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1. The Einstein Summation Convention. 2. Basic Linear Algebra for Tensors. 3. General Tensors. 4. Tensor Operations. 5. Tests for Tensor Character. 6. The Metric Tensor. 7. The Derivative of a Tensor. 8. Further Riemannian Geometry. 9. Riemannian Curvature. 10. Spaces of Zero Curvature. 11. Tensors in Differential Geometry. 12. Tensors in Mechanics. 13. Tensors in Special Relativity. 14. Tensors Without Coordinates. 15. Introduction to Tensor Manifolds.
David C. Kay, Ph.D. is a professor and chairman of mathematics at the University of North Carolina at Asheville. Formerly he taught in the graduate program at the University of Oklahoma for 17 years. He is the author of more than 30 articles in the areas of distance geometry, convexity theory, and related functional analysis.