Class: TuTh, 10:30-12:00AM, Old Physics Building F12
Instructor: Ved Datar
Email: vv lastname at math.iisc.ac.in, no spaces
Office: X05
Tutorial information: Friday, 11:00-12:00.
| Name | Section | Class number |
| Geethika Sebastian | Section A | Tutorial Room 3 (UG building) |
| Manpreet Singh | Section B | F8A (OPB) |
| Rumpa Masanta | Section C | F12 (OPB) |
| Arnabpal | Section D | Tutorial room 1 (UG building) |
| Abhay Jindal | Section E | Tutorial room 2 (UG building) |
Reference books: Tom Apostol, Calculus - II , Wiley, 2ed (Indian edition).
Pre-requisites: UM 101
Topics to be covered: Linear Algebra continued: Inner products and Orthogonality; Determinants; Eigenvalues and Eigenvectors; Diagonalisation of symmetric matrices. Introduction to Ordinary Differential Equations; Linear ODEs and Canonical forms for linear transformations. Multivariable calculus: Functions of several (real) variables, partial and total derivatives; Chain rule; Maxima, minima and saddles; Lagrange multipliers; Multiple Integration , change of variables, Fubini’s theorem; Gradient, Divergence and Curl; Line and Surface integrals; Stokes, Green’s and Divergence theorems.
Attendance - 5%, Quizzes - 25%, Midterm - 30%, Final - 40%
Homeworks: There will be a homework problem sheet posted every week. These are only meant for practice and do not have to be turned in. The quiz will consist of problems taken either directly from, or based on, the homework problems. So it is highly recommended that you regularly work on the practice problems to make sure that you do not lag behind. This is not a difficult course, but it is a fast paced one, so once you lag behind it will be difficult to play catch up.
Quizzes and Tutorials: The quizzes will be taken during the tutorials, so make sure you attend them (or at least attend the ones that have a quiz). There will be a total of eleven (or twelve quizzes if time permits) and only the top ten scores will be counted towards the final grade. There will be no makeover of the quiz, unless there is a valid medical reason or some other emergency. If you miss a quiz, your score for that quiz will be zero. The tutorials are also meant for you to ask questions and clarify your concepts. This is You are strongly encouraged to attend the tutorials.
There will be one midterm of 60 points each and a final exam of 80 points. To pass the class, you have to take the final exam.
| Name | Designation | Section | Office hours | Office number (in the math department) |
| Ved Datar | Instructor | Full class | Tuesday, 5:15-6:15PM | X05 |
| Dharmendra Kumar | Back-up TA | Full Class | Monday, 5-6PM | R28 |
| Jyotirmoy Ganguly | Back-up TA | Full Class | TBD (will begin after March 20) | TBD |
| Geethika Sebastian | TA | Section A | Thursday, 5:30-6:30 | L-18 |
| Manpreet Singh | TA | Section B | Thursday, 5-6PM | N-11 |
| Rumpa Masanta | TA | Section C | Wednesday, 6:30-7:30 PM | L-26 |
| Arnabpal | TA | Section D | Thursday 5 pm-6pm | N-04 |
| Abhay Jindal | TA | Section E | Thursday, 5-6 | X-22 |
| Number | Date | Topic | Homework | Notes |
| 1 | Tu 02/28 | Introduction, A review of vector spaces and linear maps | ||
| 2 | Th 03/02 | Similarity, solving linear equations | ||
| 3 | Tu 03/07 | Inner product, orthogonality | ||
| 4 | Th 03/09 | Gram-Schmidt, Best Approximations | ||
| 5 | Tu 03/14 | Axiomatic definition of determinant, existence | ||
| 6 | Th 03/16 | Determinants (cont) | ||
| 7 | Tu 03/21 | Eigenvalues | ||
| 8 | Th 03/23 | Linear ODEs, space of solutions, Wronskian | ||
| 9 | Tu 03/30 | Linear second order ODEs | ||
| 10 | Th 04/01 | Canonical forms of matrices - symmetric and Hermitian matrices, diagonalization | ||
| 11 | Tu 04/06 | Canonical forms (cont.) Jordan canonical form | ||
| 12 | Th 04/08 | Catch-up | ||
| 13 | Tu 04/13 | Functions in R^n, limits, continuity | ||
| 14 | Th 04/18 | directional derivatives, differentiability | ||
| 15 | Tu 04/25 | Chain rule, Tangent planes | ||
| 16 | Th 04/27 | Crietria for differentiability, critical points | ||
| 17 | Tu 05/02 | Higher order derivatives, Taylor's theorem | ||
| 18 | Th 05/04 | Second derivative test for maxima and minima | ||
| 19 | Tu 05/09 | Lagrange multipliers | ||
| 20 | Th 05/11 | Double integrals | ||
| 21 | Tu 05/16 | Fubini's theorem, some examples | ||
| 22 | Th 05/18 | Multiple integrals | ||
| 23 | Tu 05/23 | Change of variable formula | ||
| 24 | Th 05/25 | Integration on parametric sub-manifolds - line integrals and surface integrals | ||
| 25 | Tu 05/30 | Integrals of vector fields - flux and work | ||
| 26 | Th 06/01 | Fundamental theorem of line integrals, Conservative vector fields, Exact ODEs. | ||
| 27 | Tu 06/06 | Curl and divergence | ||
| 28 | Th 06/08 | Curl and divergence (cont) | ||
| 29 | Tu 06/13 | Orientation, Stokes theorem | ||
| 30 | Th 06/15 | Stokes theorem (cont.) |