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 : LH1, Tue, Thur 2:00 pm - 3:30 pm. The classes will be offline (hybrid) from March 1.
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 online on Thur, Feb 24 from 2-4 pm. It will be a live online exam (invigilated). The syllabus will be everything covered until then.
The Final shall be held on Mon, Apr 25 from 2-5 pm. In all likelihood, it will be offline. The syllabus will be everything taught in this course.
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), paracompactness (Thursday slides) |
|
5 |
31 Jan - 6 Feb |
Partitions of unity, derivations on R^n (Tuesday slides), Tangent spaces (Thursday slides) |
|
6 |
7 Feb - 13 Feb |
Alternative definitions of tangent spaces (Tuesday slides), immersions, submersions, and embeddings (Thursday slides) |
|
7 |
14 Feb - 20 Feb |
Whitney embedding, constant rank theorem (Tuesday slides), Submanifolds and Sard's theorem (Thursday slides) |
|
8 |
21 Feb - 27 Feb |
Midterm week (no classes) |
|
9 |
28 Feb - 6 Mar |
Smooth vector fields and the tangent bundle (Tuesday slides), Vector bundles, cotangent bundle (Thursday slides) |
|
10 |
7 Mar - 13 Mar |
Flows of vector fields (Tuesday slides), Lie bracket - motivation (Thursday slides) |
|
11 |
14 Mar - 20 Mar |
Lie brackets, one-forms (Tuesday slides) Tensor products (Thursday slides) |
|
12 |
21 Mar - 27 Mar |
Alternating tensors (Tuesday slides), Wedge product (Thursday slides) |
|
13 |
28 Mar - 3 April |
Exterior derivative (Tuesday slides), Change of variables (Thursday slides) |
|
14 |
4 April - 10 April |
Orientation (Tuesday slides) Integration on manifolds (Tuesday slides) |
|
15 |
11 April - 17 April |
Stokes' theorem (Tuesday slides) |
|
Week |
HW to be submitted before |
Homework (subject to changes; please check regularly) |
|
1 |
7 Jan |
No HW |
|
2 |
14 Jan |
No HW |
|
3 |
21 Jan |
|
|
4 |
28 Jan |
|
|
5 |
4 Feb |
No HW |
|
6 |
9 Feb (Note the unusual day!) |
|
|
7 |
18 Feb |
|
|
8 |
25 Feb |
No HW |
|
9 |
4 Mar |
No HW |
|
10 |
25 Mar |
|
|
11 |
8 Apr |