Applied Mathematics Logan

May 20, 2020


Applied Mathematics, 4th

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
Source: www.math.ucdavis.edu
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