CDS 102: The Geometry of Nonlinear Systems.

Instructor

Herbert K. Struemper, 135A Steele
herb@cds.caltech.edu
Office Hours: Mo 4-5 pm, Tu 3-4 pm, We 3-4 pm.

Teaching Assistant

Yong Wang, 0021 Thomas
yongwang@cco.caltech.edu
Office Hours: TBA

This course is an introduction to basic differential geometry, oriented towards applications in control and dynamical systems. Topics include:

• Motivation for Geometric Methods
• Introduction to Topological Spaces
• Manifolds, Mappings, Submanifolds
• Tangent Vectors, Tangent Space, Tangent Mappings, Tangent Bundle
• Vector Fields, Lie Brackets, Lie Algebras
• Distributions, Frobenius's Theorem
• Lie Groups and Lie Algebras
• Differential Forms, Exterior Algebra
• Integration on Manifolds

Announcements: none so far

Homework Assignments (ps-files):

Homework 1: Topological Spaces

Homework 2: Manifolds, Mappings

Homework 3: Tangent Space, Tangent Bundle

Homework 4: Lie brackets, Distributions, Frobenius Theorem

Homework 5: Lie Groups

Homework 6: Covector Fields

Homework 7: Differential Forms

Homework 8: Exterior Derivative

Homework 9: Poincare Lemma, Integration on Manifolds, Stokes' Theorem