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Department:
MATH
Course Number:
4441
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Every fall semester
The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem
Course Text:
No text
Topic Outline:
- Part (1): Theory of Curves Curves in R^2 and R^3 Velocity, speed, arclength, acceleration Curvature, torsion, the moving trihedron Frenet-Serret equations
- Part (2): Theory of Surfaces Regular surfaces in R^3 First and Second Fundamental Forms, the mean and Gaussian curvatures Gauss-Weingarten equations, Gauss's Theorema Egregium Introduction to Tensors, Their use in the theory of surfaces Intrinsic geometry of surfaces, geodesic curvature, geodesic coordinates, Gauss-Bonnet Theorem