M375T: Multivariable Analysis

Announcements

I am posting projects below as I receive them. I also posted a reading on integration on manifolds.

Basic Information

Professor: Dan Freed, RLM 9.162

Office Hours: Tuesdays 2:00-3:00, Wednesdays 2:00-3:00

For more details, see the First Day Handout.

Final Projects

Abraham Frei-Pearson on Second order differential equations and Sturm-Liouville value problems

Maggie Miller on Minimal surfaces of revolution

Jacob Pollard on An introduction to the calculus of variations and the Brachistochrone Problem

Homework

Projects

General description of the project assignment.

Suggested projects, but keep in mind that you are encouraged to invent your own.

Grade sheet for the projects.

Readings

A brief history of linear algebra

A quick reminder about sets and functions (from Hoffman-Kunze's Linear Algebra)

Vector spaces (Notes by Peter Cameron)

Linear maps (Notes by Peter Cameron)

Wikipedia entry on Stefan Banach

Norms on vector spaces (from Loomis-Sternberg's Advanced Calculus)

Review of metric spaces and completeness (from Loomis-Sternberg's Advanced Calculus)

Handout on the chain rule and Lagrange multipliers

Handout on the inverse and implicit function theorems

Handout on the second differential, its symmetry and the second derivative test

Old notes on affine spaces and spacetime

Informal text on differential forms and exterior differentiation (by Steven Weintraub)

Integration theory (by Loomis and Sternberg)

Integration on manifolds (by Spivak)

Tests

Solutions to Test #1

Solutions to Test #2