Math336 Second Semester 2007

PARTIAL DIFFERENTIAL EQUATIONS

Department of Mathematics

Macquarie University

Study Guide

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Assignments

1. Assignment 1
2. Assignment 2
3. Assignment 3
4. Assignment 4
5. Assignment 5
   

Solutions

• Solutions to Part C of assignment 1.
• Solutions to Part J of assignment 1.
• Solutions to Part C of assignment 2.
• Solutions to Part J of assignment 3.
  
• Solutions to Part C of assignment 3.
• Solutions to Part C of assignment 4.
• Solutions to Part C of assignment 5.

Notes

Bon Clarke's PDE lecture notes.

Table of Contents

1. Introduction

2. First order partial differential equations in two variables

3. First integrals and general solutions

4. The Cauchy Problem for first order quasi–linear equations

5. Second order partial differential equations in two variables

6. The Cauchy problem for second order hyperbolic equations

7. The wave equation in one space variable

8. The Cauchy problem for the wave equation

9. Second order linear equations in n variables

10. The Cauchy Problem for linear equations in R^n

11. Mixed problems for the wave equation

12. The wave equation in higher space dimensions

13. Huyghens principle

14. The non- homogeneous wave equation

15. Well posed problems

16. Boundary value problems for elliptic partial differential equations

17. Adjoints and Green's identity

18. Fundamental solutions, Greens functions and the solution of Poissons equation

19. The Dirichlet problem for a circle and Fourier series

20. The Dirichlet problem for a rectangle and Fourier series

21. Mean value properties and extremum principles for harmonic functions

22. The Heat equation

23. The Cauchy problem for the heat equation