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 April 23 from 2-5 in LH4. 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) |
|
9 |
24 Feb - 2 Mar |
Sturm-Liouville theorem and the oscillation theorem(Monday notes), The oscillation theorem and the Sturm comparison theorem(Wednesday notes), The Sturm comparison theorem (Friday notes) |
|
10 |
3 Mar - 9 Mar |
Linear stability theory(Monday notes), Equilibria, orbits, and cycles (Wednesday notes), Liapunov stability (Friday notes) |
|
11 |
10 Mar - 16 Mar |
Perron's theorem (Monday notes), Examples and Liapunov functions (Wednesday notes), Stability and instability results (Friday notes) |
|
12 |
17 Mar - 23 Mar |
Stability and instability examples (Monday notes), Stable and unstable invariant sets (Wednesday notes), Manifolds and the stable manifold theorem (Friday notes) |
|
13 |
24 Mar - 30 Mar |
Phase plane analysis (Monday notes), Phase plane analysis; Paths and curves (Wednesday notes), Poincare index (Friday notes) |
|
14 |
31 Mar - 6 Apr |
Monday was a holiday, Index of regular Jordan curves (Wednesday notes), Poincare-Bendixon, Bendixon, and Leinard's theorems (Friday notes) |
|
15 |
7 Apr - 13 Apr |
Proof of the stable manifold theorem (Monday notes), Guest lecture on Wednesday, No class on Friday |
|
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) |
|
|
9 |
Tutorial in the second week of March |
|
|
10 |
Ask TA |
|
|
11 |
Ask TA |
|
|
12 |
Ask TA |