# IST Differential Equations (2018)- Speakers and Syllabus

Differential Equations is a basic topic of research and teaching in mathematics. The abstract theory behind this topic is also most important from the point of view of applications in large number of areas iin mathematics itself and, of course, in science and engineering. A few examples are geometry (including differential geometry), economics, hydrodynamics, elasticity, general relativity, geometric flows, biology etc. There are a few excellent research groups in India, especially in partial differential equations (PDE), but these are in a very small number of central institutes and the manpower available for teaching this topic in universities, and colleges is too small. In Indian curriculum, the topic “differential equations” is introduced to the students as a set of artificially created methods to solve differential equations. In the process, the whole beauty and importance is lost. Through this course, we will introduce the basics of differential equations through various aspects of mathematics, in particular analysis and linear algebra.

Syllabus to be covered:

 Name of the Speaker with affiliation, who will cover each module of 6 lectures. No. of Lectures (each of 1 ½ hours) Detailed Syllabus Raju K. George (AKN) IIST, Trivandrum 4 Motivational Examples from ODE, General Theory of ODEs including existence, uniqueness, continuous dependence, maximal interval of existence etc. Arun, K.R. (KRA) IISER, Trivandrum 5 Linear Systems and Stability Analysis, non linear stability theory including Lyapunov theory, Poincare Bendixon and if possible Hartman-Grobman theorem etc. K. Sakthivel (KS) IIST, Trivandrum 3 Application to Optimal Control Problems A.K. Nandakumaran (AKN), IISd, Bangalore 6 First Order Equation; Method of Characteristics, Second Order Elliptic Equations P.S. Datti (PSD), Formerly TIFR-CAM, Bangalore 6 Linear Parabolic and Hyperbolic Equations

References:

1. A.K. Nandakumaran, P.S. Datti and R.K. George, Ordinary Differential Equations: Principles and Applications, Cambridge, 2017.
2. Tyn Myint-U, \textit{Ordinary Differential Equations,} Elsevier North-Holland, 1978.
3. E.A. Coddington and N. Levinson,Theory of ODE's, Tata McGraw-Hill, 1972.
4. Prasad, P. and Ravindran, R, Partial Differential Equations, New Age, 2015.
5. Pinchover, Y. and Rubinstein, J. An Introduction to Partial Differential Equations, Cambridge, 2005.
6. Han, Q, A Basic Course in Partial Differential Equations, AMS, 2011.
7. McOwen, R. C, Partial Differential Equations: Methods and Applications}, Pearson, 2002.

Tentative time-table:

 Day Date Lecture 1 (9.30–11.00) Tea (11.00–11.30) Lecture 2 (11.30–1.00) Lunch (1.00–2.30) Tutorial 1 (2.30–3.30) Tea (3.30-4.00) Tutorial 2 (4.00-5.00) Tea & Snacks 5.00-5.30 name of the speaker name of the speaker name of the speaker/tutor Name of the speaker/tutor) Mon 14-5-2018 RKG KRA RKG/Ts KRA/Ts Tues 15-5-2018 RKG KRA RKG/Ts KRA/Ts Wed 16-5-2018 RKG KRA RKG/Ts KRA/Ts Thu 17-5-2018 KS KRA KS/Ts KRA/Ts Fri 18-5-2018 RKG KS RKG/Ts KS/Ts Sat 19-5-2018 KS KRA KS/Ts KRA/Ts Sunday: Off Mon 21-5-2018 AKN PSD AKN/Ts PSD/Ts Tue 22-5-2018 AKN PSD AKN/Ts PSD/Ts Wed 23-5-2018 AKN PSD AKN/Ts PSD/Ts Thur 24-5-2018 AKN PSD AKN/Ts PSD/Ts Fri 25-5-2018 AKN PSD AKN/Ts PSD/Ts Sat 26-5-2018 AKN PSD AKN/Ts PSD/Ts

Ts = Tutors