MATHEMATICS 563 A1: Introduction to Differential Geometry
Spring 1999
Instructor: Takashi Kimura
Lectures: MWF 1:00-2:00, Room TBA
Phone: 353-1486
Office: MCS 234
Text:Differential Geometry and Its Applications, by
John Oprea, ISBN 0-13-340738-1, Prentice-Hall, 1997.
Office Hours: TBA
Class Web Page: http://math.bu.edu/people/kimura/Spring99/563/index.html
Content: Geometry is the study of objects such as lines and
surfaces as well as their higher dimensional analogs. Differential
geometry is an application of the ideas from calculus to characterize
geometric objects. An example of a question which differential geometry
addresses is, for example, ``What is the proper notion of the curvature of a
surface?'' This subject is an active area of research and has various
applications in science and engineering, e.g. computer graphics,
Einstein's theory of gravitation (general relativity), and so forth. We
shall also be using the computer algebra package Maple to help visualize
these geometric objects as well as to help perform algebraic
manipulations. Maple is available on the ACS UNIX machines in the computer
room in the basement of the Math/Computer Science Building.
Prerequisites: The material in the course is nontrivial so
please make sure that you satisfy the prerequesites. The prerequisites to
this course are multivariate calculus and some linear algebra. A knowledge
of analysis or topology is useful but is not necessary. We will introduce
these ideas as necessary. Some knowledge of Maple will also be useful
although we will introduce this in class.
Homework: Generally, homework will be assigned on a weekly basis
and will be due the following week. Late homework will not be
accepted. Students may discuss homework with each other (and are encouraged
to do so) but all written work must be prepared independently.
Exams: There will be a take home midterm and a take home final.
Grades: Your final grade is determined by three categories - the
exams, the homework, and the final. Grades are based upon the formula: