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An introduction to partial differential equations
Arrigo D., Morgan&Claypool Publishers, San Rafael, CA, 2018. 168 pp. Type: Book (978-1-681732-54-1)
Date Reviewed: Jul 27 2018

Partial differential equations (PDEs) are used in several branches of engineering and science. For example, physical laws (like conservation of mass, momentum, and energy) model many physical, chemical, and biological processes. These laws are often expressed using PDEs. PDEs are expressions involving functions of several variables and their partial derivatives, along with suitable initial or/and boundary conditions depending on the physics of the problems. Some well-known PDEs are Laplace’s equation, Poisson’s equation, Navier-Stokes equations, Euler’s equation, the Black–Scholes PDE, the Korteweg–de Vries (KdV) equation, and so on. Therefore, it is essential to study the theory of PDEs and methods to obtain their solutions. Generally, obtaining analytical solutions to PDEs is difficult or impossible. Here, the author describes several techniques to obtain the exact solutions for some specific first-order and second-order PDEs. This is a good book on problem solving in PDEs for undergraduate students in science and engineering.

The book contains seven chapters. Chapter 1 provides a nice introduction to PDEs, including the advection equation, the diffusion equation, Laplace’s equation, and the wave equation, as well as several examples of PDEs in other branches of science and engineering. Chapter 2 focuses on solution techniques for first-order PDEs, mainly linear, quasilinear, and nonlinear PDEs, using the method of characteristics. Chapter 3 covers standard canonical forms of second-order linear PDEs. Chapter 4, “Fourier Series,” presents several examples for various cases. Chapter 5 focuses on the solution of second-order linear PDEs, namely parabolic, hyperbolic, and elliptic PDEs, via the separation of variables method. Chapter 6 is on obtaining solutions through the Fourier transform. All the chapters include exercises, and solutions to these exercises are given in chapter 7.

This book provides various solution techniques for first-order and second-order PDEs. The methods are explained very well with several examples. Students can use the provided exercises for practice. The book is well written and could be a good option for beginners.

Reviewer:  Srinivasan Natesan Review #: CR146177 (1810-0530)
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Partial Differential Equations (G.1.8 )
 
 
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