Cover is for reference only

Analysis in vector spaces a course in advanced calculus /

A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject thro...

Full description

Saved in:
Bibliographic Details
Main Authors: Akcoglu, Mustafa A. Mustafa Agah, 1934
Corporate Authors: Wiley InterScience Online service
Group Author: Bartha, Paul F. A., 1964; Ha, Dzung Minh
Published:
Literature type: Electronic eBook
Language: English
Subjects:
Vector spaces
Functional analysis
MATHEMATICS > Algebra > Linear
Espaces vectoriels
Electronic books
Online Access: http://onlinelibrary.wiley.com/book/10.1002/9781118164587
Summary: A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject through rigorous arguments, discussions, and examples. The book aims to cultivate not only knowledge of the major theoretical results, but also the geometric intuition needed for both mathematical problem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, t
Item Description: Includes index.
Carrier Form: 1 online resource (xii, 465 pages) : illustrations
ISBN: 9781118164587 (electronic bk.)
111816458X (electronic bk.)
9781118164594 (electronic bk.)
1118164598 (electronic bk.)
Index Number: QA186
CLC: O177
Contents: Front Matter -- Background Material. Sets and Functions -- Real Numbers -- Vector Functions -- Differentiation. Normed Vector Spaces -- Derivatives -- Diffeomorphisms and Manifolds -- Higher-Order Derivatives -- Integration. Multiple Integrals -- Integration on Manifolds -- Stokes' Theorem -- Appendices. Appendix A: Construction of the real numbers -- Appendix B: Dimension of a vector space -- Appendix C: Determinants -- Appendix D: Partitions of unity -- Index.
PART: I BACKGROUND MATERIAL. 1. Sets and Functions. 1.1 Sets in General. 1.2 Sets of Numbers. 1.3 Functions. 2. Real Numbers. 2.1 Review of the Order Relations. 2.2 Completeness of Real Numbers. 2.3 Sequences of Real Numbers. 2.4 Subsequences. 2.5 Series of Real Numbers. 2.6 Intervals and Connected Sets. 3. Vector Functions. 3.1 The Basics. 3.2 Bilinear Functions. 3.3 Multilinear functions. 3.4 Inner Products. 3.5 Orthogonal Projections. 3.6 Spectral Theorem. PART II: DIFFERENTIATION. 4. Normed. 4.1 Preliminaries. 4.2 Convergence in Normed Spaces. 4.3 Norms of Linear and Multilinear Transfor

Related Book Recommendations