Applied Functional Analysis (Softcover)

Condition

GOOD: This book is in good condition, showing a few signs of use and wear, particularly on the cover corners. The pages are free of writing.

Product Details

From the back cover: "A stimulating introduction to functional analysis, this volume—aimed at undergraduate students of mathematics, mathematical physics, and engineering—examines many important applications to mechanics, fluid mechanics, diffusive growth, and approximation.

"Detailed enough to impart a thorough understanding, the text is also sufficiently straightforward for those unfamiliar with abstract analysis. Its four-part treatment begins by introducing distribution theory with discussions of Green's functions, including a consideration of retarded solutions of the wave equation. The second and third parts are essentially independent of the preceding material, dealing with such central concepts as Banach spaces, Hilbert space, spectral theory, and variational techniques. The final part outlines the ideas behind Freshet calculus, stability and bifurcation theory, and Sobolev spaces.

"Prerequisites include some familiarity with calculus, elementary differential equations, the epsilon-delta theory of convergence, vectors, and matrices. The book develops the necessary topological concepts of open and closed sets, compactness, and related matters, as well as that of an abstract vector space. All presentations of theoretical ideas are accompanied by practical applications, and students will find much useful information in the extensive appendices."

BRIEF CONTENTS

Most chapters end with "Summary and References" and "Problems." There are notes on the problems and supplementary problems following the Appendices.

Part I: Distribution Theory and Green's Functions—Chapter 1: Generalised [sic] Functions; Chapter 2: Differential Equations and Green's Functions; Chapter 3: Fourier Transforms and Partial Differential Equations.

Part II: Banach Spaces and Fixed Point Theorems—Chapter 4: Normed Spaces; Chapter 5: The Contraction Mapping Theorem; Chapter 6: Compactness and Schauder's Theorem.

Part III: Operations in Hilbert Space—Chapter 7: Hilbert Space; Chapter 8: The Theory of Operators; Chapter 9: The Spectral Theorem; Chapter 10: Variational Methods.

Part IV: Further Developments—Chapter 11: The Differential Calculus of Operators and Its Applications; Chapter 12: Distributional Hilbert Space.

Appendices—A: Sets and Mappings; B: Sequences, Series, and Uniform Convergence; C: Sup and Inf; D: Countability; E: Equivalence Relations; F: Completion; G: Sturm-Liouville Systems; H: Fourier's Theorem; I: Proofs of 9.24 and 9.25.