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Introduction to Tensor Analysis and the Calculus of Moving Surfaces


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Table of Contents

Preface.- Why Tensor Calculus?.- 1. Rules of the Game.- 2. Coordinate Systems and the Role of Tensor Calculus.- 3. Change of Coordinates.- 4. Tensor Description of Euclidean Spaces.- 5. The Tensor Property.- 6. Covariant Differentiation.- 7. Determinants and the Levi-Civita Symbol.- 8. Tensor Description of Surfaces.- 9. Covariant Derivative of Tensors with Surface Indices.- 10. The Curvature Tensor.- 11. Covariant Derivative of Tensors with Spatial Indices.- 12. Integration and Gauss's Theorem.- 13. Intrinsic Features of Embedded Surfaces.- 14. Further Topics in Differential Geometry.- 15. Classical Problems in the Calculus of Variations.- 16. Equations of Classical Mechanics.- 17. Equations of Continuum Mechanics.- 18. Einstein's Theory of Relativity.- 19. The Rules of Calculus of Moving Surfaces.- 20. Applications of the Calculus of Moving Surfaces.

About the Author

Pavel Grinfeld is currently a professor of mathematics at Drexel University, teaching courses in linear algebra, tensor analysis, numerical computation, and financial mathematics. Drexel is interested in recording Grinfeld's lectures on tensor calculus and his course is becoming increasingly popular. Visit Professor Grinfeld's series of lectures on tensor calculus on YouTube's playlist: http://bit.ly/1lc2JiY http://bit.ly/1lc2JiY Also view the author's Forum/Errata/Solution Manual (Coming soon): http://bit.ly/1nerfEfThe author has published in a number of journals including 'Journal of Geometry and Symmetry in Physics' and 'Numerical Functional Analysis and Optimization'. Grinfeld received his PhD from MIT under Gilbert Strang.


From the book reviews:"The textbook is meant for advanced undergraduate and graduate audiences. It is a common language among scientists and can help students from technical fields see their respective fields in a new and exiting way." (Maido Rahula, zbMATH, Vol. 1300, 2015)

"This book attempts to give careful attention to the advice of both Cartan and Weyl and to present a clear geometric picture along with an effective and elegant analytical technique ... . it should be emphasized that this book deepens its readers' understanding of vector calculus, differential geometry, and related subjects in applied mathematics. Both undergraduate and graduate students have a chance to take a fresh look at previously learned material through the prism of tensor calculus." (Andrew Bucki, Mathematical Reviews, November, 2014)

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