Research Catalog

Title

An introduction to partial differential equations with MATLAB / Matthew P. Coleman.

Author

Coleman, Matthew P.

Publication

Boca Raton, Fla. : CRC Press, ©2005.

Items in the Library & Off-site

Details

Description

671 pages o : illustrations; 25 cm.

Summary

"An Introduction to Partial Differential Equations with MATLAB exposes the basic ideas critical to the study of PDEs - characteristics, integral transforms, Green's functions, and most importantly, Fourier series and related topics. The author uses MATLAB software for solving exercises and generating tables and figures, and includes examples of many important PDEs and their applications."--Jacket.

Series Statement

Chapman & Hall/CRC applied mathematics and nonlinear science series

Uniform Title

Chapman & Hall/CRC applied mathematics and nonlinear science series.

Subject

• MATLAB
• Differential equations, Partial > Computer-assisted instruction
• Partiële differentiaalvergelijkingen

Bibliography (note)

• Includes bibliographical references and index.

Contents

1.1 What are Partial Differential Equations? 3 -- 1.2 PDEs We Can Already Solve 6 -- 1.3 Initial and Boundary Conditions 10 -- 1.4 Linear PDEs-Definitions 12 -- 1.5 Linear PDEs-The Principle of Superposition 16 -- 1.6 Separation of Variables for Linear, Homogeneous PDEs 19 -- 1.7 Eigenvalue Problems 25 -- 2 The Big Three PDEs 43 -- 2.1 Second-Order, Linear, Homogeneous PDEs with Constant Coefficients 43 -- 2.2 The Heat Equation and Diffusion 44 -- 2.3 The Wave Equation and the Vibrating String 53 -- 2.4 Initial and Boundary Conditions for the Heat and Wave Equations 58 -- 2.5 Laplace's Equation-The Potential Equation 65 -- 2.6 Using Separation of Variables to Solve the Big Three PDEs 70 -- 3 Fourier Series 79 -- 3.2 Properties of Sine and Cosine 80 -- 3.3 The Fourier Series 89 -- 3.4 The Fourier Series, Continued 95 -- 3.5 The Fourier Series-Proof of Pointwise Convergence 104 -- 3.6 Fourier Sine and Cosine Series 115 -- 3.7 Completeness 121 -- 4 Solving the Big Three PDEs 127 -- 4.1 Solving the Homogeneous Heat Equation for a Finite Rod 127 -- 4.2 Solving the Homogeneous Wave Equation for a Finite String 135 -- 4.3 Solving the Homogeneous Laplace's Equation on a Rectangular Domain 145 -- 4.4 Nonhomogeneous Problems 151 -- 5 Characteristics 163 -- 5.1 First-Order PDEs with Constant Coefficients 163 -- 5.2 First-Order PDEs with Variable Coefficients 173 -- 5.3 The Infinite String 180 -- 5.4 Characteristics for Semi-Infinite and Finite String Problems 191 -- 5.5 General Second-Order Linear PDEs and Characteristics 200 -- 6 Integral Transforms 213 -- 6.1 The Laplace Transform for PDEs 213 -- 6.2 Fourier Sine and Cosine Transforms 220 -- 6.3 The Fourier Transform 230 -- 6.4 The Infinite and Semi-Infinite Heat Equations 242 -- 6.5 Distributions, the Dirac Delta Function and Generalized Fourier Transforms 254 -- 6.6 Proof of the Fourier Integral Formula 266 -- 7 Bessel Functions and Orthogonal Polynomials 277 -- 7.1 The Special Functions and Their Differential Equations 277 -- 7.2 Ordinary Points and Power Series Solutions; Chebyshev, Hermite and Legendre Polynomials 285 -- 7.3 The Method of Frobenius; Laguerre Polynomials 292 -- 7.4 Interlude: The Gamma Function 300 -- 7.5 Bessel Functions 305 -- 7.6 Recap: A List of Properties of Bessel Functions and Orthogonal Polynomials 317 -- 8 Sturm-Liouville Theory and Generalized Fourier Series 329 -- 8.1 Sturm-Liouville Problems 329 -- 8.2 Regular and Periodic Sturm-Liouville Problems 337 -- 8.3 Singular Sturm-Liouville Problems; Self-Adjoint Problems 345 -- 8.4 The Mean-Square or L[superscript 2] Norm and Convergence in the Mean 354 -- 8.5 Generalized Fourier Series; Parseval's Equality and Completeness 361 -- 9 PDEs in Higher Dimensions 375 -- 9.1 PDEs in Higher Dimensions: Examples and Derivations 375 -- 9.2 The Heat and Wave Equations on a Rectangle; Multiple Fourier Series 386 -- 9.3 Laplace's Equation in Polar Coordinates: Poisson's Integral Formula 402 -- 9.4 The Wave and Heat Equations in Polar Coordinates 414 -- 9.5 Problems in Spherical Coordinates 425 -- 9.6 The Infinite Wave Equation and Multiple Fourier Transforms 439 -- 9.7 Postlude: Eigenvalues and Eigenfunctions of the Laplace Operator; Green's Identities for the Laplacian 456 -- 10 Nonhomogeneous Problems and Green's Functions 465 -- 10.1 Green's Functions for ODEs 465 -- 10.2 Green's Function and the Dirac Delta Function 484 -- 10.3 Green's Functions for Elliptic PDEs (I): Poisson's Equation in Two Dimensions 500 -- 10.4 Green's Functions for Elliptic PDEs (II): Poisson's Equation in Three Dimensions; the Helmholtz Equation 516 -- 10.5 Green's Functions for Equations of Evolution 525 -- 11 Numerical Methods 539 -- 11.1 Finite Difference Approximations for ODEs 539 -- 11.2 Finite Difference Approximations for PDEs 551 -- 11.3 Spectral Methods and the Finite Element Method 565 -- A Uniform Convergence; Differentiation and Integration of Fourier Series 587 -- B Other Important Theorems 593 -- C Existence and Uniqueness Theorems 599 -- D A Menagerie of PDEs 609.

ISBN

• 1584883731
• 9781584883739

LCCN

2004051928

OCLC

• ocm55596539
• 55596539
• SCSB-9412885

Owning Institutions

Princeton University Library