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Solution Techniques for Elementary Partial Differential Equations

Christian Constanda
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
[Reviewed by
Lakshmi Chandrasekaran
, on

Solution Techniques for Elementary Partial Differential Equations is an interesting read. Each chapter begins with a very brief theoretical introduction and continues with plenty of examples. Some of the worked-out examples cover not only the conventional topics of heat and wave problems but also applications to a wide variety of fields, from stock markets to Brownian motion.

Chapter 5 is one of the best chapters in the book. It discusses the method of separation of variables. The examples in this chapter are sequentially built to introduce the different scenarios that could be encountered in problems the heat and wave equations by discussing a variety of initial and boundary conditions. Chapter 7 serves as a good complement to chapter 5, as it discusses the method of eigenfunction expansion with examples that are very similar to those in the former chapter, thus exposing the reader to two different ways of solving such problems.

The chapter on asymptotics and perturbation methods towards the end of the book discusses material that is rarely found in elementary PDE books. It should serve as a good motivation for the reader to understand problems in real life that sometimes do not have exact solutions.

Each chapter has many problems for practice, with solutions for some of them provided at the very end. The book is well written, concise, has adequate examples and can be used as a textbook for beginners to learn the techniques of PDE solvers.

Lakshmi Chandrasekaran ( is a postdoctoral fellow at the Louisiana State University Health Sciences Center. She works in Mathematical and  Computational Neuroscience. Whenever she has some free time she like to read pretty much anything and to listen to music.

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

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