The Book
This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathe- matics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory: This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised.
Table of Contents
Chapter 1
Geometry in Regions of a Space, Basic Concepts
Chapter 2
The Theory of Surfaces
Chapter 3
Tensors: The algebraic Theory
Chapter 4
The Differential calculus of Tensors
Chapter 5
The Elements of the Calculus of Variations
Chapter 6
The Calculus of Variations in Several Dimensions, Fields and Their Geometric Invariants