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Analysis in Vector Spaces - A Course in Advanced Calculus by Mustafa A. Akcoglu; Paul F. A. Bartha; Dzung Minh Ha is a nonfiction available to read on EtoBox.

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Analysis in Vector Spaces: A Course in Advanced Calculus 5 CONTENTS 7 Preface 11 PART I BACKGROUND MATERIAL 15 1 Sets and Functions 17 1.1 Sets in General 17 1.2 Sets of Numbers 24 1.3 Functions 31 2 Real Numbers 45 2.1 Review of the Order Relations 46 2.2 Completeness of Real Numbers 50 2.3 Sequences of Real Numbers 54 2.4 Subsequences 59 2.5 Series of Real Numbers 64 2.6 Intervals and Connected Sets 68 3 Vector Functions 75 3.1 Vector Spaces: The Basics 76 3.2 Bilinear Functions 96 3.3 Multilinear Functions 102 3.4 Inner Products 109 3.5 Orthogonal Projections 117 3.6 Spectral Theorem 123 PART II DIFFERENTIATION 135 4 Normed Vector Spaces 137 4.1 Preliminaries 138 4.2 Convergence in Normed Spaces 142 4.3 Norms of Linear and Multilinear Transformations 149 4.4 Continuity in Normed Spaces 156 4.5 Topology of Normed Spaces 170 5 Derivatives 189 5.1 Functions of a Real Variable 190 5.2 Differentiable Functions 204 5.3 Existence of Derivatives 215 5.4 Partial Derivatives 219 5.5 Rules of Differentiation 225 5.6 Differentiation of Products 232 6 Diffeomorphisms and Manifolds 239 6.1 The Inverse Function Theorem 240 6.2 Graphs 252 6.3 Manifolds in Parametric Representations 257 6.4 Mani

Who reads Analysis in Vector Spaces - A Course in Advanced Calculus?

Author

Mustafa A. Akcoglu; Paul F. A. Bartha; Dzung Minh Ha

Publisher

Wiley & Sons, Incorporated, John

Published

2009

Language

EN

ISBN

9780470148242

Category

nonfiction

Subjects

Mathematics, Stem