Solution Techniques for Elementary Partial Differential Equations, Second Edition
Taylor & Francis Inc (Verlag)
978-1-4398-1139-9 (ISBN)
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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.
Christian Constanda is the Charles W. Oliphant Endowed Chair in Mathematical Sciences in the Department of Mathematical and Computer Sciences at the University of Tulsa. He is also an Emeritus Professor at the University of Strathclyde in Glasgow, UK.
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.
| Erscheint lt. Verlag | 17.6.2010 |
|---|---|
| Zusatzinfo | 4 Tables, black and white; 41 Illustrations, black and white |
| Verlagsort | Washington |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 476 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4398-1139-3 / 1439811393 |
| ISBN-13 | 978-1-4398-1139-9 / 9781439811399 |
| Zustand | Neuware |
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