Differential Geometry with Applications

Professor Weiqing Gu
Fall 2023

Readings should be done before class. All resources (including lecture slides, homework, starter files, hw solution, articles) can be found under the Resources tab.

The topics to cover and the readings to be assigned are subject to change.

Date Topics Homework
Review linear algebra and overview of applications in computer vision (No class 9/4-Holiday)
Aug 28		 Notes
Curves and Applications
Sep 11		 Notes Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due
Due:
Homework 1
Cuvature, torsion and the frenet frame
Sep 18		 Notes Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due
Due:
Midterm project proposal is due at 11:59pm Homework 2
Surfaces and applications
Sep 25		 Notes Slides Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due
Due:
Homework 3
Change of parameters; Differential functions on surfaces and introduction to manifold
Oct 2		 Notes Slides Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due
Due:
Homework 4
Tangent plane, the differential of a map, first fundamental form
Oct 9		 Notes
Slides 		Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due
Due:
Homework 5
Fall break. No class
Oct 16
In class presentations
Oct 23		 Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due

Due:
Midterm report due at 11:59pm
Definition of Gauss map and fundamental properties. Then curvatures
Oct 30		 Slides Notes Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due

Due:
Homework 6
Tensor, Differential forms and applications
Nov 6		 Slides
Notes 		Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due

Due:
Homework 7
Isometries and conformal maps
Nov 13		 Slides
Notes 		Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due
Due:
Homework 8
Parallel transpot and geodesics
Nov 20		 Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due
Discrete Differential Geometry
Nov 27		 Notes Read:
Reading sections from Do Carmo specified in your homework assignment. Summary for computer vision book due
Final Project presentations
Dec 4		 Due:
Draft of final report is due at 11:59pm
No class. Final Report due
Dec 11		 Due:
Final report is due at 11:59pm