printer friendly pageCME 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:
CME 100/
ENGR 154 or
MATH 51.
Terms: Win, Spr, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Le, H. (PI)
;
Moin, P. (PI)
CME 102A: Ordinary Differential Equations for Engineers, ACE
Students attend
CME102/ENGR155A lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Prerequisite: application at:
http://soe.stanford.edu/current_students/edp/programs/ace.html
Terms: Win, Spr
| Units: 6
| UG Reqs: WAY-FR, GER:DB-Math
Instructors:
Le, H. (PI)
;
Moin, P. (PI)
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, non-parametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields. Prerequisite:
CME 100/ENGR154 or
MATH 51.
Terms: Win, Sum
| Units: 3-4
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
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, floating-point 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.nImplementation of numerical methods in MATLAB programming assignments.nPrerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).
Terms: Win, Sum
| Units: 3-4
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR
Instructors:
Navalpakkam Srinivasan Acharya, S. (PI)
;
Sing Long Collao, C. (PI)
CME 181: Projects in Applied and Computational Mathematics
Teams of students use techniques in applied and computational mathematics to tackle problems of their choosing. Students will have the opportunity to pursue open-ended projects in a variety of areas: economics, physics, political science, operations research, etc. Projects can cover (but are not limited to!) topics such as mathematical modeling of real-world phenomena (population dynamics), data-driven applications (movie recommendations) or complex systems in engineering (optimal control). Each team will be paired with a graduate student mentor working in applied and computational mathematics. Limited enrollment. Prerequisites:
CME 100/102/104 or equivalents, or instructor consent. Recommended:
CME 106/108 and familiarity with programming at the level of
CME 192/193.
Terms: Win
| Units: 3
Instructors:
Minion, M. (PI)
CME 192: Introduction to MATLAB
This short course runs for the first four weeks of the quarter and is offered each quarter during the academic year. It is highly recommended for students with no prior programming experience who are expected to use MATLAB in math, science, or engineering courses. It will consist of interactive lectures and application-based assignments.nThe goal of the short course is to make students fluent in MATLAB and to provide familiarity with its wide array of features. The course covers an introduction of basic programming concepts, data structures, and control/flow; and an introduction to scientific computing in MATLAB, scripts, functions, visualization, simulation, efficient algorithm implementation, toolboxes, and more.
Terms: Aut, Win, Spr
| Units: 1
CME 193: Introduction to Scientific Python
This short course runs for the first four weeks of the quarter and is offered each quarter during the academic year. It is recommended for students who want to use Python in math, science, or engineering courses and for students who want to learn the basics of Python programming. The goal of the short course is to familiarize students with Python¿s tools for scientific computing. Lectures will be interactive with a focus on learning by example, and assignments will be application-driven. No prior programming experience is needed.nTopics covered include control flow, basic data structures, File I/O, and an introduction to NumPy/SciPy.
Terms: Aut, Win, Spr
| Units: 1
CME 204: Partial Differential Equations in Engineering (ME 300B)
Geometric interpretation of partial differential equation (PDE) characteristics; solution of first order PDEs and classification of second-order PDEs; self-similarity; separation of variables as applied to parabolic, hyperbolic, and elliptic PDEs; special functions; eigenfunction expansions; the method of characteristics. If time permits, Fourier integrals and transforms, Laplace transforms. Prerequisite:
CME 200/
ME 300A, equivalent, or consent of instructor.
Terms: Win
| Units: 3
Instructors:
Lele, S. (PI)
CME 212: Advanced Programming for Scientists and Engineers (ENERGY 212)
Advanced topics in software programming, debugging, and performance optimization are covered. The capabilities and usage of common libraries and frameworks such as BLAS, LAPACK, FFT, PETSc, and MKL/ACML are reviewed. Computer representation of integer and floating point numbers, and interoperability between C/C++ and Fortran is described. More advanced software engineering topics including: representing data in files, application checkpoint/restart, signals, unit and regression testing, and build automation. The use of debugging tools including static analysis, gdb, and Valgrind are introduced. An introduction to computer architecture covering processors, memory hierarchy, storage, and networking provides a foundation for understanding software performance. Profiles generated using gprof and perf are used to help guide the performance optimization process. Computational problems from various science and engineering disciplines will be used in individual and group assignments. Prerequisites:
CME 200/
ME 300A and
CME 211 or equivalent level of programming proficiency in Python and C/C++.
Terms: Win
| Units: 3
Instructors:
LeGresley, P. (PI)
CME 215A: Advanced Computational Fluid Dynamics (AA 215A)
High resolution schemes for capturing shock waves and contact discontinuities; upwinding and artificial diffusion; LED and TVD concepts; alternative flow splittings; numerical shock structure. Discretization of Euler and Navier Stokes equations on unstructured meshes; the relationship between finite volume and finite element methods. Time discretization; explicit and implicit schemes; acceleration of steady state calculations; residual averaging; math grid preconditioning. Automatic design; inverse problems and aerodynamic shape optimization via adjoint methods. Pre- or corequisite: 214B or equivalent.
Terms: Win
| Units: 3
Instructors:
Jameson, A. (PI)
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