Differential Geometry of Curves and Surfaces

1. 1. Curves in R2 and R3-Arc Length Lecture Notes Homework
2. 2. Reparametrization of Curves and Closed Curves Lecture Notes Homework
3. 3. Curvature of Curves Lecture Notes Homework
4. 4. Plane Curves Lecture Notes Homework
5. 5. Space Curves and the Frenet Formulas Lecture Notes Homework
6. 6. Simple Closed Curves, the Isoperimetric and Four Vertex Theorems Lecture Notes Homework
7. 7. Surfaces in R3 Lecture Notes Homework
8. 8. Smooth Surfaces Lecture Notes Homework
9. 9. Smooth Maps, Tangent Planes and Derivatives Lecture Notes Homework
10. 10. Level Surfaces and Quadric Surfaces Lecture Notes Homework
11. 11. The First Fundamental Form- Lengths of Curves on Surfaces Lecture Notes Homework
12. 12. The First Fundamental Form- Surface Area Lecture Notes Homework
13. 13. The Second Fundamental Form Lecture Notes Homework
14. 14. The Gauss and Weingarten Maps Lecture Notes Homework
15. 15. Normal Curvature and Geodesic Curvature Lecture Notes Homework
16. 16. Gaussian Curvature and Mean Curvature Lecture Notes Homework
17. 17. Principal Curvatures of a Surface Lecture Notes Homework
18. 18. The Gauss Equations and the Codazzi-Mainardi Equations Lecture Notes Homework
19. 19. The Gauss -Bonnet Theorem Lecture Notes Homework