printer friendly pageCME 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
| Units: 3
Instructors:
Vasy, A. (PI)
CME 304: Numerical Optimization (MS&E 315)
Solution of nonlinear equations; unconstrained optimization; linear programming; quadratic programming; global optimization; general linearly and nonlinearly constrained optimization. Theory and algorithms to solve these problems. Prerequisite: background in analysis and numerical linear algebra.
Terms: Win
| Units: 3
Instructors:
Murray, W. (PI)
CME 305: Discrete Mathematics and Algorithms (MS&E 316)
Topics: enumeration such as Cayley's theorem and Prufer codes, SDR, flows and cuts (deterministic and randomized algorithms), probabilistic methods and random graphs, asymptotics (NP-hardness and approximation algorithms). Topics illustrated with EE, CS, and bioinformatics applications. Prerequisites:
MATH 51 or 103 or equivalents.
Terms: Win
| Units: 3
Instructors:
Saberi, A. (PI)
CME 306: Numerical Solution of Partial Differential Equations
Hyperbolic partial differential equations: stability, convergence and qualitative properties; nonlinear hyperbolic equations and systems; combined solution methods from elliptic, parabolic, and hyperbolic problems. Examples include: Burger's equation, Euler equations for compressible flow, Navier-Stokes equations for incompressible flow. Prerequisites:
MATH 220A or
CME 302.
Terms: Spr
| Units: 3
Instructors:
Garapon, P. (PI)
CME 308: Stochastic Methods in Engineering (MATH 228)
Review of basic probability; Monte Carlo simulation; state space models and time series; parameter estimation, prediction, and filtering; Markov chains and processes; stochastic control; and stochastic differential equations. Examples from various engineering disciplines. Prerequisites: exposure to probability; background in real variables and analysis.
Terms: Spr
| Units: 3
Instructors:
Papanicolaou, G. (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.
CME 334: Advanced Methods in Numerical Optimization (MS&E 312)
Topics include interior-point methods, relaxation methods for nonlinear discrete optimization, sequential quadratic programming methods, optimal control and decomposition methods. Topic chosen in first class; different topics for individuals or groups possible. Individual or team projects. May be repeated for credit.
Last offered: Autumn 2008
| Repeatable
for credit
CME 337: Information Networks (MS&E 337)
Network structure of the Internet and the web. Modeling, scale-free graphs, small-world phenomenon. Algorithmic implications in searching and inter-domain routing; the effect of structure on performance. Game theoretic issues, routing games, and network creation games. Security issues, vulnerability, and robustness. Prerequisite: basic probability and graph theory.
Terms: Spr
| Units: 3
Instructors:
Saberi, A. (PI)
CME 338: Large-Scale Numerical Optimization (MS&E 318)
The main algorithms and software for constrained optimization emphasizing the sparse-matrix methods needed for their implementation. Iterative methods for linear equations and least squares. Interior methods. The simplex method. Factorization and updates. The reduced-gradient, augmented Lagrangian, and SQP methods. Recommended: MS&E 310, 311, 312, 314, or 315;
CME 108 or 302.
Terms: Spr
| Units: 3
Instructors:
Saunders, M. (PI)
CME 356: Engineering Functional Analysis and Finite Elements (ME 412)
Concepts in functional analysis to understand models and methods used in simulation and design. Topology, measure, and integration theory to introduce Sobolev spaces. Convergence analysis of finite elements for the generalized Poisson problem. Extensions to convection-diffusion-reaction equations and elasticity. Upwinding. Mixed methods and LBB conditions. Analysis of nonlinear and evolution problems. Prerequisites: 335A,B,
CME 200,
CME 204, or consent of instructor. Recommended: 333,
MATH 171.
Terms: Win
| Units: 3
Instructors:
Lew, A. (PI)
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