Below is a list of the topics covered in this course with the corresponding sections of the book and supplement. Please note that some deviations might be necessary.
(Week 1) Sec. 1.1, 1.2: Parametrized curves in ℝ3, Reparametrization by arclength
(Week 2) Sec. 1.3, 1.4: Frenet formulas, curvature and torsion, Frenet formulas for general parametrizations
(Week 3) Sec. 1.5, 1.6: Applications of Frenet formulas, The isoperimetric inequality
(Week 4) Sec. 2.1, 2.2: Surfaces in ℝ3, Tangent plane, covariant derivative, shape operator
(Week 5) Sec. 2.3, 2.4: Linear algebra and the shape operator, Normal and principal curvatures
(Week 6) Sec. 3.1, 3.2: Gaussian and mean curvatures, Computations with metric coefficients
(Week 7) Sec. 3.3, 3.4: Surfaces of revolution, Gauss' Theorem Egregium
(Week 8) Sec. 3.5, 5.1: Global theorems about curvature, Geodesics, geodesic curvature
(Week 9) Sec. 5.2, 5.5: Geodesic differential equations, examples of geodesics, Isometries