Because of ChatGPT and other AI softwares the homeworks will not be graded. However, I will assign exercises weekly. It is completely voluntary to do them or not.
Sept 1
Sept 8
Sept 15
Sept 22
Sept 29
Oct 6
Oct 27
Nov 3
Nov 10
Nov 17
Nov 24
Dec 1
Dec 8
Derivatives, Directional Derivatives
Mean Value Theorem, Inverse and Implicit Function Theorems
Wedge product
Parametrized Curves
Local theory of Curves, 3D and 2D curves
Surfaces, change of variables
Tangent spaces, First fundamental form
Surface area, Orientation
Second fundamental form
H, K, Gauss map in local coordinates, Isometries
Theorem of Gauss, Euler-Lagrange
Geometry of the sphere
Manifolds in general