Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.
Author(s): Vivian Hutson, John S. Pym and Michael J. Cloud (Eds.)
Series: Mathematics in Science and Engineering 200
Edition: 2
Publisher: Elsevier Science
Year: 2005
Language: English
Pages: 1-426
Content:
Preface
Pages v-vii
V. Hutson, J.S. Pym, M.J. Cloud
Acknowledgements
Page ix
Chapter 1 Banach spaces Original Research Article
Pages 1-38
Chapter 2 Lebesgue integration and the ℳp spaces Original Research Article
Pages 39-64
Chapter 3 Foundations of linear operator theory Original Research Article
Pages 65-113
Chapter 4 Introduction to nonlinear operators Original Research Article
Pages 115-146
Chapter 5 Compact sets in Banach spaces Original Research Article
Pages 147-156
Chapter 6 The adjoint operator Original Research Article
Pages 157-187
Chapter 7 Linear compact operators Original Research Article
Pages 189-215
Chapter 8 Nonlinear compact operators and monotonicity Original Research Article
Pages 217-239
Chapter 9 The spectral theorem Original Research Article
Pages 241-268
Chapter 10 Generalized eigenfunction expansions associated with ordinary differential equations Original Research Article
Pages 269-301
Chapter 11 Linear elliptic partial differential equations Original Research Article
Pages 303-342
Chapter 12 The finite element method Original Research Article
Pages 343-357
Chapter 13 Introduction to degree theory Original Research Article
Pages 359-383
Chapter 14 Bifurcation theory Original Research Article
Pages 385-407
References Original Research Article
Pages 409-416
List of symbols
Pages 417-420
Index
Pages 421-426
