Tensor Analysis with Applications

Tensor Analysis with Applications

James Clerk Maxwell

Tensor Analysis with Applications
Fall 2017
Instructor: Barry Jessup

Welcome to the Mat 4183 home page. Here's a copy of the course outline.
Einstein on a bad hair day

ANNOUNCEMENTS (as of 19-Dec-2017.)

Here are my partial solutions to the final exam. If you see any more errors and/or typos, please let me know. Thanks to Dene for finding a couple already.
Happy holidays!
Here are my partial solutions to the assignment 3.I you require more details, please see me. I hope to have your assignments (#3) marked by FridayÉ
Here is the Assignment 4, which is due on Friday 1-Dec. at 4pm.
Here is the fifth and final instalment of suggested exercises. Note: some question numbers may have changed.
The following are a couple of articles which give some geometric and physical interpretations of the tensors we will discuss in the last 3 lectures. (In class we will present some details only for the Riemann tensor).
- "The Meaning of Einstein's Equation" by J. Baez and E. Bunn (2006). In general, I find anything co-written by Baez to be quite readable and interesting.
- "Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature" by L. Loveridge (2016).
Here is the final version of Assignment 3. Note that E:90 (c) has been amended. Assignment 3 is due on Wednesday 22-Nov. at 6:30pm.
Here are the gritty details of the check on the definition of the exterior derivative for those amongst you who may have suspected me of some using smoke and mirrors on Wednesday.
Here is the fourth instalment of suggested exercises. Note: some question numbers may have changed.
Here is a link that shows (in several ways) that S^2 x R^2 and TS^2 are not even homeomorphic. The proofs are not elementary; the last might be accessible to those with some topology who've also heard of the fundamental group. In any case, some algebraic topology is used in each case! (Neat stuff, algebraic topology.)
Here is the fourth instalment of suggested exercises. Note: some question numbers may have changed, and there's material there we haven't covered yet.
Here are my partial solutions to the mid-term.
Here is the third instalment of suggested exercises. Note: some question numbers may have changed.
Here are partial solutions for Assignment 2.
Here are some details of notes on the lecture of 13-Oct. regarding the confusion I tried to sow.
Please read them.
And here are some notes on a topic I didn't want to spend class time on.
Please read them.
Here is the second instalment of suggested exercises. Note: some question numbers may have changed.
Here is a the final version of Assignment 2.
Here are partial solutions for Assignment 1.
Here is Assignment 1.
Effective 17-Sep-2017, my regular office hours will be Wednesdays 3:00-4:00pm and 5:30-6:30pm, Fridays 2:30-4:00pm, or by special appointment, until the end of classes this term (excluding study week).
Here is the first instalment of suggested exercises.