Dear Colleagues,

We continue our Colloquium in the Math Department.

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Dr. Peter Groves

Department of Physics, Geology, and Astronomy

University of Tennessee at Chattanooga

Wednesday, February 2, EMCS 218, 3:00 pm.

Use of the Covariant Derivative in Physics

Abstract. In Calculus, you learn about "total derivatives" and "partial
derivatives". It turns out that the partial derivative is very important in
describing phenomena in everyday physics. In Einstein's General Relativity
(GR), however, one deals with "curved space", and one must learn how to
define a derivative on such a curved space. Once defined, this derivative is
called the "covariant derivative", and is essential to the understanding of
GR, as well as the understanding of even more general theories (for
instance, theories that attempt to unify gravitation and quantum mechanics).

A relatively low level introduction will be given to curvature, and then the
form of the covariant derivative (of a vector) will be derived. This lecture
will be most interesting to math and physics students who have some
knowledge or experience with calculus. As a matter of fact, since the method
of curved spaces has also been applied to material science, engineering
students who have had some calculus could also benefit from the talk.

All students majoring in Math, Physics, and Engineering, as well as faculty
who use methods of Calculus in their courses, are invited.

Important remark. We have Room 218 instead of our usual 422.

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Boris P Belinskiy

Department of Mathematics, Dept. 6956

University of Tennessee at Chattanooga

Ph. (423) 425-4748