Introduction to integral equations with applications

著者

書誌事項

Introduction to integral equations with applications

Abdul J. Jerri

（A Wiley-Interscience publication）

Wiley, c1999

2nd ed

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注記

Includes bibliographical references (p. 421-424) and index

内容説明・目次

内容説明

From the reviews of the First Edition: "Extremely clear, self-contained text ...offers to a wide class of readers the theoretical foundations and the modern numerical methods of the theory of linear integral equations."-Revue Roumaine de Mathematiques Pures et Appliquees. Abdul Jerri has revised his highly applied book to make it even more useful for scientists and engineers, as well as mathematicians. Covering the fundamental ideas and techniques at a level accessible to anyone with a solid undergraduate background in calculus and differential equations, Dr. Jerri clearly demonstrates how to use integral equations to solve real-world engineering and physics problems. This edition provides precise guidelines to the basic methods of solutions, details more varied numerical methods, and substantially boosts the total of practical examples and exercises. Plus, it features added emphasis on the basic theorems for the existence and uniqueness of solutions of integral equations and points out the interrelation between differentiation and integration. Other features include: A new section on integral equations in higher dimensions. An improved presentation of the Laplace and Fourier transforms. A new detailed section for Fredholm integral equations of the first kind. A new chapter covering the basic higher quadrature numerical integration rules. A concise introduction to linear and nonlinear integral equations. Clear examples of singular integral equations and their solutions. A student's solutions manual available directly from the author.

目次

  • Integral Equations, Origin, and Basic Tools
  • Modeling of Problems as Integral Equations
  • Volterra Integral Equations
  • The Green's Function
  • Fredholm Integral Equations
  • Existence of the Solutions: Basic Fixed Point Theorems
  • Higher Quadrature Rules for the Numerical Solutions
  • Appendices
  • Answers to Exercises
  • References
  • Index.

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