Solution Techniques for Elementary Partial Differential Equations

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.

Table of Contents:
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

Review :
"The book contains a large number of worked examples and exercises. Useful for the student who might be interested in learning the manipulating skills of solution methods of first- and second-order partial differential equations." - Zentralblatt MATH, 1042 Winner of the CHOICE Outstanding Academic Title Award for 2002!" The author, a skilled classroom performer with considerable experience, understands exactly what students want and has given them just that: a textbook that explains the essence of the method briefly and then proceeds to show it in action. In my opinion, this is quite simply the best book of its kind that I have seen thus far. The book not only contains solution methods for some very important classes of PDEs, in easy-to-read format, but is also student-friendly and teacher-friendly at the same time. It is definitely a textbook for adoption." -Peter Schiavone, Department of Mechanical Engineering, University of Alberta, Canada "successfully addresses a difficult problem of undergraduate teaching: how to make students understand and become adept at using a class of practical tools that are essential in the study of many mathematical models clear, concise, and easy to read --- places the emphasis on worked examples and exercises .Someone who needs a book that goes straight to the point and shows what partial differential equations are and how they can be solved, should find this textbook to be one of the best suited for the purpose." - Barbara Bertram, Department of Mathematical Sciences, Michigan Technological University, USA "The study of partial differential equations is of great importance to the scientists and engineers who work with mathematical models.Consequently, it is necessary for these professionals to learn in their formative years how to set up and apply the most suitable methods for solving various types of PDEs. Students in such disciplines who need a book that gives them the required knowledge in an easily understandable, yet rigorous, manner will find Christian Constanda's book an invaluable resource. .. The fact that no computing devices are needed to work through this text is a distinct advantage an ideal tool for students taking a first course in PDEs, as well as for the lecturers who teach such courses." -Dr. Marian Aron, Department of Mathematics and Statistics, Plymouth University, UK "an easy-to-read and straight-to-the-point book for all those who want to familiarize themselves with concepts and solution techniques for partial differential equationsA writing style special to this author is the complete departure from the arid theorem-proof approach to PDEs. Abstract concepts are carefully explained and supported with a wealth of remarks, application-oriented illustrations, and a wonderful collection of problems, a few elementary enough for any beginner. On the whole, the material is very well presented; this is one of the best books on elementary PDEs this reviewer has read so far. Highly recommended." -CHOICE, October 2002