Solution techniques for elementary partial differential equations

著者

• Constanda, C. (Christian)

書誌事項

Solution techniques for elementary partial differential equations

Christian Constanda

（Chapman & Hall/CRC mathematics）

Chapman & Hall/CRC, c2002

注記

Includes bibliographical references (p. 247) and index

内容説明・目次

内容説明

Of the many available texts on partial differential equations (PDEs), most are too detailed and voluminous, making them daunting to many students. In sharp contrast, Solution Techniques for Elementary Partial Differential Equations is a no-frills treatment that explains completely but succinctly some of the most fundamental solution methods for PDEs. After a brief review of elementary ODE techniques and discussions on Fourier series and Sturm-Liouville problems, the author introduces the heat, Laplace, and wave equations as mathematical models of physical phenomena. He then presents a number of solution techniques and applies them to specific initial/boundary value problems for these models. Discussion of the general second order linear equation in two independent variables follows, and finally, the method of characteristics and perturbation methods are presented. Most students seem to like concise, easily digestible explanations and worked examples that let them see the techniques in action. This text offers them both. Ideally suited for independent study and classroom tested with great success, it offers a direct, streamlined route to competence in PDE solution techniques.

目次

Preface ORDINARY DIFFERENTIAL EQUATIONS: BRIEF REVISION First-Order Equations Homogeneous Linear Equations with Constant Coefficients Nonhomogeneous Linear Equations with Constant Coefficients Linear Operators Exercises FOURIER SERIES The Full Fourier Series Fourier Sine Series Fourier Cosine Series Convergence and Differentiation Exercises STURM-LIOUVILLE PROBLEMS Regular Sturm-Liouville Problems Other Sturm-Liouville Problems Exercises THREE FUNDAMENTAL EQUATIONS OF MATHEMATICAL PHYSICS The Heat Equation The Laplace Equation The Wave Equation THE METHOD OF SEPARATION OF VARIABLES The Heat Equation The Wave Equation The Laplace Equation Equations with More than Two Variables Exercises LINEAR NONHOMOGENEOUS PROBLEMS Equilibrium Solutions Nonhomogeneous Problems Exercises THE METHOD OF EIGENFUNCTION EXPANSION The Heat Equation The Wave Equation The Laplace Equation Exercises THE FOURIER TRANSFORMATIONS The Full Fourier Transformation The Fourier Sine and Cosine Transformations Exercises THE LAPLACE TRANSFORMATION Definition and Properties Applications Exercises THE METHOD OF GREEN'S FUNCTIONS The Heat Equation The Laplace Equation The Wave Equation Exercises GENERAL SECOND-ORDER LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH TWO INDEPENDENT VARIABLES The Canonical Form Hyperbolic Equations Parabolic Equations Elliptic Equations Exercises THE METHOD OF CHARACTERISTICS First-Order Linear Equations First-Order Quasilinear Partial Equations The One-Dimensional Wave Equation Exercises PERTURBATION AND ASYMPTOTIC METHODS Asymptotic Series Regular Perturbation Problems Singular Perturbation Problems Exercises APPENDIX BIBLIOGRAPHY INDEX

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詳細情報

• NII書誌ID(NCID): BA58088827
• ISBN:
  • 1584882573
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Boca Raton, Fla
• ページ数/冊数: xvi, 253 p.
• 大きさ: 24 cm
• 親書誌ID:
  • BA50255823