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# An Introduction to Partial Differential Equations with MATLAB by Matthew P. Coleman (Hardback, 2013)

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## About this product

### Key Features

- Author(s)Matthew P. Coleman
- PublisherTaylor & Francis Ltd
- Date of Publication26/07/2013
- Language(s)English
- FormatHardback
- ISBN-101439898464
- ISBN-139781439898468
- GenreScience & Mathematics: Textbooks & Study Guides
- Series TitleChapman & Hall/CRC Applied Mathematics & Nonlinear Science
- Series Part/Volume Number27

### Publication Data

- Country of PublicationUnited States
- ImprintChapman & Hall/CRC
- Content Note116 black & white illustrations, 9 black & white tables

### Dimensions

- Weight1065 g
- Width156 mm
- Height235 mm
- Spine36 mm
- Pagination683

### Editorial Details

- Format DetailsUnsewn / adhesive bound
- Edition Statement2nd Revised edition

### Description

- Table Of ContentsIntroduction 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 PDEs Second-Order, Linear, Homogeneous PDEs with Constant Coefficients The Heat Equation and Diffusion The Wave Equation and the Vibrating String Initial and Boundary Conditions for the Heat and Wave Equations Laplace's Equation-The Potential Equation Using Separation of Variables to Solve the Big Three PDEs Fourier Series Introduction Properties of Sine and Cosine The Fourier Series The Fourier Series, Continued The Fourier Series-Proof of Pointwise Convergence Fourier Sine and Cosine Series Completeness Solving the Big Three PDEs Solving the Homogeneous Heat Equation for a Finite Rod Solving the Homogeneous Wave Equation for a Finite String Solving the Homogeneous Laplace's Equation on a Rectangular Domain Nonhomogeneous Problems Characteristics First-Order PDEs with Constant Coefficients First-Order PDEs with Variable Coefficients The Infinite String Characteristics for Semi-Infinite and Finite String Problems General Second-Order Linear PDEs and Characteristics Integral Transforms The Laplace Transform for PDEs Fourier Sine and Cosine Transforms The Fourier Transform The Infinite and Semi-Infinite Heat Equations Distributions, the Dirac Delta Function and Generalized Fourier Transforms Proof of the Fourier Integral Formula Bessel Functions and Orthogonal Polynomials The Special Functions and Their Differential Equations Ordinary Points and Power Series Solutions; Chebyshev, Hermite and Legendre Polynomials The Method of Frobenius; Laguerre Polynomials Interlude: The Gamma Function Bessel Functions Recap: A List of Properties of Bessel Functions and Orthogonal Polynomials Sturm-Liouville Theory and Generalized Fourier Series Sturm-Liouville Problems Regular and Periodic Sturm-Liouville Problems Singular Sturm-Liouville Problems; Self-Adjoint Problems The Mean-Square or L2 Norm and Convergence in the Mean Generalized Fourier Series; Parseval's Equality and Completeness PDEs in Higher Dimensions PDEs in Higher Dimensions: Examples and Derivations The Heat and Wave Equations on a Rectangle; Multiple Fourier Series Laplace's Equation in Polar Coordinates: Poisson's Integral Formula The Wave and Heat Equations in Polar Coordinates Problems in Spherical Coordinates The Infinite Wave Equation and Multiple Fourier Transforms Postlude: Eigenvalues and Eigenfunctions of the Laplace Operator; Green's Identities for the Laplacian Nonhomogeneous Problems and Green's Functions Green's Functions for ODEs Green's Function and the Dirac Delta Function Green's Functions for Elliptic PDEs (I): Poisson's Equation in Two Dimensions Green's Functions for Elliptic PDEs (II): Poisson's Equation in Three Dimensions; the Helmholtz Equation Green's Functions for Equations of Evolution Numerical Methods Finite Difference Approximations for ODEs Finite Difference Approximations for PDEs Spectral Methods and the Finite Element Method 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 Index

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