This schedule is tentative. It will get more accurate as the semester
progresses. No week's topics should be taken as final until the homework
is linked.
 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. Non-Unit 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 Mid-Semester 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 Gauss-Bonnet 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 Gauss-Bonnet Theorem.
|
Week #15:
Apr 26 - 30
Homework
|
6.7. Application of Gauss-Bonnet.
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.
|
Display a 
