Differential Geometry
3
In person
MWF 11:00-11:50 A.M.
Wachman 406
Wachman 512
MW 1:30-2:30
F 10:00-10:55
Tapp, Kristopher. Differential Geometry of Curves and Surfaces. Springer, 2016.
Midterm exams: 20% each
Final exam: 30%
Homework: 20%
Participation: 10%
Calculus I-III and Linear Algebra.
1. To work with curves and compute their invariants.
2. To work with surfaces and compute their invariants.
3. To prove theorems relating to curves and surfaces, in particular, the fundamental theorem for space curves, Gauss' Theorem Egregium, and The Gauss-Bonnet Theorem.
4. To master the basic differential geometry of curves and surfaces to a point where the student is then ready for study of higher dimensional manifolds and Riemannian Geometry.
5. To build mathematical maturity; to be able to independently explore differential geometric concepts and problems.
We will apply the concepts of calculus and linear algebra to study curves and surfaces in R^3.
Differential Geometry of Curves: Curves, Curvature and Torsion, Frenet Equations, Fundamental Theorem of Space Curves. Differential Geometry of Surfaces: Surfaces, Gauss Map, Normal Curvature, Gauss and Mean Curvatures, Theorem Egregium, Geodesics, Parallel Transport, Gauss-Bonnet Theorem.
Test 1 - Wed, February 11th, (in class).
Test 2 - Mon, March 30, (in class).
Final Exam - Apr 28-May 5 (TBA).
Attendance is required. Students who miss more than 6 classes without an excuse will have their grades lowered by one notch (e.g., from B to B-). Those who miss more than 12 classes without an excuse will have their grades lowered by two notches, etc.
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Homework will be assigned throughout the class and will be graded on completion, correctness, and presentation. Homework will count for 20% of your final grade. Points will be deducted for late homework.
Homework rules:
1) Use standard size paper.
2) Staple multiple pages.
3) Remove kadoobies.
4) Put your name, date, and homework number at the top.
5) Skip a space between each problem.
6) Clearly number each problem.
7) Write the problem on which you are working. Show all steps.