TEW - Partial Differential Equations and Applications (2023)

Speakers and Syllabus

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Dr. S. Aiyappan
Asst. Professor
Dept. of Mathematics
IIT Hyderabad

6

Preliminary Analysis: Multivariable calculus, Integration by parts and divergence theorem, Integration over balls and spheres, ODE existence and uniqueness theory, Fourier transform, convolution, mollifiers.

Dr. K.R. Arun
Associate Professor
School of Mathematics
IISER Thiruvananthapuram

6

First order PDE and weak notions: First order linear and quasi-linear PDE. Method of characteristics. A brief discussion on Conservation Laws and an introduction to weak solutions.

Prof. A. K. Nandakumaran
Professor
Department of Mathematics
Indian Institute of Science
Bengaluru

6

Laplace (Elliptic) equation: Fundamental solution, mean value property. Maximum principle and Perrons method of existence. A brief introduction to potential theory.

Prof. P.S. Datti
Former Faculty
TIFR-CAM
Bangalore

6

Heat equation (Parabolic): Fundamental solution, initial value problem and properties of solutions. Temperature distribution in a finite rod with prescribed physical conditions at the ends.

Wave equation (Hyperbolic): Vibrating string. Wave equation in one space dimension: D ’Alembert’s formula, non-homogeneous equation. Duhamel’s principle. Higher order equation in one space dimension.

References:
    1. A. K.Nandakumaran, P. S. Datti, Partial Differential Equations; Classical Theory with a Modern Touch, Cambridge - IISc, Series, Cambridge University press (2020).
    2. R. C. McOwen, Partial Differential Equations; Methods and Applications, 2nd Ed., Pearson Education, Delhi (2005).
    3. Y. Pinchover and J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University press (2005).

 

Name of the tutors:

 

S. No.

Name

Affiliation

1

Dr. Renjith T

Indian Institute of Science, Bangalore

Time Table

 Time-table (with names of speakers and tutors):

Day

Date

Lecture 1

(9.30
to
10.30)

Tea

(10.35
to
10.55)

Lecturer 2

(11.00
to
12.00)

Lecture 3

(12.00
to
1.00)

Lunch

(1.00
to
2.20)

Lecture 4

(2.30
to
3.30)

Tea

(3.35
to
3.55)

Discussion

(4.00
to
5:00)

Snacks

(5.05
to
5.35)

Mon

27.11.2023

SA

 

KRA

SA

 

KRA

 

SA/RT

 

Tue

28.11.2023

SA

 

KRA

SA

 

KRA

 

KRA/RT

 

Wed

29.11.2023

SA

 

KRA

SA

 

KRA

 

KRA/RT

 

Thu

30.11.2023

AKN

 

PSD

AKN

 

PSD

 

AKN/RT

 

Fri

01.12.2023

AKN

 

PSD

AKN

 

PSD

 

PSD/RT

 

Sat

02.12.2023

AKN

 

PSD

AKN

 

PSD

 

PSD/RT

 

 

Full forms for the abbreviations of speakers and tutors:

SA:        Dr. S. Aiyappan
KRA:     Dr. K. R. Arun
AKN:     Prof. A. K. Nandakumaran
PSD:     Dr. P. S. Datti
RT:        Dr. Renjith, T (Tutor)

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