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This archived information is dated to the 2008-09 academic year only and may no longer be current.

For currently applicable policies and information, see the current Stanford Bulletin.

Undergraduate courses in Computational and Mathematical Engineering

In this section:

CME 100. Vector Calculus for Engineers

CME 102. Ordinary Differential Equations for Engineers

CME 104. Linear Algebra and Partial Differential Equations for Engineers

CME 105. Introduction to Discrete Mathematics and Algorithms

CME 106. Introduction to Probability and Statistics for Engineers

CME 108. Introduction to Scientific Computing

Up one level:

Computational and Mathematical Engineering (CME) Courses

CME 100. Vector Calculus for Engineers

(Same as 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. GER:DB-Math

5 units, Aut (Khayms, V)

CME 102. Ordinary Differential Equations for Engineers

(Same as 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 non-linear 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. GER:DB-Math

5 units, Win (Darve, E)

CME 104. Linear Algebra and Partial Differential Equations for Engineers

(Same as ENGR 155B.) Linear algebra: matrix operations, systems of algebraic equations, Gaussian elimination, undertermined and overdetermined systems, coupled systems of ordinary differential equations, eigensystem analysis, normal modes. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications from various engineering fields. Prerequisite: CME 102/ENGR 155A. GER:DB-Math

5 units, Spr (Khayms, V)

CME 105. Introduction to Discrete Mathematics and Algorithms

Discrete mathematics and algorithms as used in modeling and problem solving technique emphasizing contemporary problems. Topics: introduction to set theory, logic, combinatorics, and graphs theory; formal proof techniques in induction, recursion, and contradiction; algorithms for sorting, shortest paths, minimum spanning trees, and bipartite matching. Applications to Internet advertising, viral marketing, routing, social networks and games of chance. Recommended: background in linear algebra/matrix theory.

3 units, Sum (Arcaute Aizpuru, E)

CME 106. Introduction to Probability and Statistics for Engineers

(Same as 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. GER:DB-Math

3-4 units, Win (Khayms, V), Sum (Khayms, V)

CME 108. Introduction to Scientific Computing

Numerical computation for mathematical, computational, and physical sciences and engineering: numerical solution of systems of algebraic equations, least squares, quadrature, minimization of a function, banded matrices, nonlinear equations, numerical solution of ordinary and partial differential equations; truncation error, numerical stability for time dependent problems, stiffness, boundary value problems. Prerequisites: CS106A or familiarity with MATLAB; MATH 51, 52, 53; inappropriate for students who have taken CME 102,104/ENGR 155A,B. GER:DB-EngrAppSci

3-4 units, Win (Lambers, J), Sum (Staff)

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