Applied Functional Analysis: Applications to Mathematical Physics / Edition 1

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This is the first part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, numerical functional analysis and their substantial applications with each other. The book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The book's approach begins with the question "what are the most important applications" and proceeds to try to answer this question. The applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schrodinger approach and the Feynman approach to quantum physics, and quantum statistics. The presentation is self-contained. As for prerequisites, the reader should be familiar with some basic facts of calculus.
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Product Details

  • ISBN-13: 9780387944425
  • Publisher: Springer New York
  • Publication date: 6/23/1995
  • Series: Applied Mathematical Sciences Series, #108
  • Edition description: 1st ed 1995. Corr. 3rd printing 1999
  • Edition number: 1
  • Pages: 481
  • Product dimensions: 1.19 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface.- Prologue.- Banach Spaces and Fixed-Point Theorems.- Hilbert Spaces.- Orthogonality, and the Dirichlet Principle.- Hilbert Spaces and Generalized Fourier Series.- Eigenvalue Problems for Linear Compact Symmetric Operators.- Self-Adjoint Operators, the Friedrichs Extension and the Partial Differential Equations of Mathematical Physics.- Epilogue.- Appendix.- References.- Hints for Further Reading.- List of Symbols.- List of Theorems.- List of Most Important Definitions.- Subject Index.
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