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A first course in integral equations. (English) Zbl 0924.45001
Singapore: World Scientific. xi, 208 p. £23.00 (1997).

This book is an elementary introduction to integral equations and the author is mainly interested in solving such equations explicitly or approximately; it contains a lot of examples. It is not concerned with the theory of integral equations, questions of existence and uniqueness of solutions, even questions of convergence of approximate solutions to a solution are not touched. In Chapter 1 the usual classification of integral equations is given. Further the question of converting integral equations and initial and boundary value problems of ordinary differential equations into each other is discussed and illustrated by examples. The further Chapters 2 to 6 are dedicated to solving explicitly Fredholm and Volterra integral equations, integro-differential equations and nonlinear integral equations by several methods which are: Decomposition method, which was developed by G. Adomian [Solving frontier problems of physics: the decomposition method (1994: Zbl 0802.65122)], the solution is given by a series $u\left(x\right)={\sum }_{n=0}^{\infty }{u}_{n}\left(x\right)$; direct computation method for special kernels; successive approximation; successive substitution; series expansion; converting of integral equations into initial or boundary value problems for ordinary differential equations. The methods are not discussed in general but illustrated by many examples, and the different methods are compared.

This book should be useful for engineers who are only interested in solving integral equations.

##### MSC:
 45-01 Textbooks (integral equations) 65R20 Integral equations (numerical methods) 00A06 Mathematics for non-mathematicians