In addition to the required textbooks, this course includes Supplemental Course Notes and some Notes on Multi-linear Algebra.
Supplemental Course Notes
Introduction (PDF)
Sard's Theorem (PDF)
The Poincare Lemma for Rectangles (PDF)
The Poincare Lemma for Open Subsets of Rn (PDF)
Proper Mappings (PDF)
The Change of Variables Formula (PDF)
The Degree of a Differentiable Mapping (PDF)
Notes on Multi-linear Algebra
Linear Algebra (PDF)
Tensors (PDF)
Alternating k-Tensors (PDF)
The Space, Λk(V*) (PDF)
The Wedge Product (PDF)
The Pull-back Operation on Λk (PDF)