Jänich K. Vector Analysis

Springer Science+Business Media, LLC, 2001. — 289 p. — (Undergraduate Texts in Mathematics) — ISBN: 0387986499.This book presents modern vector analysis and carefully describes the classical notation and understanding of the theory. It covers all of the classical vector analysis in Euclidean space, as well as on manifolds, and goes on to introduce de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality. The material is accessible to readers and students with only calculus and linear algebra as prerequisites. A large number of illustrations, exercises, and tests with answers make this book an invaluable self-study source.Differentiable Manifolds
The Thngent Space
Differential Forms
The Concept of Orientation
Integration on Manifolds
Manifolds-with-Boundary
The Intuitive Meaning of Stokes's Theorem
The Wedge Product and the Definition of the Cartan Derivative
Stokes's Theorem
Classical Vector Analysis
De Rham Cohomology
Differential Forms on Riemannian Manifolds
Calculations in Coordinates
Answers to the Thst Questions