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
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)
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 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)
;
Bian, A. (TA)
;
Bindhi, M. (TA)
...
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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)
;
Giesecke, K. (PI)
;
Glynn, P. (PI)
;
Grundfest, J. (PI)
;
Iaccarino, G. (PI)
;
Lai, T. (PI)
;
Leskovec, J. (PI)
;
Marsden, A. (PI)
;
Papanicolaou, G. (PI)
;
Pelger, M. (PI)
;
Re, C. (PI)
;
Suckale, J. (PI)
;
Ying, L. (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)
;
Wong, W. (PI)
;
Xing, L. (PI)
;
Ye, Y. (PI)
;
Ying, L. (PI)
CME 801: TGR Project
Terms: Aut, Win, Spr, Sum

Units: 0

Repeatable for credit

Grading: TGR