Solution Techniques for Elementary Partial Differential Equations

Name: Solution Techniques for Elementary Partial Differential Equations
Price: 12.55 USD
Availability: InStock
ISBN: 9781439811399

ISBN-10: 1439811393

ISBN-13: 9781439811399

Edition: 2nd 2010 (Revised)

Authors: Christian Constanda

List price: $30.99

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Description:

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…

Book details

List price: $30.99
Edition: 2nd
Copyright year: 2010
Publisher: Taylor & Francis Group
Publication date: 6/17/2010
Binding: Paperback
Pages: 344
Size: 5.75" wide x 9.00" long x 0.75" tall
Weight: 1.056
Language: English



Foreword


Preface to the Second Edition


Preface to the First Edition



Ordinary Differential Equations: Brief Review



First-Order Equations



Homogeneous Linear Equations with Constant Coefficients



Nonhomogeneous Linear Equations with Constant Coefficients



Cauchy-Euler Equations



Functions and 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 Problems



Bessel Functions



Legendre Polynomials



Spherical Harmonics


Exercises



Some Fundamental Equations of Mathematical Physics



The Heat Equation



The Laplace Equation



The Wave Equation



Other Equations


Exercises



The Method of Separation of Variables



The Heat Equation



The Wave Equation



The Laplace Equation



Other Equations



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



Other Equations


Exercises



The Fourier Transformations



The Full Fourier Transformation



The Fourier Sine and Cosine Transformations



Other Applications


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 Equations



The One-Dimensional Wave Equation



Other Hyperbolic Equations


Exercises



Perturbation and Asymptotic Methods



Asymptotic Series



Regular Perturbation Problems



Singular Perturbation Problems


Exercises



Complex Variable Methods



Elliptic Equations



Systems of Equations


Exercises


Answers to Odd-Numbered Exercises


Appendix


Bibliography


Index