Applied Mathematics Logan

MAT 207B, Winter Quarter, 2012

Lectures: MWF 10:00–10:50 a.m., Wellman 209

Office hours:

MWF 2:30–3:30 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