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