Solution Techniques for Elementary Partial Differential Equations (Chapman & Hall/CRC Mathematics)

Christian Constanda

ISBN 10: 1584882573 / ISBN 13: 9781584882572

Editore: Chapman and Hall/CRC, 2002

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Dati bibliografici

• Titolo: Solution Techniques for Elementary Partial Differential Equations (Chapman & Hall/CRC Mathematics)
• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 1584882573
• ISBN 13: 9781584882572
• Rilegatura: Soft cover
• Edizione: 1st Edition
• Condizione: Very Good

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Riassunto

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.

Contenuti

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