MA 229 :Calculus on Manifolds, Feb 2021

Basic Information

Class: Online on MS teams (Please send me an email if you are not a part of IISc but would still like to attend the course).

Instructor: Ved Datar

Email: vv lastname at, no spaces

Office hours: Fridays 11:00-12:00PM, or by appointment (only if you have another class during office hours). Office hours will be on MS teams

TA: Kartick Ghosh. He will be a grader for this course, but I will also request him to conduct a weekly office hour to help you with any questions you might have.

Textbooks: Michael Spivaks, Calculus on Manifolds , Addison Wesley.

John Milnor, Topology from a differentiable viewpoint, Princeton University Press.

Pre-requisites: MA 221

Topics to be covered: Inverse and Implicit function theorems, regular vs critical values, Lagrange multipliers, manifolds in R^n, tangent spaces, derivative of funtions between manifolds, Sard's theorem, degree theory, Integration on manifolds, Stokes' theorem, De Rham cohomology

Grade Distribution

Homeworks - 20%, Midterms - 30%, Final - 50%

There will be 6 homeworks each worth 20 points. The best five will be counted towards the grade. Assignments will be posted on MS teams. Late submission of homework will be penalized at the rate of 2 points per hour of delay. Clearly a 10 hour delay will result in zero points for that assignment.

There will be one midterm of 60 points each and a final exam of 100 points. To pass the class, you have to take the final exam.

Tentative schedule, homeworks and lecture notes

Number Date Topic Homework Notes
1 M 22/02 Introduction to the course, topology of R^n
2 W 24/02 Derivative as linear map
3 F 26/02 Inverse and Implicit function theorems

Last modified: Sun Feb 21 10:27:05 IST 2021