Week #1:
Jan 12  16
Homework

1.1. Introduction.
1.2. Arclength Parametrization.
1.3. Frenet Formulas.

Week #2:
Jan 19  23
Homework

1.4. NonUnit Speed Curves.
1.5. Some Implications of Curvature and Torsion.
Administrative Note: Monday 19 January is Martin Luther King Day.
Class will not meet.

Week #3:
Jan 26  30
Homework

1.6. Green's Theorem and the Isoperimetric Inequality.
2.1. Introduction (Surfaces).
2.2 The Geometry of Surfaces.

Week #4:
Feb 2  8
Homework

2.2 The Geometry of Surfaces.
2.3. The Linear Algebra of Surfaces.
2.4. Normal Curvature.

Week #5:
Feb 9  13
Homework

2.4. Normal Curvature.
DoCarmo 0.2. Differentiable Manifolds

Week #6:
Feb 16  20
Homework

DoCarmo 0.2. Tangent Vectors.
Exam #1 will be given on Wednesday 18 February.
The exam will be held during your regular class time.
Administrative Note: Monday 16 February is Presidents Day. Class will
not be held.

Week #7:
Feb 23  27
Homework

DoCarmo 0.2. Tangent Space.
DoCarmo 0.3, 0.4. Immersions and Embeddings, Orientation
DoCarmo 0.5. Vector Fields; Brackets.

Week #8:
Mar 1  5
Homework

3.1. Introduction (Curvatures).
3.2. Calculating Curvature.
3.3. Surfaces of Revolution.
Administrative note: Friday 5 March is the MidSemester Break.
Class will not meet.

Mar 8  12 
Spring Break! 
Week #9:
Mar 15  19
Homework

3.4. A Formula for Gauss Curvature.
3.5. Some Effects of Curvature(s).
3.6. Surfaces of Delaunay.

Week #10:
Mar 22  26
Homework

5.1. Introduction (Geodesids Metrics and Isometries).
5.2. The Geodesic Equations and the Clairaut Relation.
5.3. A Brief Digression on Completeness.

Week #11:
Mar 29  Apr 2
Homework

5.4. Surfaces not in R3.
5.5. Isometries and Conformal Maps.
.
Exam #2 will be given on Wednesday 31
March.

Week #12:
Apr 5  9
Homework

5.7. An Industrial Application.
6.1. Introduction (Holonomy and the GaussBonnet Theorem).

Week #13:
Apr 12  16
Homework

6.2. The Covarient Derivative Revisited.
6.3. Parallel Vector Fields and Holonomy.
6.4. Foucaults Pendulum.
Administrative Note: Friday 16 April is Spring Carnival. Class will
not meet.

Week #14:
Apr 19  23
Homework

6.5. The Angle Excess Theorem.
6.6. The GaussBonnet Theorem.

Week #15:
Apr 26  30
Homework

6.7. Application of GaussBonnet.
Relativity, Special and Generarl.
The Riemannian Curvature Tensor
Administrative note: Friday 30 April is the last day of class.

Final Exams
May 3  11

The Final Exam will be given as a
take home exam. You may pick the exam up in my office, and return it
to me, or to the main Math Sciences office (WEH 6113). You can make
arrangemtnes with me via email to pick up the exam.
