Linear and Nonlinear Functional Analysis with Applications
Linear and Nonlinear Functional Analysis with Applications
£69.99
GBPFunctional analysis occupies a central position in modern mathematics, and has powerful applications in many other branches of the subject. This book provides a thorough and self-contained introduction to the basic aspects of both linear and nonlinear functional analysis. Most of the major results are accompanied by complete proofs, and illustrated with a variety of applications to numerical analysis, optimisation theory, and partial differential equations. As well as covering a vast amount of foundational material, historical notes and many original references are included to help the reader explore the genesis of some important results. This book is intended for advanced undergraduates, graduate students, and researchers. With illustrations and over 400 problems, it is ideal for both teaching and self-study.
- Covers all the basic material in one volume, with complete proofs of most results
- Presents applications of functional analysis to PDEs, numerical analysis and optimisation
- The pedagogical appeal of the book is enhanced by over 400 exercises
Product details
November 2013Hardback
9781611972580
840 pages
260 × 182 × 38 mm
1.32kg
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Table of Contents
- Preface
- 1. Real analysis and theory of functions: a quick review
- 2. Normed vector spaces
- 3. Banach spaces
- 4. Inner-product spaces and Hilbert spaces
- 5. The 'great theorems' of linear functional analysis
- 6. Linear partial differential equations
- 7. Differential calculus in normed vector spaces
- 8. Differential geometry in Rn
- 9. The 'great theorems' of nonlinear functional analysis
- Bibliographical notes
- Bibliography
- Main notations
- Index.
