Solution Techniques Elemen Partial

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 RevisionFirst-Order Equations Homogeneous Linear Equations with Constant Coefficients Nonhomogeneous Linear Equations with Constant Coefficients Cauchy–Euler Equations Functions and Operators

Fourier SeriesThe Full Fourier Series Fourier Sine Series Fourier Cosine Series Convergence and Differentiation
Sturm–Liouville ProblemsRegular Sturm–Liouville Problems Other Problems Bessel Functions Legendre Polynomials Spherical Harmonics

Some Fundamental Equations of Mathematical PhysicsThe Heat Equation The Laplace Equation The Wave EquationOther Equations

The Method of Separation of VariablesThe Heat Equation The Wave Equation The Laplace EquationOther Equations Equations with More than Two Variables

Linear Nonhomogeneous ProblemsEquilibrium Solutions Nonhomogeneous Problems

The Method of Eigenfunction ExpansionThe Heat Equation The Wave Equation The Laplace Equation Other Equations

The Fourier TransformationsThe Full Fourier Transformation The Fourier Sine and Cosine TransformationsOther Applications

The Laplace TransformationDefinition and Properties Applications

The Method of Green’s FunctionsThe Heat Equation The Laplace Equation The Wave Equation

General Second-Order Linear Partial Differential Equations with Two Independent VariablesThe Canonical Form Hyperbolic Equations Parabolic Equations Elliptic Equations

The Method of CharacteristicsFirst-Order Linear Equations First-Order Quasilinear Equations The One-Dimensional Wave Equation Other Hyperbolic Equations

Perturbation and Asymptotic MethodsAsymptotic 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.