Boundary Value Problems

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Welcome to An Introduction to Boundary Value Problems (Orthogonal Functions and Partial Differential Equations)

[edit] Course Introduction

This is a adaptive course. By this it is meant that the structure of the educational materials will be adapted based on feedback from users, both instructors and students. The course may be edited and modified by students, and as they do this they will manipulate the content and structures to meet their learning style. Possibly there will be several mainstream approaches. That is the hope. My job as the site manager is to keep the content bounded (Boundary Value Problems) and sort successful learning structures from ones that are not as successful (Probably based on usage.)

[edit] Course Description

Introduction to boundary value problems and partial differential equations. Emphasis on boundary values problems that arise from the

  • diffusion equation and
  • wave equation

in one, two and three dimensions.

Solutions to such boundary value problems will be discussed using

  • Fourier series,
  • Bessel functions
  • Legendre Polynomials
  • Numerical techniques

[edit] Prerequisites

Calculus - Functions, Derivatives and Integrals for single and multivariable functions.
Differential Equations - Ordinary Differential Equations - First and second order.

[edit] Lessons

Initially we will use a fixed sequence of lessons (like a regular text book) to cover the material and test you on your understanding. In the future the course should provide a tree structure whereby a student may tailor the presentation to their needs. I will need help in developing this flexible structure.

  1. Review: ODEs
  2. Introduction to BVPs
  3. Review of Partial Differentiation
  4. Vector Field and Flow
  5. Main PDE's to be addressed in course
  6. 1-D Heat Equation \scriptstyle u_{xx} =\frac{1}{k}u_t
  7. 1-D Wave equation \scriptstyle u_{xx}=\frac{1}{c^2}u_{tt}
  8. 2-D Potential Equation \scriptstyle \nabla^2 u =0
  9. 2-D Heat \scriptstyle \nabla^2u = u_t
  10. 2-D Wave \scriptstyle \nabla^2u = u_{tt}
  11. 3-D Spherical Cylindrical and Spherical
  12. Numerical Methods

[edit] References

David L. Powers, 5th edition. Boundary Value Problems and Partial Differential Equations. Elsevier Academic Press,ISBN 13: 978-0-12-563738

Ruel V. Churchill, 2nd Edition, Fourier Series and Boundary Value Problems, McGraw Hill, ISBN 07-010841-2

David Betounes, Partial Differential Equations for Computational Science: with Maple and Vector Analysis, Springer-Verlag, ISBN 0-387-98300-7

[edit] Other Wikiprojects

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