PDEs arise naturally in many mathematical modelling describing physical phenomenon and engineering applications. It is therefore important to understand the PDEs and their solution process. The theory of PDEs consists of studying the existence, uniqueness of the solution and further to establish its stability and regularity. The solution process includes to develop methodologies to find solutions either in closed form or by an approximation. The instructional school aims to provide the participants a tour to classical theory of second order PDEs and to introduce to them the advanced PDEs through variational approach. Furthermore, the school aims to demonstrate numerical analysis and techniques to solve the PDEs, in particular, finite difference methods and finite element methods . The topics in the school are designed in such way that the participants get exposure to topics in both classical and modern approach in the theory and computation of PDEs which are also part of the curriculum in the universities and post graduate colleges.
Syllabus:
Name of the Speaker with affiliation

No. of Lectures 
Detailed Syllabus 
Sandeep Kunnath TIFRCAM Bangalore 
6 
Classical PDE:

A. K. Nandakumaran Dept. Math. IISc Bangalore 
6 
Variational Approach for PDE:

A.S. Vasudevamurthy TIFRCAM Bangalore 
6 
Finite Difference Methods: Analysis(consistency, stability and error estimate) of finite difference schemes for
Highlighting new phenomenon discovered through numerics. 
Thirupathi Gudi Dept. Math. IISc Bangalore 
6 
Finite Element Methods: Introduction to finite element methods, construction of finite element spaces, Interpolation theory, applications to elliptic and parabolic PDEs. Error analysis and implementation aspects. 
References:
 L. C. Evans. Partial Differential Equations, AMS.
 S. Kesavan. Topics in Functional Analysis and Applications, New Age Int. Publ.
 P. G. Ciarlet. The finite element method for elliptic problems
 S. Larsson and V. Thomee. Partial differential equations with numerical methods. Springer.
 J. C. Strikwerda. Finite difference schemes and PDEs.
TimeTable (with initials of speakers and course associates for entire days of the programme ):
Day 
Date 
Lecture 1 (9.30–11.00) 
Tea (11.00–11.30) 
Lecturer 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) 
Snacks 5.005.30 



(name of the speaker 

(name of the speaker 

(name of the speaker/tutor 

(name of the speaker/tutor 


Mon 
23/07/ 2018 
KS 
Tea 
AN 
Lunch 
KS/SA/AS 
Tea 
AN/SA/AS 
Snacks 

Tues 
24/07/2018 
KS 
Tea 
AN 
Lunch 
KS/SA/AS 
Tea 
AN/SA/AS 
Snacks 

Wed 
25/07/2018 
KS 
Tea 
AN 
Lunch 
KS/SA/AS 
Tea 
AN/SA/AS 
Snacks 

Thu 
26/07/2018 
KS 
Tea 
AN 
Lunch 
KS/SA/AS 
Tea 
AN/SA/AS 
Snacks 

Fri 
27/07/2018 
KS 
Tea 
AN 
Lunch 
KS/SA/AS 
Tea 
AN/SA/AS 
Snacks 

Sat 
28/07/2018 
KS 
Tea 
AN 
Lunch 
KS/SA/AS 
Tea 
AN/SA/AS 
Snacks 

SUNDAY 

Mon 
30/07/2018 
AV 
Tea 
TG 
Lunch 
AV/AJ/AD 
Tea 
TG/AD/GS 
Snacks 

Tues 
31/07/2018 
AV 
Tea 
TG 
Lunch 
AV/AJ/AD 
Tea 
TG/AD/GS 
Snacks 

Wed 
1/08/2018 
AV 
Tea 
TG 
Lunch 
AV/AJ/AD 
Tea 
TG/AD/GS 
Snacks 

Thu 
2/08/2018 
AV 
Tea 
TG 
Lunch 
AV/AJ/AD 
Tea 
TG/AD/GS 
Snacks 

Fri 
3/08/2018 
AV 
Tea 
TG 
Lunch 
AV/AJ/AD 
Tea 
TG/AD/GS 
Snacks 

Sat 
4/08/2018 
AV 
Tea 
TG 
Lunch 
AV/AJ/AD 
Tea 
TG/AD/GS 
Snacks 
Tutorial Assistants:
S. No. 
Name 
Affiliation 
1 
A. S. Vasudevamurthy 
TIFR CAM 
2 
K. Sandeep 
TIFR CAM 
3 
Ameya Jagpat 
TIFR CAM 
4 
Thirupathi Gudi 
Mathematics, IISc Bangalore 
5 
A. K. Nandakumaran 
Mathematics, IISc Bangalore 
6 
Asha K. Dond 
Mathematics, IISc Bangalore 
7 
Gaddam Sharat 
Mathematics, IISc Bangalore 
8 
S. Ayyappan 
Mathematics, IISc Bangalore 
9 
Abu Sufian 
Mathematics, IISc Bangalore 