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. Prerequisite: 10 units of AP credit (Calc BC with 5, or Calc AB with 5 or placing out of the single variable math placement test:
https://exploredegreesnextyear.stanford.edu/undergraduatedegreesandprograms/#aptextt),), or
Math 1921. Recommended:
CME100.
Terms: Aut, Win, Spr, Sum

Units: 5

UG Reqs: GER:DBMath, WAYFR

Grading: Letter or Credit/No Credit
Instructors:
Le, H. (PI)
;
Moin, P. (PI)
;
Ahn, S. (TA)
;
Amidi, S. (TA)
;
DePaul, G. (TA)
;
FournierBidoz, E. (TA)
;
Gallegos Ortega, D. (TA)
;
Infanger, A. (TA)
;
Lachevre, P. (TA)
;
Patel, H. (TA)
;
Wang, R. (TA)
;
Westhoff, P. (TA)
;
Wu, H. (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)
;
Amidi, S. (TA)
;
Chhor, G. (TA)
;
Chu, C. (TA)
;
Lakshman, V. (TA)
;
Pyron, J. (TA)
;
Sagastuy Brena, J. (TA)
;
Wu, Y. (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
CME 232: Introduction to Computational Mechanics (ME 332)
Provides an introductory overview of modern computational methods for problems arising primarily in mechanics of solids and is intended for students from various engineering disciplines. The course reviews the basic theory of linear solid mechanics and introduces students to the important concept of variational forms, including the principle of minimum potential energy and the principles of virtual work. Specific model problems that will be considered include deformation of bars, beams and membranes, plates, and problems in plane elasticity (plane stress, plane strain, axisymmetric elasticity). The variational forms of these problems are used as the starting point for developing the finite element method (FEM) and boundary element method (BEM) approaches providing an important connection between mechanics and computational methods.
Terms: Sum

Units: 3

Grading: Letter (ABCD/NP)
Instructors:
Pinsky, P. (PI)
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)
;
Shah, K. (PI)
;
Aboumrad, G. (TA)
...
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Instructors:
Nasiri Mahalati, R. (PI)
;
Shah, K. (PI)
;
Aboumrad, G. (TA)
;
Chemparathy, A. (TA)
;
Kossyrev, M. (TA)
;
Momeni, A. (TA)
;
Shah, K. (TA)
;
Zhou, Z. (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)
;
Bosagh Zadeh, R. (PI)
...
more instructors for CME 291 »
Instructors:
Begenau, J. (PI)
;
Biondi, B. (PI)
;
Bosagh Zadeh, R. (PI)
;
Boyd, S. (PI)
;
Carlsson, G. (PI)
;
Darve, E. (PI)
;
Farhat, C. (PI)
;
Gerritsen, M. (PI)
;
Giesecke, K. (PI)
;
Glynn, P. (PI)
;
Gous, A. (PI)
;
Grundfest, J. (PI)
;
Guibas, L. (PI)
;
Kahn, S. (PI)
;
Lai, T. (PI)
;
Leskovec, J. (PI)
;
Ng, A. (PI)
;
Papanicolaou, G. (PI)
;
Pelger, M. (PI)
;
Rajagopal, R. (PI)
;
Re, C. (PI)
;
Schwartzman, A. (PI)
;
Suckale, J. (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:
Lall, S. (PI)
;
Pathak, R. (PI)
;
Angeris, G. (TA)
;
Choudhary, D. (TA)
;
Gu, A. (TA)
;
Jiang, Q. (TA)
;
Kim, J. (TA)
;
Mani, N. (TA)
;
Momeni, A. (TA)
;
Pathak, R. (TA)
;
Shah, K. (TA)
;
Song, R. (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
Instructors:
Boyd, S. (PI)
;
Candes, E. (PI)
;
Carlsson, G. (PI)
;
Darve, E. (PI)
;
Gerritsen, M. (PI)
;
Hastie, T. (PI)
;
Kamvar, S. (PI)
;
Levi, O. (PI)
CME 400: Ph.D. Research
Terms: Aut, Win, Spr, Sum

Units: 115

Repeatable for credit

Grading: Satisfactory/No Credit
Instructors:
Beroza, G. (PI)
;
Bimpikis, K. (PI)
;
Biondi, B. (PI)
...
more instructors for CME 400 »
Instructors:
Beroza, G. (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)
;
Leskovec, J. (PI)
;
Lobell, D. (PI)
;
Marsden, A. (PI)
;
Moin, P. (PI)
;
Montanari, A. (PI)
;
Papanicolaou, G. (PI)
;
Rajagopal, R. (PI)
;
Re, C. (PI)
;
Reed, E. (PI)
;
Ryzhik, L. (PI)
;
Saban, D. (PI)
;
Saberi, A. (PI)
;
Saunders, M. (PI)
;
Sidford, A. (PI)
;
Suckale, J. (PI)
;
Tibshirani, R. (PI)
;
Wong, W. (PI)
;
Xing, L. (PI)
;
Ye, Y. (PI)
;
Ying, L. (PI)