IST  Analysis and PDE
Speakers and Syllabus
Analysis and Partial differential equations (PDEs) are now the integral part of the curriculum in any postgraduate course in Mathematics. Advanced analysis like Measure Theory and Functional Analysis are playing a vital role in many mathematical disciplines including PDEs. PDEs naturally arise often in many mathematical modeling of physical phenomenon and engineering applications. Measure Theory and Functional analysis are the backbones for setting up the study of PDEs in the modern sense. Functional Analysis studies linear spaces provided with suitable topological structures and continuous linear transformations between such spaces. It has farreaching applications in several disciplines. An introduction to the theory of measure and integration is helpful since the richest examples in functional analysis come from function spaces whose study demands such a knowledge. The topics in the school are designed in such a way that the participants get exposure to topics in Linear Algebra, Measure Theory, Functional analysis and Partial Differential Equations.
Name of the Speaker with affiliation 
No. of Lectures 
Detailed Syllabus 
R. Venkatesh Dept. Math.IISc, Bangalore 
6 
Finite dimensional spectral theory. Inner product spaces, Orthonormal sets. Spectral theorem for the Hermitian and normal operators on finite dimensional inner product spaces. 
ManjunathKrishnapur Dept. Math.IISc, Bangalore 
6 
Lebesgue measure and integration. Construction of Lebesgue measure, Measurable functions, Lebesgue integration, convergence theorems and Lpspaces. 
Tirthankar Bhattacharyya Dept. Math. IISc, Bangalore 
6 
Spectral theory for compact selfadjoint operators.Hilbert spaces, Bounded and compact operators on a Hilbert space. Spectrum of a compact operators and the spectral theorem for compact selfadjoint operators. 
A. K. Nandakumaran Dept. Math.IISc, Bangalore 
6 
Partial Differential Equations. First order PDEMethod of characteristicsElliptic PDE, in particular Laplacian, fundamental solution, Green’s functions, Mean value theorem, maximum principle, regularity. 
References:
 Hoffman, K. and Kunze, R., Linear Algebra (2nd Ed.) ,PrenticeHall of India, 1992.
 Artin, M., Algebra, PrenticeHall of India, 1994.
 Terence Tao. An Introduction to Measure Theory.American Mathematical Society. Graduate Studies in Mathematics Vol. 126; 2011.
 Elias M Stein and Rami Shakarchi. Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Princeton University Press (2005).
 Conway, J. B., A course in functional analysis, GTM 96, Springer.
 Rudin, Walter., Functional Anaysis (2nd Ed.) ,McGrawHill, 2006.
 Garabedian, P. R., Partial Differential Equations, John Wiley and Sons, 1964.
 Renardy, M. and Rogers, R. C., An Introduction to Partial Differential Equations, SpringerVerlag, 1992.
Tutors:
S. No. 
Name 
Affiliation 
1 
R. Venkatesh 
Mathematics, IISc Bangalore 
2 
ManjunathKrishnapur 
Mathematics, IISc Bangalore 
3 
Tirthankar Bhattacharya 
Mathematics, IISc Bangalore 
4 
A. K. Nandakumaran 
Mathematics, IISc Bangalore 
5 
G.V.K. Teja 
Mathematics, IISc Bangalore 
6 
SubhajitGhosh 
Mathematics, IISc Bangalore 
7 
Lakshmi Priya M.E. 
Mathematics, IISc Bangalore 
8 
Rahul Biswas/Ramesh ChSau 
Mathematics, IISc Bangalore 
9 
Poornendu Kumar 
Mathematics, IISc Bangalore 
10 
ShubhamRastogi 
Mathematics, IISc Bangalore 
11 
Abu Sufian 
Mathematics, IISc Bangalore 
12 
S. Aiyyappan 
Mathematics, IISc Bangalore 
Time Table
Day 
Date 
Lecture 1 (9.30 
Tea (11.00 to 
Lecturer 2 (11.30 
Lunch (1.00 to 
Tutorial 1 (2.30 
Tea (3.30 to 
Tutorial 2 (4.00 
Snacks 5.005.30 



(name of the speaker 

(name of the speaker 

(name of the speaker/tutor 

(name of the speaker/tutor 


Mon 
06/05/ 2019 
RV 
Tea 
MK 
Lunch 
RV/T12 
Tea 
MK/T34 
Snacks 

Tues 
07/05/ 2019 
RV 
Tea 
MK 
Lunch 
RV/T12 
Tea 
MK/T34 
Snacks 

Wed 
08/05/ 2019 
RV 
Tea 
MK 
Lunch 
RV/T12 
Tea 
MK/T34 
Snacks 

Thu 
09/05/ 2019 
RV 
Tea 
MK 
Lunch 
RV/T12 
Tea 
MK/T34 
Snacks 

Fri 
10/05/ 2019 
RV 
Tea 
MK 
Lunch 
RV/T12 
Tea 
MK/T34 
Snacks 

Sat 
11/05/ 2019 
RV 
Tea 
MK 
Lunch 
RV/T12 
Tea 
MK/T34 
Snacks 

SUNDAY 

Mon 
13/05/ 2019 
TB 
Tea 
AN 
Lunch 
TB/T56 
Tea 
AN/T78 
Snacks 

Tues 
14/05/ 2019 
TB 
Tea 
AN 
Lunch 
TB/T56 
Tea 
AN/T78 
Snacks 

Wed 
15/05/ 2019 
TB 
Tea 
AN 
Lunch 
TB/T56 
Tea 
AN/T78 
Snacks 

Thu 
16/05/ 2019 
TB 
Tea 
AN 
Lunch 
TB/T56 
Tea 
AN/T78 
Snacks 

Fri 
17/05/ 2019 
TB 
Tea 
AN 
Lunch 
TB/T56 
Tea 
AN/T78 
Snacks 

Sat 
18/05/ 2019 
TB 
Tea 
AN 
Lunch 
TB/T56 
Tea 
AN/T78 
Snacks 
RV: R. Venkatesh, MK: ManjunathKrishnapur, TB: Tirthankar Bhattacharyya, AN: A.K. Nandakumaran.
T12: G.V.K. Teja&SubhajitGhosh, T34: Lakshmi Priya M.E. & Rahul/Ramesh
T56: Poornendu Kumar &ShubhamRastogi, T78: Abu Sufian& S. Aiyyappan.