UM 102 - Analysis and Linear Algebra - 2 - Spring 2022 - 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, vamsipingali@iisc.ac.in.

Office : N23 in the mathematics building.

Office Hours : By appointment.

Classroom and timings : UG building, MWF - 9:30 - 10:30 AM

Tutorials : The sessions will be held on Thurs 8:30 - 9:30 in the tutorial rooms (UG building).

Teaching Assistants (Their email addresses have to be completed with @iisc.ac.in) :
Section 1/A. Aashirwad N. Ballal (aashirwadb)
Section 2/B. Geethika Sebastian (geethikas)
Section 3/C. Mrigendra K (mrigendrak)
Section 4/D. Sivaram P (sivaramp)


The Grading policy: There will be three quizzes out of which the best two (each carrying 10% weightage) will be chosen for grading. The quizzes will be based on the HW problems (which we will be assigned almost every week but will never have to be submitted). The midterm (during April 25-30) will carry 30% and the final (during June 20-25) will carry 50%.

Exams:

Quiz 1 shall be held on April 7 (during the tutorial) . The syllabus is everything until (and including) inverses of matrices (that is, everything covered until (and including) the 1st of April).

Quiz 2 shall be held on May 19 (during the tutorial). The syllabus is ODE (linear systems) and everything we did after the midterm until (and including) 13 May.

Quiz 3 shall be held on June 2 (during the tutorial). The syllabus is everything we did from 16 May to (and including) 27 May, that is, weeks 10 and 11.

The Midterm shall be held on April 27 from 9:30 to 11:30. The syllabus is all of linear algebra (that we covered).

The Final shall be held on June 22 from 9:30 to 12:30. 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

14 March - 20 March

Review of vector spaces, dimension, etc (Monday notes, Wednesday notes) Inner products (Friday notes)

2

21 March - 27 March

Cauchy-Schwarz inequality (Monday notes), Orthogonality (Wednesday notes), Gram-Schmidt (Friday notes)

3

28 March - 3 April

Inverses of linear maps (Monday notes), Gauss-Jordan elimination (Wednesday notes), Inverses (Friday notes)

4

4 April - 10 April

Determinants (Monday notes, Wednesday notes, Friday notes)

5

11 April - 17 April

Determinants (Monday notes), Eigenvalues and Eigenvectors (Wednesday notes), Friday is a holiday

6

18 April - 24 April

Diagonalising matrices (Monday notes), Hermitian and Skew-Hermitian maps/matrices (Wednesday notes), Spectral theorem (Friday notes)

7

25 April - 1 May

Midterm week

8

2 May - 8 May

Monday was a holiday, Linear systems of ODE(Wednesday notes), Limits and continuity for multivariable functions (Friday notes)

9

9 May - 15 May

Limit laws (Monday notes), Directional derivatives (Wednesday notes), Differentiability (Friday notes)

10

16 May - 22 May

Monday was a holiday, C1 implies differentiability (Wednesday notes), Chain rule and level sets(Friday notes)

11

23 May - 29 May

Chain rule for vector fields (Monday notes), Local and global extrema (Wednesday notes), Second derivative test (Friday notes)

12

30 May - 5 Jun

Line integrals (Monday notes), Double integrals over rectangles (Wednesday notes), Double integrals over non-rectangular domains (Friday notes)

13

6 Jun - 12 Jun

Green's theorem (Monday notes), Change of variables formula (Wednesday notes), Parametrised surfaces (Friday notes)

14

13 Jun - 19 Jun

Stokes' theorem (Monday notes), Divergence theorem (Wednesday notes), No class on Friday



HW, taggede le

Week

 Homework (subject to changes; please check regularly)

1

No HW

2

HW 1

3

HW 2

4

HW 3

5

HW 4

6

No HW

7

No HW

8

HW 5

9

HW 6

10

HW 7

11

HW 8

12

No HW

13

HW 9