An Introduction to Partial Differential Equations with MATLAB, Second Edition

✍ Scribed by Coleman, Matthew P

• Publisher: CRC Press
• Year: 2013
• Tongue: English
• Leaves: 670
• Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science
• Edition: 2nd ed
• Category: Library

✦ Synopsis

Introduction What are Partial Differential Equations? PDEs We Can Already Solve Initial and Boundary Conditions Linear PDEs-Definitions Linear PDEs-The Principle of Superposition Separation of Variables for Linear, Homogeneous PDEs Eigenvalue Problems The Big Three PDEsSecond-Order, Linear, Homogeneous PDEs with Constant CoefficientsThe Heat Equation and Diffusion The Wave Equation and the Vibrating String Initial and Boundary Conditions for the Heat and Wave EquationsLaplace's Equation-The Potential Equation Using Separation of Variables to Solve the Big Three PDEs Fourier Series Introduction. Read more...

Abstract: Introduction What are Partial Differential Equations? PDEs We Can Already Solve Initial and Boundary Conditions Linear PDEs-Definitions Linear PDEs-The Principle of Superposition Separation of Variables for Linear, Homogeneous PDEs Eigenvalue Problems The Big Three PDEsSecond-Order, Linear, Homogeneous PDEs with Constant CoefficientsThe Heat Equation and Diffusion The Wave Equation and the Vibrating String Initial and Boundary Conditions for the Heat and Wave EquationsLaplace's Equation-The Potential Equation Using Separation of Variables to Solve the Big Three PDEs Fourier Series Introduction

✦ Table of Contents

Content: Front Cover
Series Page
Dedication
Contents
Preface
Prelude to Chapter 1
Chapter 1: Introduction
Prelude to Chapter 2
Chapter 2: The Big Three PDEs
Prelude to Chapter 3
Chapter 3: Fourier Series
Prelude to Chapter 4
Chapter 4: Solving the Big Three PDEs on Finite Domains
Prelude to Chapter 5
Chapter 5: Characteristics
Prelude to Chapter 6
Chapter 6: Integral Transforms
Prelude to Chapter 7
Chapter 7: Special Functions and Orthogonal Polynomials
Prelude to Chapter 8
Chapter 8: Sturm-Liouville Theory and Generalized Fourier Series
Prelude to Chapter 9 Chapter 9: PDEs in Higher DimensionsPrelude to Chapter 10
Chapter 10: Nonhomogeneous Problems and Green's Functions
Prelude to Chapter 11
Chapter 11: Numerical Methods
Appendix A: Uniform Convergence
Differentiation and Integration of Fourier Series
Appendix B: Other Important Theorems
Appendix C: Existence and Uniqueness Theorems
Appendix D: A Menagerie of PDEs
Appendix E: MATLAB Code for Figures and Exercises
Appendix F: Answers to Selected Exercises
References
Back Cover

✦ Subjects

Differential equations, Partial -- Computer-assisted instruction.