Elements of Partial Differential Equations by Ian N. Sneddon: A Review
Partial differential equations (PDEs) are mathematical equations that involve functions of several variables and their partial derivatives. They are widely used to model various phenomena in physics, engineering, and other sciences. However, finding solutions of PDEs is not always easy, and often requires a combination of analytical and numerical methods.
In this article, we will review a classic book on the subject: Elements of Partial Differential Equations by Ian N. Sneddon. This book was first published in 1957 and has been reprinted several times since then. It is aimed at students and researchers who are interested in finding solutions of particular equations rather than in the general theory of PDEs. The book covers topics such as separation of variables, Fourier series, Fourier transforms, Laplace transforms, Bessel functions, Legendre polynomials, Green's functions, and boundary value problems.
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The book is divided into 12 chapters, each with a number of worked examples and exercises. The first chapter introduces the basic concepts and notation of PDEs, and gives some examples of physical problems that lead to PDEs. The second chapter discusses the method of separation of variables for solving linear PDEs with constant coefficients. The third chapter deals with Fourier series and their applications to solving PDEs on finite intervals. The fourth chapter extends the method of separation of variables to infinite intervals using Fourier transforms. The fifth chapter introduces Laplace transforms and their use in solving PDEs on semi-infinite intervals.
The sixth chapter covers Bessel functions and their properties, and shows how they can be used to solve PDEs in cylindrical coordinates. The seventh chapter does the same for Legendre polynomials and PDEs in spherical coordinates. The eighth chapter introduces Green's functions as a tool for solving nonhomogeneous PDEs with boundary conditions. The ninth chapter applies Green's functions to solve various types of boundary value problems for the Laplace equation. The tenth chapter discusses the wave equation and its solutions using separation of variables and d'Alembert's formula. The eleventh chapter covers the heat equation and its solutions using separation of variables and the method of characteristics. The twelfth chapter concludes the book with some topics on nonlinear PDEs and their applications.
The book is written in a clear and concise style, with a focus on practical aspects rather than abstract theory. The author assumes that the reader has some background in calculus, complex analysis, and ordinary differential equations, but does not require any prior knowledge of PDEs. The book provides a solid foundation for further study of PDEs and their applications in various fields.
If you are looking for a book that presents the elements of the theory of partial differential equations in a form suitable for finding solutions of particular equations, then Elements of Partial Differential Equations by Ian N. Sneddon is a good choice. You can download a free PDF copy of the book from [^1^] or [^3^]. 29c81ba772