
Glynn, P. (PI)
;
Goel, A. (PI)
;
Grundfest, J. (PI)
;
Iaccarino, G. (PI)
;
Lai, T. (PI)
;
Leskovec, J. (PI)
;
Marsden, A. (PI)
;
Osgood, B. (PI)
;
Papanicolaou, G. (PI)
;
Pelger, M. (PI)
;
Re, C. (PI)
;
Suckale, J. (PI)
;
Wong, W. (PI)
;
Wootters, M. (PI)
;
Ying, L. (PI)
CME 364A: Convex Optimization I (CS 334A, EE 364A)
Convex sets, functions, and optimization problems. The basics of convex analysis and theory of convex programming: optimality conditions, duality theory, theorems of alternative, and applications. Leastsquares, linear and quadratic programs, semidefinite programming, and geometric programming. Numerical algorithms for smooth and equality constrained problems; interiorpoint methods for inequality constrained problems. Applications to signal processing, communications, control, analog and digital circuit design, computational geometry, statistics, machine learning, and mechanical engineering. Prerequisite: linear algebra such as
EE263, basic probability.
Terms: Win, Sum

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Boyd, S. (PI)
;
Barratt, S. (TA)
;
CreusCosta, J. (TA)
...
more instructors for CME 364A »
Instructors:
Boyd, S. (PI)
;
Barratt, S. (TA)
;
CreusCosta, J. (TA)
;
Dean, J. (TA)
;
Diamond, S. (TA)
;
Garg, S. (TA)
;
Kim, J. (TA)
;
Mani, N. (TA)
;
Pathak, R. (TA)
;
Sholar, J. (TA)
;
Spear, L. (TA)
;
Tefagh, M. (TA)
CME 390: Curricular Practical Training
Educational opportunities in high technology research and development labs in applied mathematics. Qualified ICME students engage in internship work and integrate that work into their academic program. Students register during the quarter they are employed and complete a research report outlining their work activity, problems investigated, results, and followon projects they expect to perform. May be repeated three times for credit.
Terms: Aut, Win, Spr, Sum

Units: 1

Repeatable for credit

Grading: Satisfactory/No Credit
Instructors:
Giesecke, K. (PI)
;
Iaccarino, G. (PI)
CME 399: Special Research Topics in Computational and Mathematical Engineering
Graduatelevel research work not related to report, thesis, or dissertation. May be repeated for credit.
Terms: Aut, Win, Spr, Sum

Units: 115

Repeatable for credit

Grading: Letter or Credit/No Credit
CME 400: Ph.D. Research
Terms: Aut, Win, Spr, Sum

Units: 115

Repeatable for credit

Grading: Satisfactory/No Credit
Instructors:
Basu, S. (PI)
;
Bimpikis, K. (PI)
;
Biondi, B. (PI)
;
Blanchet Mancilla, J. (PI)
;
Bosagh Zadeh, R. (PI)
;
Boyd, S. (PI)
;
Bump, D. (PI)
;
Bustamante, C. (PI)
;
Candes, E. (PI)
;
Carlsson, G. (PI)
;
Darve, E. (PI)
;
Dror, R. (PI)
;
Farhat, C. (PI)
;
Gerritsen, M. (PI)
;
Giesecke, K. (PI)
;
Guibas, L. (PI)
;
Hastie, T. (PI)
;
Holmes, S. (PI)
;
Iaccarino, G. (PI)
;
James, D. (PI)
;
Johari, R. (PI)
;
Kahn, S. (PI)
;
Khatri, P. (PI)
;
Lai, T. (PI)
;
Lobell, D. (PI)
;
Marsden, A. (PI)
;
Montanari, A. (PI)
;
Papanicolaou, G. (PI)
;
Re, C. (PI)
;
Ryzhik, L. (PI)
;
Saban, D. (PI)
;
Saberi, A. (PI)
;
Sidford, A. (PI)
;
Suckale, J. (PI)
;
Wein, L. (PI)
;
Wong, W. (PI)
;
Xing, L. (PI)
;
Ye, Y. (PI)
;
Ying, L. (PI)