Vector Analysis

Description

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 Front Matter....Pages i-xiv Differentiable Manifolds....Pages 1-24 The Tangent Space....Pages 25-48 Differential Forms....Pages 49-64 The Concept of Orientation....Pages 65-78 Integration on Manifolds....Pages 79-100 Manifolds-with-Boundary....Pages 101-115 The Intuitive Meaning of Stokes’s Theorem....Pages 117-131 The Wedge Product and the Definition of the Cartan Derivative....Pages 133-149 Stokes’s Theorem....Pages 151-165 Classical Vector Analysis....Pages 167-193 De Rham Cohomology....Pages 195-213 Differential Forms on Riemannian Manifolds....Pages 215-237 Calculations in Coordinates....Pages 239-268 Answers to the Test Questions....Pages 269-271 Back Matter....Pages 273-283