UM 102 - Analysis and Linear Algebra - 2 - Spring 2021 - Vamsi Pingali

The texts we will be referring to are as follows :
1. Apostol, Calculus 2 (primary text).
2. Apostol, Calculus 1 (for ODE).
3. Hirsch, Smale, and Devaney, Differential Equations, Dynamical Systems, and An Introduction to Chaos (for ODE).

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

Instructor : Vamsi Pritham Pingali,

Office : N23 in the mathematics building.

Office Hours : By appointment.

Classroom and timings : TBA on Mon, Wed, Fri 9:30 - 10:30. The classes will be online at least until March 31. I shall post pre-recorded lectures on YouTube as well as on the Microsoft Teams group. The links will be provided on the channel or email.

Tutorials : The sessions will be held on Thur from 8:30 AM - 9:30 AM. At least until Mar 31, they will be held online on MS Teams.

Teaching Assistants (Their email addresses have to be completed with :
1. Deb Kumar Giri : debkumarg (You are assigned to Deb if your student ID number leaves a remainder of 0 when divided by 5)
2. Gouranga Mallik : gourangam (You are assigned to Gouranga if your student ID number leaves a remainder of 1 when divided by 5)
3. Mihir Sheth : mihirsheth (You are assigned to Mihir if your student ID number leaves a remainder of 2 when divided by 5)
4. Sumana Hatui : sumanahatui (You are assigned to Sumana if your student ID number leaves a remainder of 3 when divided by 5)
5. Vijay Kumar : vijayak (You are assigned to Vijay if your student ID number leaves a remainder of 4 when divided by 5)

Online classes will be held at least until March 31st. To this end, please join the sharepoint group UM 102 2021 on Microsoft Office. Moreover, I shall upload lectures on youtube as well as on Microsoft teams. I shall send you the links on the Team channel chat and/or email.

The Grading policy : 40% for the Quizzes based on Homeworks, 30% for the Midterm, and 30% for the Final.

Exams :

The Midterm shall be held on 1st May from 9:30 AM to 12:30 PM (including buffer time for submitting answers) (the syllabus is: All of linear algebra (Apostol Volume 2: Chapter 1,2,3 (only the sections from 3.1 to 3.14), Chapter 4, Chapter 5 (only the sections from 5.1 to 5.10)) and ODE (Apostol Volume 1: Chapter 8 (only the sections from 8.1 to 8.18 and section 8.23), Hirsch, Smale, and Devaney (Chapter 2)).

The Final shall be held on 30 June from 9:30 AM to 12:45 PM (including buffer time for submitting answers. NO LATE SUBMISSIONS!) (the syllabus is everything not covered in the Midterm: Multivariable calculus (Apostol Volume 2: Chapter 8, Chapter 9 (9.10, 9.11, 9.12, 9.14), Chapter 10 (10.1 to 10.14), Chapter 11 (11.1 to 11.14, 11.19,11.20, 11.26, 11.31, 11.32), Chapter 12 (12.1 to 12.14, 12.19., 12.20)))

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.)



 Syllabus covered


8 Mar - 14 Mar

Logistics, Review of Vector Spaces (Monday slides), Rank-Nullity theorem (Wednesday slides), Inner products and the Cauchy-Schwarz inequality (Friday slides)


15 Mar - 21 Mar

Orthogonality and Gram-Schmidt (Monday slides), Orthogonal complements, Approximation theorem (Wednesday slides), Inverses, Systems of equations (Friday slides)


22 Mar - 28 Mar

Gauss-Jordan elimination (Monday slides), Inverses of matrices (Wednesday slides), Determinants (Friday slides)


29 Mar - 4 Apr

Determinant functions and their uniqueness(Monday slides), Computing determinants, invertibility, and similar matrices (Wednesday slides), No class on Friday


5 Apr - 11 Apr

Eigenvalues and eigenvectors (Monday slides), Computing eigenvalues and eigenvectors (Wednesday slides), The spectral theorem (Friday slides)


12 Apr - 18 Apr

First-order Linear systems of Ordinary Differential Equations (Monday slides), No class on Wednesday, Second order homogeneous ODE with constant coefficients (Friday slides)


19 Apr - 25 Apr

(Monday slides) Variation of parameters - Please see this document for a correction: Erratum, (Wednesday slides) Open sets in higher dimensions, Limits and continuity (Friday slides)


26 Apr - 2 May

No classes (Midterm week)


3 May - 9 May

(Monday slides) Limit and continuity laws, (Wednesday slides) Directional derivatives, No class on Friday.


10 May - 16 May

(Monday slides) Differentiability in the multivariable sense, (Wednesday slides) A digression into limits and a sufficient condition for differentiability, No class on Friday because of a public holiday


17 May - 23 May

(Monday slides) The chain rule, (Wednesday slides) Differentiability of vector fields, (Friday slides) Chain rule for vector fields, second derivative test in one-variable calculus


24 May - 30 May

(Monday slides) Local and global, Wednesday is a public holiday, (Friday slides) Second derivative test, Line integrals


31 May - 6 June

(Monday slides) Double integrals and Fubini's theorem, (Wednesday slides) Green's theorem, (Friday slides) Change of variables


7 June - 13 June

(Monday slides) Parametrised surfaces, (Wednesday slides) Stokes' theorem, (Friday slides) Divergence theorem


14 June - 20 June

(Monday slides) Lagrange's multipliers

HW/Quiz : Making HW great again.


 Quiz to be conducted on

 Homework (subject to changes; please check regularly)


11 Mar

No HW/Quiz


18 Mar

HW 1


25 Mar

HW 2


1 Apr

HW 3


8 Apr

HW 4


15 Apr

HW 5


22 Apr

HW 6


29 Apr

No HW (Midterm week)


6 May



13 May

HW 7


20 May

HW 8


27 May

HW 9


3 June

HW 10


10 June

HW 11