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The CSE core is required for all CSE students in M.S. and Ph.D. programs.
It consists of six one-quarter courses which are distributed over the
three areas of numerical methods, parallel computing and applied mathematics.
Numerical Methods:
A broad-based introductory graduate-level numerical analysis course
(CHE230D/MEE244D) is available for students who do not have the background
to begin the core CSE graduate sequence in numerical methods immediately.
CSE students must take at least three of the following courses. The courses
need not be taken in sequence, although it may be advantageous to do so.
These courses arecross-listed with Math, CS, ECE and CHE.
CS/MEE/ECE/MATH 210 Sequence: Numerical Methods in Computational Science
and Engineering
Prerequisite: Consent of instructor. Students should be proficient
in basic numerical methods, linear algebra, mathematically rigorous proofs,
and some programming language.
210A Matrix Analysis and Computation
Graduate level-matrix theory with introduction to matrix computations.
SVD's, pseudoinverses, variational characterization of eigenvalues, perturbation
theory, direct and iterative methods for matrix computations.
210B Numerical Simulation
Linear multistep methods and Runge-Kutta methods for ordinary differential
equations: stability, order and convergence. Stiffness. Differential algebraic
equations. Numerical solution of boundary value problems.
210C Numerical Solution of Partial Differential Equations
Finite Difference Methods
Finite difference methods for hyperbolic, parabolic and elliptic PDEs,
with application to problems in science and engineering. Convergence,
consistency, order and stability of finite difference methods. Dissipation
and dispersion. Finite volume methods. Software design and adaptivity.
210D Numerical Solution of Partial Differential Equations Finite Element
Methods
Weighted residual and finite element methods for the solution of hyperbolic,
parabolic and elliptic partial differential equations, with application
to problems in science and engineering. Error estimates. Standard and
discontinuous Galerkin methods.
Parallel Computing:
CSE students must take of the following: CS 240A or CS 240B. Note that
CS 240B does not require CS 240A as a prerequisite.
240A. High-Performance Parallel Systems and Languages
Prerequisites: Computer Science 154 and 160.
Overview of parallel architectures and communication; parallel programming
paradigms; performance models of parallel computation; parallel algorithms
and applications; systems and compilers for parallel languages.
240B. Parallel Computing and Program Parallelization
Prerequisites: Computer Science 130A and 160.
Parallel programming; representation of parallelism, program dependence
analysis, loop transformation; program and data partitioning, locality
optimization; task scheduling and load balancing; parallelizing compilers
and run-time support.
Applied Mathematics:
CSE students must take one of the following sequences:
CHE 230A,B / MEE 244A,B Advanced Theoretical Methods in Engineering
CHE 230A. Advanced Theoretical Methods in Engineering
Prerequisite: consent of instructor.
Same course as ME 244A.
Methods of solution of partial differential equations and boundary value
problems. Linear vector and function spaces, generalized Fourier analysis,
Sturm-Liouville theory, calculus of variations, and conformal mapping
techniques.
230B. Advanced Theoretical Methods in Engineering
Prerequisites: Chemical Engineering 230A and consent of instructor.
Same course as ME 244B.
Advanced mathematical methods for engineers and scientists. Complex analysis,
integral equations and Green's functions. Asymptotic analysis of integrals
and sums. Boundary layer methods and WKB theory.
Math 214A, B Ordinary Differential Equations, Chaotic Dynamics and Bifurcation
Theory
214A. Ordinary Differential Equations
Prerequisite: Not open to mathematics majors.
Existence, uniqueness, and stability; the geometry of phase space; linear
systems and hyperbolicity; maps and diffeomorphisms.
214B. Chaotic Dynamics and Bifurcation Theory
Prerequisite: Not open to mathematics majors.
Hyperbolic structure and chaos; bifurcation theory; and the Feigenbaum
and Ruelle-Takens cascades to strange attractors.
Math 215A, B Partial Differential Equations, Fourier Transform and Numerical
Methods
215A. Partial Differential Equations
Prerequisite: Not open to mathematics majors.
Wave, heat, and potential equations.
215B. Fourier Series and Numerical Methods
Prerequisite: Not open to mathematics majors.
Fourier series; generalized functions; and numerical methods.
Advanced courses may be substituted, with approval, as follows: Math
243 instead of Math 214, and Math 246 instead of Math 215.
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