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 :
Vamsi Pritham Pingali, vamsipingali@iisc.ac.in
Classroom and timings : LH-4, Tu, Thu 3:30-5
Teaching Assistant: Aashirwad N. Ballal
Tutorials: Wed from 4-5
The Grading policy : 20% for the HW, 30% for the Midterm, and 50% for the Final.
Exams:
The Midterm shall be held on Feb 22 (Thur) 3-5 PM in LH-4. The syllabus is everything taught until then (including all of Harish's lectures).
The Final shall be held on April 29 (Mon) 2-5 PM in LH-4. 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 |
1 Jan - 7 Jan |
Logistics, review of multivariable calculus - continuity, differentiability, chain rule (Tuesday notes), review of multivariable calculus - Clairaut's theorem, Taylor's theorem, second derivative test (Thursday notes) |
|
2 |
8 Jan - 14 Jan |
Bump functions, Inverse function theorem (Tuesday notes), Implicit function theorem and Lagrange's multipliers (Thursday notes) |
|
3 |
15 Jan - 21 Jan |
Smooth manifolds - definition and examples (Tuesday notes), Manifolds-with-boundary (Thursday notes) |
|
4 |
22 Jan - 28 Jan |
Smooth functions on manifolds (Tuesday notes), Partitions-of-unity (Thursday notes) |
|
5 |
29 Jan - 4 Feb |
Tangent spaces (Tuesday notes), Thursday-taught by Harish |
|
6 |
5 Feb - 11 Feb |
Harish's lectures |
|
7 |
6 Feb - 18 Feb |
Harish's lectures (My take on the material taught by him) |
|
8 |
19 Feb - 25 Feb |
Midterm week |
|
9 |
26 Feb - 3 Mar |
Regular value theorem, definition of smooth vector fields (Tuesday notes), Tangent bundle and vector bundles (Thursday notes) |
|
10 |
4 Mar - 10 Mar |
Flows of vector fields (Tuesday notes), Flows, diffeomorphisms, and the Lie bracket (Thursday notes) |
|
11 |
11 Mar - 17 Mar |
One-forms and tensors (Tuesday notes), Tensor products, symmetric and alternating tensors, and Tensor bundles (Thursday notes) |
|
12 |
18 Mar - 25 Mar |
Alternating tensors and the wedge product (Tuesday notes), Wedge products and the exterior derivative(Thursday notes) |
|
13 |
26 Mar - 1 Apr |
Exterior derivative on manifolds and Integration in Rn (Tuesday notes), Orientability (Thursday notes) |
|
14 |
2 Apr - 8 Apr |
Orientation of hypersurfaces and boundaries (Tuesday notes), Integration on manifolds (Thursday notes) |
|
15 |
9 Apr - 15 Apr |
Stokes' theorem (Tuesday notes) |
|
Week |
HW to be submitted on |
Homework (subject to changes; please check regularly) |
|
1 |
12 Jan |
|
|
2 |
31 Jan |
|
|
4 |
7 Feb |
|
|
5 |
14 Feb |
|
|
10 |
8 Mar |
|
|
11 |
15 Mar |
|
|
12 |
29 Mar |
|
|
13 |
5 Apr |