A Collection of expository notes on various
mathematical topics.

- The Method of Undetermined
Coefficients and the Shifting Rule [PDF]

The most efficient way of doing the method of undetermined coefficients for linear, constant coefficient,

ordinary differential equations. Suitable for undergraduate ODE courses.

- Change of Basis and All of That
[PDF]

Change of basis in vector spaces, matries of linear transformations with respect to arbitrary bases.

Suitable for a first course in Linear Algebra.

- Notes on Principal Bundles,
Connections and Homogenous Spaces [PDF]

Notes to accompany talks in the Geometry Seminar at Texas Tech in Spring 2009. Updated on

a regular basis. Assumes some familarity with differential geometry and connections on principal

bundles.

Last Updated:04/04/07