Solution techniques for elementary partial differential equations

著者

書誌事項

Solution techniques for elementary partial differential equations

Christian Constanda

Chapman & Hall/CRC, c2010

2nd ed

大学図書館所蔵 件 / 全7件

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注記

Includes bibliographical references (p. [319]-320) and index

内容説明・目次

内容説明

Incorporating a number of enhancements, Solution Techniques for Elementary Partial Differential Equations, Second Edition presents some of the most important and widely used methods for solving partial differential equations (PDEs). The techniques covered include separation of variables, method of characteristics, eigenfunction expansion, Fourier and Laplace transformations, Green's functions, perturbation methods, and asymptotic analysis. New to the Second Edition New sections on Cauchy-Euler equations, Bessel functions, Legendre polynomials, and spherical harmonics A new chapter on complex variable methods and systems of PDEs Additional mathematical models based on PDEs Examples that show how the methods of separation of variables and eigenfunction expansion work for equations other than heat, wave, and Laplace Supplementary applications of Fourier transformations The application of the method of characteristics to more general hyperbolic equations Expanded tables of Fourier and Laplace transforms in the appendix Many more examples and nearly four times as many exercises This edition continues to provide a streamlined, direct approach to developing students' competence in solving PDEs. It offers concise, easily understood explanations and worked examples that enable students to see the techniques in action. Available for qualifying instructors, the accompanying solutions manual includes full solutions to the exercises. Instructors can obtain a set of template questions for test/exam papers as well as computer-linked projector files directly from the author.

目次

Ordinary Differential Equations: Brief Revision First-Order Equations Homogeneous Linear Equations with Constant Coefficients Nonhomogeneous Linear Equations with Constant Coefficients Cauchy-Euler Equations Functions and Operators Fourier Series The Full Fourier Series Fourier Sine Series Fourier Cosine Series Convergence and Differentiation Sturm-Liouville Problems Regular Sturm-Liouville Problems Other Problems Bessel Functions Legendre Polynomials Spherical Harmonics Some Fundamental Equations of Mathematical Physics The Heat Equation The Laplace Equation The Wave Equation Other Equations The Method of Separation of Variables The Heat Equation The Wave Equation The Laplace Equation Other Equations Equations with More than Two Variables Linear Nonhomogeneous Problems Equilibrium Solutions Nonhomogeneous Problems The Method of Eigenfunction Expansion The Heat Equation The Wave Equation The Laplace Equation Other Equations The Fourier Transformations The Full Fourier Transformation The Fourier Sine and Cosine Transformations Other Applications The Laplace Transformation Definition and Properties Applications The Method of Green's Functions The Heat Equation The Laplace Equation The Wave Equation General Second-Order Linear Partial Differential Equations with Two Independent Variables The Canonical Form Hyperbolic Equations Parabolic Equations Elliptic Equations The Method of Characteristics First-Order Linear Equations First-Order Quasilinear Equations The One-Dimensional Wave Equation Other Hyperbolic Equations Perturbation and Asymptotic Methods Asymptotic Series Regular Perturbation Problems Singular Perturbation Problems Complex Variable Methods Elliptic Equations Systems of Equations Answers to Odd-Numbered Exercises Appendix Bibliography Index Exercises appear at the end of each chapter.

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