Techniques of Functional Analysis for Differential and Integral Equations

Techniques of Functional Analysis for Differential and Integral Equations

1st Edition - April 25, 2017

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  • Author: Paul Sacks
  • eBook ISBN: 9780128114575
  • Paperback ISBN: 9780128114261

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Description

Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature.

Key Features

  • Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas
  • Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations
  • Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics

Readership

Graduate students and 1st year PhDs across applied mathematics, mathematics and in disciplines making use of applied mathematics

Table of Contents

  • 1. Introduction
    2. Preliminaries
    3. Vector spaces
    4. Metric spaces
    5. Normed linear spaces and Banach spaces
    6. Inner product spaces and Hilbert spaces
    7. Distributions
    8. Fourier analysis and distributions
    9. Distributions and Differential Equations
    10. Linear operators
    11. Unbounded operators
    12. Spectrum of an operator
    13. Compact Operators
    14. Spectra and Green's functions for differential operators
    15. Further study of integral equations
    16. Variational methods
    17. Weak solutions of partial differential equations
    18. Appendices

Product details

  • No. of pages: 320
  • Language: English
  • Copyright: © Academic Press 2017
  • Published: April 25, 2017
  • Imprint: Academic Press
  • eBook ISBN: 9780128114575
  • Paperback ISBN: 9780128114261

About the Author

Paul Sacks

Professor Paul Sacks received his B.S. degree from Syracuse University and M.S. and Ph.D. degrees from the University of Wisconsin-Madison, all in Mathematics. Since 1981 he has been in the Mathematics department at Iowa State University, as Full Professor since 1990. He is particularly interested in partial differential equations and inverse problems. He is the author or co-author of more than 60 scientific articles and conference proceedings. For thirty years he has regularly taught courses in analysis, differential equations and methods of applied mathematics for mathematics graduate students.

Affiliations and Expertise

Professor, Mathematics Department, Iowa State University, Ames, IA, USA

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