A First Course in Integral Equations

This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods.

This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering.

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Contents:Introductory ConceptsFredholm Integral EquationsVolterra Integral EquationsFredholm Integro-Differential EquationsVolterra Integro-Differential EquationsSingular Integral EquationsNonlinear Fredholm Integral EquationsNonlinear Volterra Integral EquationsApplications of Integral Equations
Readership: Advanced undergraduates, graduate students, and researchers in mathematics, science and engineering.
Key Features:Treatment of integral equations without having extensive background in mathematics for non-mathematics studentsA concise introduction to highlight the classifications of integral equations and calculus materialPresents up-to-date developments and approaches in the field of integral equationsIncludes more theorems, new techniques, well-explained new examples and scientific applicationsIncludes adomian decomposition method and the variational iteration method to provide insight-oriented approachesIncludes two exclusive chapters to handle the nonlinear Volterra and Fredholm integral equationsDetailed sections on using the regularization method to solve the Fredholm integral equations of the first kind and usage of weakly-singular linear and nonlinear integral equations