Instructor: Debra Lewis
Office: 359B Baskin Engineering
Phone: 459-2718
E-mail: lewis at ucsc dot edu
(checked more often than voicemail or gmail)
and/or DebraKLewis at gmail dot com
Office hours: Tuesday 2:30-3:30, Wednesday 2:30-3:30, Friday 12:00-1:00
Course web page: http://people.ucsc.edu/~lewis/Math208
(here)
Introduction to Smooth Manifolds, John M. Lee, Springer.
Possible supplemental texts: An Introduction to Differentiable Manifolds and Riemannian Geometry, Boothby. Topology from a Diffential Viewpoint, Milnor.
Some material on the phase flow and matrix exponential:
The midterm. (11/5/08)
Topics:
Definition of manifolds, tangent bundle, inverse and implicit function theorems, transversality, Sard's theorem and the Whitney embedding theorem, vector fields, flows, and Lie bracket, Frobenius' theorem.
VERY TENTATIVE SCHEDULE
| Monday | Wednesday |
| September 27: Topological and smooth manifolds | September 29: Smooth functions and maps |
| October 4: Tangent vectors and derivations | October 6: Pushforwards, coordinate calculations, and partitions of unity |
| October 11: Submersions, immersions, and embeddings | October 13: Inverse and Implicit Function Theorems |
| October 18: IFT continued and submanifolds | October 20: Level sets and Lie groups |
| October 25: Vector fields and the tangent bundle | October 27: Integral curves and flows |
| November 1: Fundamental flow theorem, existence and uniqueness | November 3: Lie brackets |
| November 8: Distributions and involutivity | November 10: Frobenius' Theorem |
| November 15: Singular points, Sard's Theorem | November 17: Whitney Embedding Theorem |
| November 22: Whitney Approximation Theorem and tubular neighborhoods | November 24: Homotopies and approximations |
| December 4: Additional topics and/or presentations |
COURSE WORK