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Publisher:

Chapman & Hall/CRC

Publication Date:

2010

Number of Pages:

325

Format:

Paperback

Edition:

2

Price:

69.95

ISBN:

9781439811399

Category:

Textbook

[Reviewed by , on ]

Lakshmi Chandrasekaran

01/17/2011

*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 (lchand@lsuhsc.edu) 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

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**

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