Welcome to the web site for
Boundary Value Problems and Partial Differential Equations,
6th edition
David L. Powers
 |
Chapter 0 -- Differential Equations |
| Chapter 1 --
Fourier Series and Integrals |
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| Chapter 2--
The Heat Equation |
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| Chapter 3 --
The Wave Equation |
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| Chapter 4 --
The Potential Equation |
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| Chapter 5 --
Higher Dimensions & Other Coordinates |
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| Chapter 6 --
Laplace Transform |
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| Chapter 7 --
Numerical Methods |
Chapter 0 -- Differential Equations
| Section 0.1 |
Example: Free vibrations (animated) Extra Exercises |
| Section 0.2 | Example: Forced vibrations
(animated) Extra Exercises |
| Section 0.3 | Special Exercise |
| Chapter Review |
Important Differential Equations Review Questions |
Chapter 1 -- Fourier Series and Integrals
| Section 1.1 |
Square
Wave (animated) |
| Section 1.3 | Sawtooth (animated) |
| Section 1.8 | Excel Spreadsheet for Example |
| Section 1.11 | Example
of sampling |
| Chapter review |
Useful Fourier Series Review Questions |
Chapter 2--Heat Equation
| Section 2.2 | Exercises on steady state Exercises on transient problems |
| Section 2.3 | Animated example Separation of variables-step by step |
| Section 2.4 | Animated example |
| Section 2.5 | Animated example Common Eigenvalue Problems--Exercise |
| Section 2.6 | Animated example |
| Section 2.10 | Animated example |
| Section 2.11 | Animated example Common Singular Eigenvalue Problems--Exercise |
| Chapter Review |
Review Questions |
| Project 2.11 |
Prof. J. Skufca's
Experiment |
Chapter 3--Wave Equation
| Section 3.2 |
Product Solutions-Animated Vibrating String Problem-Triangular Initial Condition |
| Section 3.3 | D'Alembert Solution of Example
Problem Traveling Wave--Effect of Boundary |
| Section 3.6 | Time-varying Boundary
Condition |
| Chapter Review |
Review Questions |
Chapter 4--Potential Equation
| Section 4.2 |
Solution of Dirichlet Problem-Color |
| Section 4.3 | Problem with Insulated
Boundaries--Color Solution of Poisson Equation--Color |
| Section 4.4 | Solution
on an Unbounded Region--Color |
| Section 4.5 | Solution on a Circular Disk-Color |
| Chapter Review | Review Questions |
Chapter 5--Higher Dimensions and Other Coordinates
| Section 5.3 |
Temperature in a
Rectangle--Animated |
| Section 5.5 | Bessel Functions |
| Section 5.6 | Bessel Eigenfunctions Bessel Eigenfunction Series--Animation of Convergence Heat Equation on a Cylinder--Animated |
| Section 5.7 | Standing Waves for a Circular
Membrane--Animated |
| Section 5.9 | Zonal Harmonics--Color |
| Section 5.10 | Temperature on a Spherical
Shell |
| Chapter Review |
Problems in Cylindrical
Coordinates--Exercise Singular Eigenvalue Problems 2 Review Questions |
Chapter 6--Laplace Transform
| Section 6.2 |
Useful Laplace Transforms |
| Chapter Review | Review Questions |
Chapter 7--Numerical Methods
| Chapter Review | Review Questions |
| Supplement |
Using a Spreadsheet for Numerical
Methods Answers to Supplement Exercises |