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 HartmanGrobman 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 TIFRCAM, Bangalore

6 
Linear Parabolic and Hyperbolic Equations 
References:
 A.K. Nandakumaran, P.S. Datti and R.K. George, Ordinary Differential Equations: Principles and Applications, Cambridge, 2017.
 Tyn MyintU, \textit{Ordinary Differential Equations,} Elsevier NorthHolland, 1978.
 E.A. Coddington and N. Levinson,Theory of ODE's, Tata McGrawHill, 1972.
 Prasad, P. and Ravindran, R, Partial Differential Equations, New Age, 2015.
 Pinchover, Y. and Rubinstein, J. An Introduction to Partial Differential Equations, Cambridge, 2005.
 Han, Q, A Basic Course in Partial Differential Equations, AMS, 2011.
 McOwen, R. C, Partial Differential Equations: Methods and Applications}, Pearson, 2002.
Tentative timetable:
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 (3.304.00) 
Tutorial 2 (4.005.00) 
Tea & Snacks 5.005.30 


name of the speaker 

name of the speaker 

name of the speaker/tutor 

Name of the speaker/tutor) 

Mon 
1452018 
RKG 

KRA 

RKG/Ts 

KRA/Ts 

Tues 
1552018 
RKG 

KRA 

RKG/Ts 

KRA/Ts 

Wed 
1652018 
RKG 

KRA 

RKG/Ts 

KRA/Ts 

Thu 
1752018 
KS 

KRA 

KS/Ts 

KRA/Ts 

Fri 
1852018 
RKG 

KS 

RKG/Ts 

KS/Ts 

Sat 
1952018 
KS 

KRA 

KS/Ts 

KRA/Ts 

Sunday: Off 

Mon 
2152018 
AKN 

PSD 

AKN/Ts 

PSD/Ts 

Tue 
2252018 
AKN 

PSD 

AKN/Ts 

PSD/Ts 

Wed 
2352018 
AKN 

PSD 

AKN/Ts 

PSD/Ts 

Thur 
2452018 
AKN 

PSD 

AKN/Ts 

PSD/Ts 

Fri 
2552018 
AKN 

PSD 

AKN/Ts 

PSD/Ts 

Sat 
2652018 
AKN 

PSD 

AKN/Ts 

PSD/Ts 

Ts = Tutors