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.