MTH 434/534: Differential Geometry
Winter 2011

Hotlist:   Announcements,   Books,   Homework.

Tevian Dray

Office hours: MW 10–11:30 AM in Kidder 298A (and by appt)

Phone: 737-5159

Email:

Class Meetings:

MWF 3–3:50 PM in Wngr 304

Required Texts:

Flanders, Differential Forms with Applications to the Physical Sciences

Bishop & Goldberg, Tensor Analysis on Manifolds

Further information about these and other books can be found on the book list.

WARNING: We will only follow the texts rather loosely.

Web Site: http://math.oregonstate.edu/~tevian/onid/MTH434

Check the announcements page frequently.

Course Evaluation:

There will be (roughly) weekly homework (30% of grade), a midterm (30%), and a final (40%).

Course Description:

This course is a self-contained introduction to the many uses of differential forms. This approach emphasizes geometric content in a coordinate independent way; a good analogy is the use of vectors, rather than their components. We will spend some time developing the necessary mathematical tools, as well as applying these tools to concrete examples drawn from the physical sciences. Some applications are:

• conserved currents
• Hamiltonian systems
• Jacobians
• Lagrangians
• Laplacians
• Maxwell's equations
• PDE's
• phase space

We will also discuss other selected topics in tensor analysis.

Prerequisites:

The main prerequisite is a certain amount of scientific maturity, rather than background in a particular area. The only specific requirements are a working knowledge of multivariable calculus and linear algebra.