The texts we will be referring to are as follows :
1. Munkres, Analysis on manifolds (Primary text).
2. Spivak, Calculus on manifolds.
3. Rudin, Principle of Mathematical Analysis.
4. J. H. Hubbard and B.B. Hubbard, Vector Calculus, Linear algebra and differential forms.
The course description (along with prerequisites) can be found on this webpage. Please join the MS Team (the link will be on the intranet).
Instructor:
Vamsi Pritham Pingali, vamsipingali@iisc.ac.in.
Office : N23 in the mathematics building.
Office Hours : By appointment.
Classroom and timings : LH4, Tue, Thu 23:30
Teaching Assistants : Arindam Mandal (arindamm@iisc.ac.in)
Tutorials : Saturdays, 1112.
The Grading policy: QuizzesbasedonHomework (20%)  A quiz based on (but not identically the same as) the HW will be conducted by the TA during tutorial session every week or so (the best n1 out of n such quizzes will be considered for averaging), Midterm (30%), and Final (50%).
Exams:
The Midterm shall be held on 20 Sept (Tue) from 24 in LH4. The syllabus is everything until (and including) Lagrange's multipliers and the injective derivative theorem (that is, all the lectures, until Sept 16).
The Final shall be held on 6 Dec (Tue) from 25 in LH4. The syllabus is everything taught in the course.
Ethics: Read the information on the
IISc student ethics page. In short, cheating is a silly thing. Don't do
it.
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 Aug to 7 Aug 
Review of linear algebra (Tuesday notes), Review of the topology of Euclidean space (Thursday notes) 
2 
8 Aug to 14 Aug 
No class on Tuesday, Differentiability (Thursday notes) 
3 
15 Aug to 21 Aug 
C^1 implies differentiability (Tuesday notes), Properties of derivatives (Thursday notes) 
4 
22 Aug to 28 Aug 
Chain rule (Tuesday notes), Clairaut's theorem and applications of the chain rule (Thursday notes) 
5 
29 Aug to 4 Sep 
Inverse function theorem (Tuesday notes, Thursday notes) 
6 
5 Sep to 11 Sep 
Implicit function theorem (Tuesday notes, Thursday notes) 
7 
12 Sep to 18 Sep 
Global extrema (Tuesday notes), Lagrange's multipliers (Thursday notes) 
8 
19 Sep to 25 Sep 
Midterm week (Midterm on Sept 20) 
9 
25 Sep to 2 Oct 
Manifolds, Taylor's theorem in one variable (Tuesday notes), Taylor's theorem in multivariable calculus (Thursday notes) 
10 
4 Oct to 9 Oct 
Definition of Riemann integration (Tuesday notes), Measure zero and Lebesgue's theorem (Thursday notes) 
11 
10 Oct to 16 Oct 
Fubini's theorem (Tuesday notes), Rectifiable sets and Improper integrals (Thursday notes) 
12 
17 Oct to 23 Oct 
Partitions of unity (Tuesday notes), Change of variables (Thursday notes) 
13 
24 Oct to 30 Oct 
Volumes of parametrised manifolds, definition of manifoldswithboundary (Tuesday notes), Integration of functions over manifoldswithboundary (Thursday notes) 
14 
31 Oct to 6 Nov 
No class on Tuesday, Orientability of manifolds (Thursday notes) 
15 
7 Nov to 13 Nov 
No class on Tuesday, Wedge product done naively (Thursday notes) 
16 
14 Nov to 20 Nov 
Wedge product done correctly, Exterior derivative (Tuesday notes), Pullback, integrating forms in R^n, smooth forms on manifolds (Thursday notes) 
17 
21 Nov to 27 Nov 
Generalised Stokes' theorem (Tuesday notes) 
Week 
Homework (subject to changes; please check regularly) 
1 
No HW 
2 

3 

4 

5 

6 

7 

8 
Midterm week 
9 

10 

11 

12 

13 

14 
HW 12 (Quiz on 14th Nov 2022, This HW has been corrected. Sorry for the mistake!) 
15 
No HW 
16 
No HW 
17 
No HW 