Math 211: Applied Partial Differential Equations and Complex Variables (Fall 2009)

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 set 1
• Problem set 2
• Problem set 3
• Problem set 4
• Problem set 5
• Problem set 6
• Problem set 7
• Problem set 8
• Problem set 9
• Problem set i

Course materials

• Course outline/syllabus

• Review sheets
  • Math Basics Summary
  • 1st order ODE and complex numbers
  • Integration Techniques
  • Trigonometric Fourier Series
  • Undetermined Coefficients
  • Vector Calculus
  • Infinite Series
• Lecture notes
  • Lecture 1: Linear algebra review
  • Lecture 2: Key elements of Linear algebra (typo fixed: eigenvalues of adjoint, final version 9/1/09: 8:22pm)
    • Note on "adjoint eigenvalues"
  • Lecture 3: Key elements of L2 inner products
  • Lecture 4: Properties of Fourier Series
  • Lecture 6: Eigen-expansions for solving inhomogeneous ODE BVP
  • Lecture 7: Sturm-Liouville theory
  • Lecture 8: The Fredholm Alternative Theorem
  • Lecture 10: Fredholm Integral Equations
  • Lecture 11a: Motivation for Variation of Parameters
  • Lecture 11: Variation of Parameters for 2nd order ODE BVP
  • Lecture 12: The Heaviside Step Fcn and Dirac Delta Fcn
  • Lecture 14: Green's functions -- further notes
  • Lecture 14: Intro to Separation of Variables for PDEs
  • Lecture 15: Separation of Variables for inhomogeneous PDEs (1.1 sign error fixed)
  • Lecture 24: Basics of Bessel functions
  • Lecture 26: Laplacian in polar coords + Classic ODE Eigenproblems from separation of variables
  • Lecture 28: Intro to Complex Variables
  • Lecture 28: Branch cuts and Multivalued functions
    • Branch cut on Wikipedia
    • Branch cut on Mathworld
  • Lecture 30: Review of line integrals and intro to contour integrals
  • Lecture 32: The complex Fourier series

• Test 1: Weds Sep 30, 2009, 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 27, 2009, 3:00-5:00pm, Room 259 Physics. No new material will be covered. Questions will be answered and examples worked out. Feel free to come to all/any-part-of the review sesssion block time.
  • Math 211 Fall 2008 Test 1
  • Math 211 Fall 2009 Test 1
  • High 88, Low 30, Avg 67
• Test 2: Mon Nov 9, 3:05(OASAEGH)-4:00pm. Green's functions for ODE BVPs (9.3), separation of variables and eigenfunction expansions for PDEs (2.3, 2.4, 8.4, 8.6), multi-dimensional problems (2.5, 7.2--7.7), the material covered on Homeworks 5-8.
  Optional review session: Friday, Nov 6, 4:05-6:00 pm, Room 259 Physics. No new material will be covered. Questions will be answered and examples worked out. Feel free to come to all/any-part-of the review sesssion block time.
  • Math 211 Fall 2008 Test 2
  • High ??, Low ??, Avg??