Partial Differential Equations,  Method and Applications
by Robert McOwen

Tentative Course Plan:

• 01/11:  Introduction and Motivation,   Examples of  PDEs;

No Assignment
 
• 01/13:     First order equations, Method of Characteristic;

Reading: 1.1  a-c
Homework: #4, #5  (p.23)
 
• 01/18:     Cauchy problem, quasi-linear equation;

Reading: 1.1 d-e;
Homework: #6, #7, #8* (p.23)
 
• 01/20:   Characteristics for 2nd order equations

Reading: 2.2 a-b
Homework:   (p. 48)
 
• 01/25:   Classification of 2nd order equations;

Reading: 2.2  a-b
Homework: # (p.48 )
 
• 01/27:  Convolution & Fundamental solutions;

Reading: 2.3  d
Homework: # (p. 71 )
 
• 02/01: The wave equation,  one-dimentional case;

Reading: 3.1  a:  Characteristic: D'Alembert solution;
                       c: Superposition: Separation of variables;

Homework: #  (p.82)
 

• 02/03  Superposition & Duhammel's principle;

Reading: 3.1  c-d
Homework: #  (p.82)
 
• 02/8:  Finite speed of propagation & Huygens' Principle;

Reading: 3.2 d-e
Homework: # (p.90)
 
• 02/10:  Midterm

 
• 02/15: Energy Methods

Reading: 3.3 a-b
Homework:  # (p. 94)
 
• 02/17: Dispersion & dissipation

Reading: 3.4 a-b
Homework: # (p.99)
 
• 02/22   Laplace equation

Reading: 4.1  a: Separation of Variables;
Homework: #  (p.107)
 
• 02/24:  Dirichlet & Neumann problems

Reading: 4.1 b: Boundary values and physics;
                      c: Green's identities and uniqueness;
Homework: # (p.107)
 
• 02/29:   Maximum Principles

Reading: 4.1 d
Homework: # (p.107)
 
• 03/02:  Potential Theory, Green functions;

Reading: 4.4 a-b
Homework: #
 
• 03/07:  Heat equations

Reading: 5.1 a: Superposition: Separation of variables;
Homework: #  (p.137)
 
• 03/09   The maximum principle

Reading:  5.1 b: Uniqueness;
                 5.2 a: Fourier Transform;
Homework: # (p.145)
 
• 03/14   The heat (Gaussian)  kernel

Reading: 5.2 b: Fourier Method;
                5.2 c-d: The fundamental solution
Homework:  # (p.145)
 
• 03/16: Review
 
• 03/ 20-24:   Final