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This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics 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 new edition offers substantial revisions, and the material is written in concrete language with terminology acceptable to physicists.
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
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