ABSTRACT

From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices

chapter 1|36 pages

Analysis of Multivariable Functions

chapter 2|42 pages

Coordinates, Frames, and Tensor Notation

chapter 3|46 pages

Differentiable Manifolds

chapter 4|60 pages

Analysis on Manifolds

chapter 5|64 pages

Introduction to Riemannian Geometry

chapter 6|46 pages

Applications of Manifolds to Physics