The texts we will be referring to are as follows :
1. Theory of ordinary differential equations, E.A. Coddington and N. Levinson.
2. Differential equations and dynamical systems, L. Perko.
3. Ordinary differential equatiosn, principles and applications, A.K. Nandakumaran, P.S. Datti, and R.K. George.
The course description (along with pre-requisites) can be found on this webpage.
Instructors :
Vamsi Pritham Pingali, vamsipingali@iisc.ac.in
Classroom and timings : Mon, Wed, and Fri - 3-4 PM in LH 4
The TA is Vaibhav Kumar (vaibhavkuma1@iisc.ac.in). Tutorials will be held on Tuesdays from 5-6 PM in LH-2
The Grading policy : 20% for quizzes based on HW (best n-2 out of n), 30% for the Midterm, and 50% for the Final.
Exams:
The Midterm shall be held on 12 Feb from 2-4 in LH4. The syllabus is everything until and including continuous dependence on parameters (that is, until and including 5 Feb).
The Final shall be held on TBA. The syllabus is everything 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 |
30 Dec - 5 Jan |
Motivation and examples (Wednesday notes), Linear systems and diagonalisability(Friday notes) |
2 |
6 Jan - 12 Jan |
Solving using the Jordan canonical form (Monday notes), Matrix exponential (Wednesday notes), Solutions of autonomous linear systems (Friday notes) |
3 |
13 Jan - 19 Jan |
Non-homogeneous non-autonomous linear systems (Monday notes), Real-analytic functions (Wednesday notes), Real-analytic linear ODE have real-analytic solutions (Friday notes) |
4 |
20 Jan - 26 Jan |
Regular singular points (Monday notes), Frobenius method - part 1 (Wednesday notes), Frobenius method - part 2 (Friday notes) |
5 |
27 Jan - 2 Feb |
Uniqueness and Lipschitz functions (Monday notes), Picard's existence theorem (V1) (Wednesday notes), Picard's theorem (V2) and maximal interval (Friday notes) |
6 |
3 Feb - 9 Feb |
Peano's theorem by approximation of the IVP (Monday notes), Peano's theorem using approximate solutions, Continuous dependence on parameters (Wednesday notes), Smooth dependence on parameters, Euler's method (Friday notes) |
8 |
17 Feb - 23 Feb |
Midpoint method, Sturm-Liouville problem(Monday notes), Fredholm's alternative and the statement of the Sturm-Liouville theorem (Wednesday notes), Prufer substitution (Friday notes) |
HW number |
Quiz on |
Homework (subject to changes; please check regularly) |
1 |
7 Jan |
No HW/Quiz |
2 |
14 Jan |
|
3 |
21 Jan |
|
4 |
28 Jan |
|
5 |
Ask TA |
|
8 |
Ask TA (Tutorial in the first week of March) |