1. Syllabus

Course description

Partial differential equations (elliptic, parabolic, hyperbolic), exact solution methods, approximate analytical solution methods.

Course objective

Develop analytical methods to solve partial differential equations with applications in many areas of engineering (solids, fluids, electromagnetics, heat).

Topics

Below is a list of tentative topics. Depth always takes precedence over breadth. So it is likely that not all of the tentative topics listed below would be covered, so a subset would be covered to some greater depth.

Overview on analytical methods of solving PDEs, caveat for PDEs, Nonlinear, quasilinear, linear PDEs. Classification of second-order PDEs.

Classical orthogonal polynomials and their applications: Legendre, Hermite, Laguerre, Jacobi, Chebyshev, Bessel. Recurrence relations, continued fraction, orthogonality, Favard theorem.

Solution of PDEs, deterministic, stochastic (generalized polynomial chaos).

Dimensional analysis, industry application of analytical methods of PDEs.

Gaussian quadratures (important application of orthogonal polynomials), principle, analysis, convergence.

Approximate analytical methods: Multiple scales, eigenvalue expansion, singularity computation (fracture mechanics, fluid mechanics, electromagnetics).

Some nonlinear PDEs and their solutions.

Contour integrals

Textbooks

Below are some recommended textbooks.

Differential Equations: Linear, Nonlinear, Ordinary, Partial by A. C. King, J. Billingham and S. R. Otto (Paperback - Jun 30, 2003)

Fourier Analysis by T. W. Korner (Paperback - Nov 24, 1989)

Handbook of Differential Equations, Third Edition by Daniel Zwillinger (Hardcover - Nov 3, 1997)

Partial Differential Equations and Boundary-value Problems With Applications by Mark A. Pinsky (Hardcover - Aug 19, 2011)

Numerical Methods for Stochastic Computations: A Spectral Method Approach by Dongbin Xiu (Hardcover - Jul 1, 2010)

Grade determination

Project reports and term paper.

Home page: Loc Vu-Quoc

E-mail: vu-quoc AT ufl.eduMAE Department