Linear and Nonlinear Functional Analysis with Applications

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en Limba Engleză Carte Hardback – 21 Nov 2013
Functional 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.
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ISBN-13: 9781611972580
ISBN-10: 1611972582
Pagini: 840
Ilustrații: Illustrations
Dimensiuni: 174 x 247 x 38 mm
Greutate: 0.13 kg
Editura: Society for Industrial and Applied Mathematics
Colecția Society for Industrial and Applied Mathematics
Locul publicării: Cambridge, United Kingdom


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.