printer friendly pageCME 100: Vector Calculus for Engineers (ENGR 154)
Computation and visualization using MATLAB. Differential vector calculus: analytic geometry in space, functions of several variables, partial derivatives, gradient, unconstrained maxima and minima, Lagrange multipliers. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green's, divergence, and Stokes' theorems. Examples and applications drawn from various engineering fields. Prerequisites:
MATH 41 and 42, or 10 units AP credit.
Terms: Aut
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Units: 5
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UG Reqs: GER:DBMath
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Grading: Letter or Credit/No Credit
Instructors:
Gerritsen, M. (PI)
;
Khayms, V. (PI)
Gerritsen, M. (PI)
;
Khayms, V. (PI)
CME 100A: Vector Calculus for Engineers, ACE
Students attend
CME100/ENGR154 lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Enrollment by department permission only. Prerequisite: application at:
https://soe.stanford.edu/current_students/edp/programs/ace.html
Terms: Aut
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Units: 6
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UG Reqs: GER:DBMath
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Grading: Letter or Credit/No Credit
Instructors:
Gerritsen, M. (PI)
;
Khayms, V. (PI)
Gerritsen, M. (PI)
;
Khayms, V. (PI)
CME 200: Linear Algebra with Application to Engineering Computations (ME 300A)
Computer based solution of systems of algebraic equations obtained from engineering problems and eigen-system analysis, Gaussian elimination, effect of round-off error, operation counts, banded matrices arising from discretization of differential equations, ill-conditioned matrices, matrix theory, least square solution of unsolvable systems, solution of non-linear algebraic equations, eigenvalues and eigenvectors, similar matrices, unitary and Hermitian matrices, positive definiteness, Cayley-Hamilton theory and function of a matrix and iterative methods. Prerequisite: familiarity with computer programming, and
MATH104, 113, or equivalent.
Terms: Aut
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Moin, P. (PI)
CME 211: Introduction to Programming for Scientists and Engineers (EARTHSCI 211)
Basic usage of the Python and C/C++ programming languages are introduced and used to solve representative computational problems from various science and engineering disciplines. Software design principles including time and space complexity analysis, data structures, object-oriented design, decomposition, encapsulation, and modularity are emphasized. Usage of ICME and campus wide Linux compute resources: login, file system navigation, editing files, compiling and linking, file transfer, etc. Versioning and revision control, software build utilities, and the LaTeX typesetting software are introduced and used to help complete individual programming assignments and a group project.
Terms: Aut
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Legresley, P. (PI)
CME 263: Introduction to Linear Dynamical Systems (EE 263)
Applied linear algebra and linear dynamical systems with application 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
MATH 103; differential equations and Laplace transforms as in
EE 102A.
Terms: Aut, Sum
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Boyd, S. (PI)
CME 291: Master's Research
Students require faculty sponsor. (Staff)
Terms: Aut, Win, Spr, Sum
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Units: 1-5
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Repeatable for credit
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Grading: Letter or Credit/No Credit
Instructors:
Aiken, A. (PI)
;
Alonso, J. (PI)
;
Boneh, D. (PI)
;
Boyd, S. (PI)
...
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Instructors:
Aiken, A. (PI)
;
Alonso, J. (PI)
;
Boneh, D. (PI)
;
Boyd, S. (PI)
;
Butte, A. (PI)
;
Carlsson, G. (PI)
;
Constantinou, C. (PI)
;
Darve, E. (PI)
;
Diaconis, P. (PI)
;
Donoho, D. (PI)
;
Farhat, C. (PI)
;
Fedkiw, R. (PI)
;
Fringer, O. (PI)
;
Fruchter, R. (PI)
;
Gerritsen, M. (PI)
;
Giesecke, K. (PI)
;
Glynn, P. (PI)
;
Goel, A. (PI)
;
Hanrahan, P. (PI)
;
Jameson, A. (PI)
;
Johari, R. (PI)
;
Kahn, S. (PI)
;
Kamvar, S. (PI)
;
Khayms, V. (PI)
;
Langley, P. (PI)
;
Lele, S. (PI)
;
Leskovec, J. (PI)
;
Levinson, D. (PI)
;
Lew, A. (PI)
;
Liu, T. (PI)
;
Manning, C. (PI)
;
McFarland, D. (PI)
;
Mignot, E. (PI)
;
Moin, P. (PI)
;
Murray, W. (PI)
;
Ng, A. (PI)
;
Papanicolaou, G. (PI)
;
Pohorille, A. (PI)
;
Rajaratnam, B. (PI)
;
Saberi, A. (PI)
;
Saunders, M. (PI)
;
Shaqfeh, E. (PI)
;
Taylor, C. (PI)
;
Wong, W. (PI)
;
Ye, Y. (PI)
Gerritsen, M. (PI)
;
Giesecke, K. (PI)
;
Glynn, P. (PI)
;
Goel, A. (PI)
;
Hanrahan, P. (PI)
;
Jameson, A. (PI)
;
Johari, R. (PI)
;
Kahn, S. (PI)
;
Kamvar, S. (PI)
;
Khayms, V. (PI)
;
Langley, P. (PI)
;
Lele, S. (PI)
;
Leskovec, J. (PI)
;
Levinson, D. (PI)
;
Lew, A. (PI)
;
Liu, T. (PI)
;
Manning, C. (PI)
;
McFarland, D. (PI)
;
Mignot, E. (PI)
;
Moin, P. (PI)
;
Murray, W. (PI)
;
Ng, A. (PI)
;
Papanicolaou, G. (PI)
;
Pohorille, A. (PI)
;
Rajaratnam, B. (PI)
;
Saberi, A. (PI)
;
Saunders, M. (PI)
;
Shaqfeh, E. (PI)
;
Taylor, C. (PI)
;
Wong, W. (PI)
;
Ye, Y. (PI)
CME 300: Departmental 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
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Units: 1
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Repeatable for credit
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Grading: Satisfactory/No Credit
Instructors:
Murray, W. (PI)
CME 302: Numerical Linear Algebra
First in a three quarter graduate sequence. Solution of systems of linear equations: direct methods, error analysis, structured matrices; iterative methods and least squares. Parallel techniques. Prerequisites:
CME 108,
MATH 103 or 113.
Terms: Aut
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Darve, E. (PI)
;
Gerritsen, M. (PI)
Gerritsen, M. (PI)
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: foundation in multivariable calculus and ordinary differential equations.
Terms: Aut
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Units: 3
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Grading: Letter or Credit/No Credit
Instructors:
Vasy, A. (PI)
CME 330: Applied Mathematics in the Chemical and Biological Sciences (CHEMENG 300)
Mathematical solution methods via applied problems including chemical reaction sequences, mass and heat transfer in chemical reactors, quantum mechanics, fluid mechanics of reacting systems, and chromatography. Topics include generalized vector space theory, linear operator theory with eigenvalue methods, phase plane methods, perturbation theory (regular and singular), solution of parabolic and elliptic partial differential equations, and transform methods (Laplace and Fourier). Prerequisites:
CME 102/
ENGR 155A and
CME 104/
ENGR 155B, or equivalents.
Terms: Aut
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Units: 3
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Grading: Letter (ABCD/NP)
Instructors:
Shaqfeh, E. (PI)
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