There already exist a number of excellent graduate textbooks on the theory of differential forms as well as a handful of very good undergraduate textbooks on multivariable calculus in which this subject is briefly touched upon but not elaborated on enough.
The goal of this textbook is to be readable and usable for undergraduates. It is entirely devoted to the subject of differential forms and explores a lot of its important ramifications.
In particular, our book provides a detailed and lucid account of a fundamental result in the theory of differential forms which is, as a rule, not touched upon in undergraduate texts: the isomorphism between the Čech cohomology groups of a differential manifold and its de Rham cohomology groups.
Contents:- Preface
- About the Authors
- Multilinear Algebra
- The Concept of a Differential Form
- Integration of Forms
- Manifolds and Forms on Manifolds
- Cohomology via Forms
- AAppendix A. Bump Functions and Partitions of Unity
- Appendix B. The Implicit Function Theorem
- Appendix C. Good Covers and Convexity Theorem
- Bibliography
- Index of Notation
- Glossary of Terminology
Readership: First-year graduate and advanced undergraduate students in math programs.Manifold;Differential Form;de Rham Cohomology0
Key Features:- Fills a gap as an intermediate-level text
- Gives a careful exposition of the theory starting from first principles
- The first author, Victor Guillemin, is a world-renowned mathematician and author of 12 books
