
- 432 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
A Course in Advanced Calculus
About this book
This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more.
Carefully chosen problems appear at the end of each chapter, and this new edition features an additional appendix of tips and solutions for selected problems.
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Information
Table of contents
- Cover
- Title Page
- Copyright Page
- Dedication Page
- Contents
- Preface
- Chapter 1 Sets and Structures
- Chapter 2 Limit and Continuity in En
- Chapter 3 Inequalities
- Chapter 4 Linear Spaces
- Chapter 5 Forms in En
- Chapter 6 Topology
- Chapter 7 Inner-Product Spaces
- Chapter 8 Measure and Integration
- Chapter 9 Differentiable Mappings
- Chapter 10 Sequences and Series
- Chapter 11 Applications of Improper Integrals
- Chapter 12 The Generalized Stokes Theorem
- Tips and Solutions for Selected Problems
- Bibliography
- Index