Linear Integral Equations

1. Front Matter

   Pages i-ix

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2. Introduction

   • Ram P. Kanwal

   Pages 1-6

3. Integral Equations With Separable Kernels

   • Ram P. Kanwal

   Pages 7-24

4. Method of Successive Approximations

   • Ram P. Kanwal

   Pages 25-40

5. Classical Fredholm Theory

   • Ram P. Kanwal

   Pages 41-60

6. Applications to Ordinary Differential Equations

   • Ram P. Kanwal

   Pages 61-96

7. Applications to Partial Differential Equations

   • Ram P. Kanwal

   Pages 97-145

8. Symmetric Kernels

   • Ram P. Kanwal

   Pages 146-180

9. Singular Integral Equations

   • Ram P. Kanwal

   Pages 181-218

10. Integral Transform Methods

    • Ram P. Kanwal

    Pages 219-236

11. Applications to Mixed Boundary Value Problems

    • Ram P. Kanwal

    Pages 237-271

12. Integral Equation Perturbation Methods

    • Ram P. Kanwal

    Pages 272-305

13. Back Matter

    Pages 306-318

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This second edition of Linear Integral Equations continues the emphasis that the first edition placed on applications. Indeed, many more examples have been added throughout the text. Significant new material has been added in Chapters 6 and 8. For instance, in Chapter 8 we have included the solutions of the Cauchy type integral equations on the real line. Also, there is a section on integral equations with a logarithmic kernel. The bibliography at the end of the book has been exteded and brought up to date. I wish to thank Professor B.K. Sachdeva who has checked the revised man­ uscript and has suggested many improvements. Last but not least, I am grateful to the editor and staff of Birkhauser for inviting me to prepare this new edition and for their support in preparing it for publication. RamP Kanwal CHAYfERl Introduction 1.1. Definition An integral equation is an equation in which an unknown function appears under one or more integral signs Naturally, in such an equation there can occur other terms as well. For example, for a ~ s ~ b; a :( t :( b, the equations (1.1.1) f(s) = ib K(s, t)g(t)dt, g(s) = f(s) + ib K(s, t)g(t)dt, (1.1.2) g(s) = ib K(s, t)[g(t)fdt, (1.1.3) where the function g(s) is the unknown function and all the other functions are known, are integral equations. These functions may be complex-valued functions of the real variables s and t.

• equations
• ksa
• mathematics
• Boundary value problem
• Integral
• Integral equation
• ordinary differential equations

"A nice introductory text... Presents the basics of linear integral equations theory in a very comprehensive way... [The] richness of examples and applications makes the book extremely useful for teachers and also researchers."

—Applications of Mathematics

"This second edition of this highly useful book continues the emphasis on applications and presents a variety of techniques with extensive examples...The book is ideal as a text for a beginning graduate course. Its excellent treatment of boundary value problems and an up-to-date bibliography make the book equally useful for researchers in many applied fields." ---MathSciNet

• Department of Mathematics, Pennsylvania State University, University Park, USA

  Ram P. Kanwal

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