M 400A : Topics in Mathematics - Differential Geometry

Section: 1

Time:  2:10 - 3 MWF

Meeting Room: EE205 Engrg

Instructor:  Jaak Vilms

Office: E114 Engrg
Phone: 491-5153 (office); 207-1909 (home); 491-6327 (math dept.)
Email: vilms@math.colostate.edu

Office Hours: 3-4 MW, 10-11 RF, also by mutual arr

Text: Lectures on classical differential geometry, 2nd edition, Dover 1988
by Dirk J. Struik

Course Outline:

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General  information:

Course: 3 cr. math elective

Prerequisites:  3rd semester calculus, some linear algebra.

Course objective:

To learn the basics of the differential geometry of curves and surfaces
in 3-space.

For curves the main topics are: arclength, curvature, torsion, Frenet formulas.
For surfaces, they are: 1st and 2nd fundamental forms, curvature,
Christoffel symbols, geodesics, inner geometry.

Material covered:

We will cover most of Chapters 1, 2, 3, and some of Chapter 4 in the text.
In addition, there will be handouts and exercises on some supplemental topics,
such as geometrical transformations, B\'ezier curves, composite curves,
tensor notation.

For those who took M261 at Colorado State, sections 11.7-9 of
Stewart's Calculus are a good introducton to Chapter 1, and section
14.6 to Chapter 2.  We work mostly with vectors and partial derivatives,
but not that much with integrals.
Grading:

Homework:  1/2,  Midterm Exam: 1/4,  Final Exam: 1/4.

Group work (limit 3 persons) is encouraged for *homework*,
and only one paper should be submitted per group.

Sample exams will be given out  before the exams.
The midterm exam is a closed-book test, covering the concepts and
theorems of roughly the first half of the course.  Usually there is
a repeat, capped at 80%, to allow students to improve their grade.
The final exam is an open-book exam, given only once.  It
usually covers only the second half of the course, namely the material
covered after the midterm exam.

Since this is an elective course, the grading is not
intended to be tough.  This means that  those who do all the
work and learn the basic material usually end
up with a good grade.

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Examinations:
There will be a Midterm Exam and a Final Exam, each counting 1/4 of the course grade. Sample exams will be given out before the exams. The midterm exam is a closed-book test, covering the concepts and theorems of roughly the first half of the course. Usually there is a repeat, capped at 80%, to allow students to improve their grade. The final exam is an open-book exam, given only once. It usually covers only the second half of the course, namely the material covered after the midterm exam.

Grading Policy:
Homework: 1/2, Midterm Exam: 1/4, Final Exam: 1/4.
Since this is an elective course, the grading is not intended to be tough. This means that those who do all the work and learn the basic material usually end up with a good grade.