MA 229/MA 235-Calculus on Manifolds/Introduction to Differentiable Manifolds Spring 2022 - Ved V. Datar, Vamsi Pritham Pingali, Harish Seshadri


The texts we will be referring to are as follows :
1. John Lee, Introduction to Smooth Manifolds (primary text).
2. Frank Warner, Foundations of Differentiable Manifolds and Lie Groups.

The course description (along with pre-requisites) can be found on this webpage.

Instructors : Ved V. Datar, vvdatar@iisc.ac.in, Vamsi Pritham Pingali, vamsipingali@iisc.ac.in and Harish Seshadri, harish@iisc.ac.in..

Classroom and timings : LH4, Tue, Thur 2:00 pm - 3:30 pm. The classes will be online at least until Jan 31.

Teaching Assistant: Ramesh Mete (rameshmete@iisc.ac.in)

The Grading policy : 25% for the HW, 35% for the Midterm, and 40% for the Final.

Exams:

The Midterm shall be held on TBA.

The Final shall be held on TBA.

Ethics: Read the information on the IISc student ethics page. In short, cheating is a silly thing. Don't do it. As for the quizzes based on HW, write them up on your own. You are NOT allowed to discuss them amongst yourselves.

Here is the tentative schedule. (It is subject to changes and hence visiting this webpage regularly is one of the best ideas in the history of best ideas.)

Week

 Dates

 Syllabus covered

1

3 Jan - 9 Jan

Logistics, review of multivariable calculus (Tuesday slides), A further review of multivariable calculus including first and second derivative tests (Thursday slides)

2

10 Jan - 16 Jan

First and second derivative tests, inverse and implicit function theorems (Tuesday and Thursday slides)

3

17 Jan - 23 Jan

Topological manifolds (Tuesday slides), Smooth manifolds and some examples (Thursday slides)

4

24 Jan - 30Jan

Smooth manifolds-with-boundary, smooth maps (Tuesday slides)



HW : This kids, is how you met your HW.

Week

 HW to be submitted before

 Homework (subject to changes; please check regularly)

1

7 Jan

No HW

2

21 Jan

HW1

3

28 Jan

HW2