Math 1140
time/place: Tu-Th 1:00-2:20 in Barus & Holley 158

instuctor: Prof. Rich Schwartz

my office hours: TBA

course description: This is an undergraduate course about real analysis on manifolds. Topics:

• Theorems about differentiation - e.g. Inverse Function Theorem
• smooth manifolds, tangent spaces, vector fields
• exterior algebra and differential forms
• Stokes' theorem on manifolds
• perhaps a bit about de Rham cohomology

Text: Mathematical Analysis by Andrew Browder, Chapters 11-14
Sometimes I will supplement the text with my own notes.

Homework There will be weekly HW assignments,
assigned each Tuesday and collected the following Tuesday.
Click here for the assignments.

Grading
HW: 35 %
Midterm: 25 %
Final: 40 %
Both exams will be take-home exams.

Notes:

• inverse function theorem
• A gap in the Lemma 11.4 in the book
• Defintion of an abstract manifold
• Tangent Space of a Manifold
• Tensor Transformations
• The Poincare Lemma
• The Change of Variables Formula
• Partitions of Unity
• Integrating Functions on Riemannian Manifolds
• The Hodge Star Operator