Math 489: Tensor Calculus
Description: Tensor Calculus is an amazing subject. It is a technique for using Calculus (as you know it) in an organized way. Tensor Calculus provides rules for conducting differential analysis in a physically meaningful way.

I may not have heard of Tensor Calculus prior to visiting this page, but it can make an unexpected difference in your life. May I share with you some feedback that I received from one of the students last year:

This course has completely changed my life. I learned how to derive everything for myself from first principles. Prior to this course, mathematics seemed like a disjoined collection of subject. This course has unified everything for me in a single framework. I now understand multivariate calculus of the linear algebra point of view and I understand linear algebra from a geometric point view and I understand the role that calculus plays in geometry. All of these subjects have become a single family for me, one in which I feel welcome. Before, when I studied mathematics textbooks, I would try as much as possible, to understand the author's point of view. Now, I couldn't care less about the author's point of view. I find myself extracting the essential ideas from the book and reformulating those ideas in my own language. And my own language is now the language of tensors.

Professor:
Pavel Grinfeld
pg@freeboundaries.com
Korman 271
(215)-219-3548
Office Hours: To be determined
Textbooks:
P. Grinfeld
Tensor Calculus
Topics:
1. Euclidean spaces
2. Coordinate systems
3. Tensor notation
4. The tensor property
5. Determinants, Etc
6. Most fundamental objects
7. Covariant differentiation
8. Covariant differentiation continued
9. Integrals in invariant form
10. Embedded surfaces
11. Covariant differentiation
12. Covariant differentiation of object with space indices
13. Gauss's theorem
14. The Riemann-Christoffel tensor
15. Gauss's Theorema Egregium
16. Applications: Calculus of Variations
17. Applications: Quadratic form minimization
18. Applications: Continuum mechanics
Copyright © 2010 by Pavel Grinfeld EMail (215) 219 3548