Solution techniques for elementary partial differential equations

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Solution techniques for elementary partial differential equations / Christian Constanda

版:: 2nd ed
資料種別:: 図書
出版情報:: Boca Raton : Chapman & Hall/CRC, c2010
形態:: xviii, 325 p. ; 24 cm
著者名:: Constanda, C. (Christian) <DA04033260>
ISBN:: 9781439811399 [1439811393]
書誌ID:: BB02656208

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注記:

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

主題:

Differential equations, Partial--Numerical solutions

言語:

英語

目次情報:

Foreword

Preface to the Second Edition

Preface to the First Edition

Ordinary Differential Equations: Brief Review / Chapter 1：

First-Order Equations / 1.1：

Homogeneous Linear Equations with Constant Coefficients / 1.2：

Nonhomogeneous Linear Equations with Constant Coefficients / 1.3：

Cauchy-Euler Equations / 1.4：

Functions and Operators / 1.5：

Exercises

Fourier Series / Chapter 2：

The Full Fourier Series / 2.1：

Fourier Sine Series / 2.2：

Fourier Cosine Series / 2.3：

Convergence and Differentiation / 2.4：

Sturm-Liouville Problems / Chapter 3：

Regular Sturm-Liouville Problems / 3.1：

Other Problems / 3.2：

Bessel Functions / 3.3：

Legendre Polynomials / 3.4：

Spherical Harmonics / 3.5：

Some Fundamental Equations of Mathematical Physics / Chapter 4：

The Heat Equation / 4.1：

The Laplace Equation / 4.2：

The Wave Equation / 4.3：

Other Equations / 4.4：

The Method of Separation of Variables / Chapter 5：

Equations with More than Two Variables / 5.1：

Linear Nonhomogeneous Problems / Chapter 6：

Equilibrium Solutions / 6.1：

Nonhomogeneous Problems / 6.2：

The Method of Eigenfunction Expansion / Chapter 7：

The Fourier Transformations / 7.1：

The Full Fourier Transformation / 8.1：

The Fourier Sine and Cosine Transformations / 8.2：

Other Applications / 8.3：

The Laplace Transformation / Chapter 9：

Definition and Properties / 9.1：

Applications / 9.2：

The Method of Green's Functions / Chapter 10：

General Second-Order Linear Partial Differential Equations with Two Independent Variables / 10.1：

The Canonical Form / 11.1：

Hyperbolic Equations / 11.2：

Parabolic Equations / 11.3：

Elliptic Equations / 11.4：

The Method of Characteristics / Chapter 12：

First-Order Linear Equations / 12.1：

First-Order Quasilinear Equations / 12.2：

The One-Dimensional Wave Equation / 12.3：

Other Hyperbolic Equations / 12.4：

Perturbation and Asymptotic Methods / Chapter 13：

Asymptotic Series / 13.1：

Regular Perturbation Problems / 13.2：

Singular Perturbation Problems / 13.3：

Complex Variable Methods / Chapter 14：

Systems of Equations / 14.1：

Answers to Odd-Numbered Exercises

Appendix

Bibliography

Index

Foreword

Preface to the Second Edition

Preface to the First Edition

Ordinary Differential Equations: Brief Review / Chapter 1：

First-Order Equations / 1.1：

Homogeneous Linear Equations with Constant Coefficients / 1.2：

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