Computational and Applied Mathematics
continued
Graduate Courses
The faculty has approval to offer the following courses in the academic years 20032004 and 20042005; however, not all courses are taught each semester or summer session. Students should consult the Course Schedule to determine which courses and topics will be offered during a particular semester or summer session. The Course Schedule may also reflect changes made to the course inventory after the publication of this catalog.
Unless otherwise stated below, each course meets for three lecture hours a week for one semester.
Computational and Applied Mathematics: CAM
380N. Algorithms for Parallel and Distributed Computation.
Same as Electrical Engineering 380N (Topic 8: Algorithms for Parallel and Distributed Computation). Prerequisite: Graduate standing, and Electrical Engineering 380K or consent of the graduate adviser.
381C. Computational Physics.
Same as Physics 381C. Dynamical and statical descriptions and solutions of manybody, nonlinear physical systems by computation. Theory of computation and applications to various branches of physics. Prerequisite: Graduate standing; and Physics 385K and 387K, or consent of instructor.
381D. Complex Analysis.
Same as Mathematics 381D. Introduction to complex analysis. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.
381M. Methods of Mathematical Physics.
Same as Physics 381M. Theory of analytic functions; linear algebra and vector spaces; orthogonal functions; ordinary differential equations; partial differential equations; Green's functions; complex variables. Prerequisite: Graduate standing.
381N. Methods of Mathematical Physics.
Same as Physics 381N. Continuation of Computational and Applied Mathematics 381M. Topology, functional analysis, approximation methods, group theory, differential manifolds. Prerequisite: Graduate standing, and Computational and Applied Mathematics 381M or Physics 381M.
381R. Real Analysis.
Same as Mathematics 381C. Measure and integration over abstract spaces; Lebesgue's theory of integration and differentiation on the real line. Prerequisite: Graduate standing and consent of instructor or the graduate adviser.
381S. Functional Analysis.
Same as Mathematics 381E. Introduction to functional analysis. Prerequisite: Graduate standing, consent of instructor, and Computational and Applied Mathematics 381R or Mathematics 381C.
382L. Numerical Methods in Petroleum and Geosystems Engineering.
Same as Petroleum and Geosystems Engineering 382L. The use of numerical methods and computers in the solution of petroleum and geosystems engineering problems. Prerequisite: Graduate standing.
383. Special Topics in Petroleum and Geosystems Engineering.
Recent literature on petroleum production practice and petroleum and geosystems engineering problems. May be repeated for credit when the topics vary. Prerequisite: Graduate standing in computational and applied mathematics, engineering, or geological sciences. Students seeking to enroll in any seminar must present technical prerequisites satisfactory to the instructor.
Topic 1: Numerical Solution of TimeDependent Problems. Same as Petroleum and Geosystems Engineering 383 (Topic 10: Numerical Solution of TimeDependent Problems).
Topic 2: Topics in Computational Methods. Same as Petroleum and Geosystems Engineering 383 (Topic 16: Topics in Computational Methods).
383C. Numerical Analysis: Linear Algebra.
Same as Computer Sciences 383C and Mathematics 383E. Survey of numerical methods in linear algebra: floatingpoint computation, solution of linear equations, least squares problems, algebraic eigenvalue problems. Prerequisite: Graduate standing, either consent of instructor or Mathematics 341 (or 311) or 340L, and either Mathematics 368K or Computer Sciences 367.
383D. Numerical Analysis: Interpolation, Approximation, Quadrature, and Differential Equations.
Same as Computer Sciences 383D and Mathematics 383F. Survey of numerical methods for interpolation, functional approximation, integration, and solution of differential equations. Prerequisite: Graduate standing; either consent of instructor or Mathematics 427K and 365C; and Computational and Applied Mathematics 383C, Computer Sciences 383C, or Mathematics 383E.
384G. Computer Graphics.
Same as Computer Sciences 384G. Advanced material in computer graphics, including indepth treatments of techniques for realistic image synthesis, advanced geometric modeling methods, animation and dynamic simulation, scientific visualization, and highperformance graphics architectures. Prerequisite: Graduate standing; and Computer Sciences 354 or another introductory course in computer graphics, or equivalent background and consent of instructor.
384K. Theory of Probability.
Same as Mathematics 385C. Prerequisite: Graduate standing and consent of instructor.
384L. Theory of Probability.
Same as Mathematics 385D. Prerequisite: Graduate standing, consent of instructor, and Computational and Applied Mathematics 384K or Mathematics 385C.
384R. Mathematical Statistics.
Same as Mathematics 384C. General theory of mathematical statistics. Hypothesis testing, estimation, decision theory. Prerequisite: Graduate standing, and Mathematics 378K or consent of instructor or the graduate adviser in mathematical statistics.
384S. Mathematical Statistics.
Same as Mathematics 384D. Continuation of Computational and Applied Mathematics 384R. Prerequisite: Graduate standing, consent of instructor, and Computational and Applied Mathematics 384R or Mathematics 384C.
385C. Methods of Applied Mathematics.
Same as Mathematics 383C. Topics include basic normed linear space theory; fixedpoint theorems and applications to differential and integral equations; Hilbert spaces and the spectral theorem; applications to SturmLiouville problems; approximation and computational methods such as the Galerkin, RayleighRitz, and Newton procedures. Prerequisite: Graduate standing.
385D. Methods of Applied Mathematics.
Same as Mathematics 383D. Topics include distributions, fundamental solutions of partial differential equations, the Schwartz space and tempered distributions, Fourier transform, Plancherel theorem, Green's functions, Sobolev spaces, weak solutions, differential calculus in normed spaces, implicit function theorems, applications to nonlinear equations, smooth variational problems, applications to classical mechanics, constrained variational problems. Prerequisite: Graduate standing and Computational and Applied Mathematics 385C.
386K. Numerical Treatment of Differential Equations.
Same as Computer Sciences 386K and Mathematics 383G. The analysis of numerical methods for solving ordinary and partial differential equations. Prerequisite: Graduate standing; and Computational and Applied Mathematics 383D, Computer Sciences 383D, Mathematics 368K, 383F, or consent of instructor.
386M. Functional Analysis in Theoretical Mechanics.
An introduction to modern concepts in functional analysis and linear operator theory, with emphasis on their application to problems in theoretical mechanics; topological and metric spaces, norm linear spaces, theory of linear operators on Hilbert spaces, applications to boundary value problems in elasticity and dynamical systems. Prerequisite: Graduate standing, Engineering Mechanics 386L, and Mathematics 365C.
386N. Qualitative Methods in Nonlinear Mechanics.
A study of methods for assessing the qualitative behavior of solutions to equations governing nonlinear continuum mechanics. Prerequisite: Graduate standing, and Computational and Applied Mathematics 386M or Engineering Mechanics 386M.
391. Introductory Dynamical Systems.
Prerequisite: Graduate standing.
391C. Topics in Analysis.
Same as Mathematics 391C. Recent topics have included measure and integration, real variables; complex analysis, functional analysis, ordinary differential equations, partial differential equations, integral transforms, operator theory, approximation theory, abstract harmonic analysis. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
393C. Topics in Applied Mathematics.
Same as Mathematics 393C. Recent topics have included quantum mechanics, statistical physics, ergodic theory, group representations, statistical mechanics, quantum field theory, introductory partial differential equations, monotone operators and partial differential equations, Hilbert space methods for partial differential equations, Hamiltonian dynamics, nonlinear functional analysis, Euler and NavierStokes equations, microlocal calculus and spectral asymptotics, calculus of variations. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
393D. Topics in Numerical Analysis.
Same as Mathematics 393D. Recent topics have included numerical methods in ordinary differential equations, numerical methods in partial differential equations, computational problems in linear algebra, numerical solution of systems of equations, numerical methods in functional approximation, numerical integration. May be repeated for credit when the topics vary. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
393M. Numerical Solution of Elliptic Partial Differential Equations.
Same as Computer Sciences 393N and Mathematics 393N. The numerical solution of large systems of linear algebraic equations arising in the solution of elliptic partial differential equations by discretization methods. Prerequisite: Graduate standing; and Computational and Applied Mathematics 386K, Computer Sciences 386K, Mathematics 383G, or consent of instructor.
393N. Numerical Methods for Flow and Transport Problems.
Approximate solution methods for flow and transport problems in engineering and applied science. Finite element, finite difference, and residual methods for linear and nonlinear problems. Prerequisite: Graduate standing.
394C. Topics in Probability and Statistics.
Same as Mathematics 394C. Recent topics have included nonparametric statistics and advanced probability. May be repeated for credit when the topics vary. Some topics are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing and consent of instructor.
394F. Finite Element Methods.
Same as Aerospace Engineering 384P (Topic 4: Finite Element Methods) and Engineering Mechanics 394F. Derivation and implementation of the finite element method; basic coding techniques; application to problems of stress and diffusion. Prerequisite: Graduate standing and consent of instructor.
394G. Computational Techniques in Finite Elements.
Organization and data management in finite element codes; element models and calculations; equation solving; preprocessing and postprocessing. Prerequisite: Graduate standing, and Aerospace Engineering 384P (Topic 4: Finite Element Methods), Computational and Applied Mathematics 394F, or Engineering Mechanics 394F.
394H. Advanced Theory of Finite Element Methods.
Contemporary topics in the theory and application of finite element methods. Prerequisite: Graduate standing, Computational and Applied Mathematics 394F or Engineering Mechanics 394F, and Engineering Mechanics 386L or the equivalent.
395T. Topics in Computer Sciences.
May be repeated for credit when the topics vary. Prerequisite: Graduate standing.
Topic 1: Parallel Computations. Same as Computer Sciences 395T (Topic 1: Parallel Computations).
397. Topics in Computational and Applied Mathematics.
Conference course. May be repeated for credit. Some sections are offered on the credit/no credit basis only; these are identified in the Course Schedule. Prerequisite: Graduate standing.
698. Thesis.
The equivalent of three lecture hours a week for two semesters. Offered on the credit/no credit basis only. Prerequisite: For 698A, graduate standing in computational and applied mathematics and consent of the graduate adviser; for 698B, Computational and Applied Mathematics 698A.
398R. Master's Report.
Preparation of a report to fulfill the requirement for the master's degree under the report option. Independent study. Offered on the credit/no credit basis only. Prerequisite: Graduate standing in computational and applied mathematics and consent of the graduate adviser.
399R, 699R, 999R. Dissertation.
Independent study. Offered on the credit/no credit basis only. Prerequisite: Admission to candidacy for the doctoral degree.
399W, 699W, 999W. Dissertation.
Independent study. Offered on the credit/no credit basis only. Prerequisite: Computational and Applied Mathematics 399R, 699R, or 999R.
