MATH 209, Manifolds II. (Mostly Differential forms.) Winter 2020. U.C. Santa Cruz.
Syllabus and Lecture Outline
Homework Assignments
Texts
:
Exterior Differential Systems
by Bryant, Chern, Gardner and Griffiths. Particularly chapter 1.
Bill Burke's Div, Grad, Curl are Dead,
Basics of forms; intuitive discussion. Computationally direct and useful
``Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach'' - by John H. Hubbard and Barbara Burke Hubbard; esp on forms, starting p. 500.
Jack Lee's `Intro to Smooth manifolds'' - the traditional text used here over the last 10 years or so.
Much too wordy. Does most of what we need.
other recommended texts - Spivak; Singer-Thorpe; Cartan.
If you read French: Weil Formes différentielles extérieure. The bulk of our whole course in 17 pages.
or Cartan
Leçons sur les Invariantes Intégraux.
Homework Solutions
Lectures
good references
REMAINING CLASS LECTURE SCHEDULE
pages from Lee
pages from Abraham-Marsden
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Recommended Wiki sites
Glossary
Swann's theorem
(vector bundles as modules)
Differential Forms
Riemannian metrics
topology of manifolds
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Links, OTHER SITES:
