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 prerequisites) can be found on this webpage.
Instructors :
Vamsi Pritham Pingali, vamsipingali@iisc.ac.in
Classroom and timings : LH4, Tu, Thu 3:305
Teaching Assistant: Aashirwad N. Ballal
Tutorials: Wed from 45
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) 35 PM in LH4. The syllabus is everything taught until then (including all of Harish's lectures).
The Final shall be held on TBA. 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), Manifoldswithboundary (Thursday notes) 
4 
22 Jan  28 Jan 
Smooth functions on manifolds (Tuesday notes), Partitionsofunity (Thursday notes) 
5 
29 Jan  4 Feb 
Tangent spaces (Tuesday notes), Thursdaytaught 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) 
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 