MAT 207B, Winter Quarter, 2012

**Lectures:** MWF 10:0010:50 a.m., Wellman 209

**Office hours:**

MWF 2:303:30 p.m.

**Text:** *Applied Mathematics*, David Logan, 3rd Ed.

### Syllabus

Here is a tentative outline of the topic we'll cover:

- Sturm-Liouville problems, Green's functions and integral equations for ODEs
- Calculus of variations and Euler-Lagrange equations for ODEs
- Laplace equation, potential theory, and Green's functions for PDEs
- The heat equation and diffusion
- The wave equation
- Some nonlinear PDEs

This material is covered in the following Chapters of Logan:

- Chapter 3. Calculus of Variations
- Chapter 4. Eigenvalue Problems, Integral Equations, and Green's Functions
- Chapter 6. Partial Differential Equations
- Chapter 7. Wave Phenomena

### Stakgold and Holst: Green's Functions and Boundary Value Problems

This book is a good resource for further information about Green's functions, BVPs, and related topics. It's available online from Wiley, free to UC addresses at:

### Notes on applied **mathematics**

Lecture notes which include further discussion of some of the topics covered in this class are here:

### Final exam topics

- 1. Sturm-Liouville problems
- 2. Eigenfunction expansions
- 3. Green's functions
- 4. Variational principles
- 5. Integral equations
- 6. Laplace's equation

Source: www.math.ucdavis.edu

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