A Course on Integral Equations

1. Front Matter

   Pages i-xiii

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2. Fredholm Theory

   • Allen C. Pipkin

   Pages 1-27

3. Fredholm Theory with Integral Norms

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   Pages 28-43

4. Hilbert—Schmidt Theory

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   Pages 44-71

5. Laplace Transforms

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   Pages 72-91

6. Volterra Equations

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   Pages 92-106

7. Reciprocal Kernels

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   Pages 107-136

8. Smoothing and Unsmoothing

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   Pages 137-159

9. Wiener—Hopf Equations

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   Pages 160-172

10. Evaluation of Principal Value Integrals

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    Pages 173-202

11. Cauchy Principal Value Equations on a Finite Interval

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    Pages 203-216

12. Principal Value Equations on a Semi-Infinite Interval

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    Pages 217-234

13. Principal Value Equations on an Infinite Interval

    • Allen C. Pipkin

    Pages 235-256

14. Back Matter

    Pages 257-268

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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas­ sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe­ matical Sciences ( AMS) series, which will focus on advanced textbooks and research level monographs. Foreword This book is based on a one-semester course for graduate students in the physical sciences and applied mathematics. No great mathematical back­ ground is needed, but the student should be familiar with the theory of analytic functions of a complex variable. Since the course is on problem­ solving rather than theorem-proving, the main requirement is that the stu­ dent should be willing to work out a large number of specific examples.

• Integral equation
• Integralgleichung
• Mathematica
• analytic function
• boundary element method
• equation
• function
• functions
• integral
• problem solving
• proving
• requirement
• theorem
• theorem proving
• variable

• Center of Fluid Mechanics, Turbulence and Computation, Brown University, Providence, USA

  Allen C. Pipkin

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