Math 211: Applied Partial Differential Equations and Complex Variables (Fall 2008)

Mathematical methods for solving problems in linear partial differential equations: linear operators and adjoint problems, eigenfunction expansions, Fourier series, Sturm-Liouville problems, orthogonal functions and generalized Fourier series. Solutions via Green's functions. Complex variables for contour integrals and solutions via integral representations. Integral transforms: Fourier and Laplace transforms.

Textbook: Applied Partial Differential Equations (4th ed), by Richard Haberman, Prentice Hall (2003)

Prerequisites

Schedule

MWF 3:05-3:55 PM, Room 259 Physics Building

Instructor

Office hours

Problem Sheets

• Problem sheet 1
• Problem sheet 2
• Problem sheet 3
• Problem sheet 4
• Problem sheet 5
• Problem sheet 5a
• Problem sheet 6

Course materials

• Course Outline
• Review sheets
  • Math Basics Summary
  • Techniques of integation
  • 1st order ODE and Complex numbers
  • Undetermined Coefficients for Inhomogeneous linear const. coeff. eqns
  • Lin. Alg. and Eigenvector expansions
  • Trig. Fourier series
  • Solving Inhomogeneous BVPs
  • Sturm-Lioville problems
  • Fredholm Alternative Theorem
  • Variation of Parameters (2nd order)
  • Variation of Parameters (II) (nth order)
  • Review of basic Separation of Variables
  • Separation of Variables for Inhom. PDE BVP
  • Separation of Variables for Inhom. PDE BVP (v2.1)
• Test 1: Monday Sep 29, 2008, Solution of inhomogeneous ODE BVP via eigenfunction expansions. Fourier series. Adjoint eigenvalue problems. Sturm-Liouville problems. Integral equations: eigenvalue and inhomogeneous problems. The Fredholm alternative theorem for existence/uniqueness/non-existence.
  Optional review session, Sunday Sep 28, 2:00-4:00pm, Room 259 Physics.
  Results (B-..A+): 40s: 3, 50s: 1, 60s: 2, 70s: 1, 80s: 1