TEW - Partial Differential Equations (2024)

Speakers and Syllabus

Syllabus:

Name of the Speaker with affiliation No. of Lectures Detailed Syllabus
Prof. Jyotshana V. Prajapat
Department of Mathematics University of Mumbai
Ranade Bhavan, Vidyanagari Santacruz, Mumbai 400098		 5 + 1 discussion session
  • First order PDEs: Curves and Surfaces, introduction to 1st order PDEs and their classification
  • Cauchy Problem, integral surface through a given curve Semi linear equations,
  • Laplace equation: Introduction, motivation, discussion on applications
    Maximum and minimum principle, Cauchy problem
  • Dirichlet and Neumann problem for the circle
  • Harnack’s theorem, Laplace equation-Green’s function
Prof. Harsha Hutridurga
Department of Mathematics IITB,
Powai Mumbai 400076		 4 + 2 discussion sessions
  • Quasi-linear equations, first order quasi-linear PDE, Initial value problem for quasi-linear equation
  • Wave equation: Introduction, motivation, discussion on applications
  • Methods to solve wave equation
  • Duhamel’s principle for wave and heat equation
Prof. Vinayak S. Kulkarni
Department of Mathematics
University of Mumbai Ranade Bhavan, Vidyanagari Santacruz, Mumbai 400098		 4
  • Heat Equation: Introduction, motivation, discussion on applications
  • Methods to solve 1dim heat equation and general heat equation
  • Heat conduction problem
  • Advanced methods to solve parabolic equations

Prof. K. Sandeep
TIFR-CAMS Bengaluru
560065 Karnataka

 4
  • Introduction to techniques of Elliptic PDE-Variational Methods
  • Sopbolev spaces, weak derivatives
  • Euler Lagrange equations: 1st variation, 2nd Variation
  • Existence of Minimizers, Coercivity

Prof. Sivaji
Ganesh Department of Mathematics
IITB, Powai Mumbai 400076

 6
  • Compatible system of 1st order PDE, Charpit’s method
  • Jacobi method of solving 1st order Pde
  • Initial value problem for Quasi-linear equation
  • Nonlinear first order PDE
  • Monge cone, Analytic expression for Monge’s cone,
  • Characteristics strip, Initial strip
Nikhil Sonawane MATLAB 1 Use of MATLAB for teaching and illustrations ODE/PDE

 References:

  1. T. Amarnath, An Elementary course in Partial Differential Equations, Narosa Publishing house
  2. L. C. Evans, Partial Differential Equations, GTM, University Press.

Name of the tutors:

S. No. Name Affiliation
1. Dr. Reema Khanna KJ Somaiya College of Science and Commerce
2. Prof. Sudha Agarwal KJ Somaiya College of Science and Commerce
3. Prof. Makarand Niphadkar KJ Somaiya College of Science and Commerce
4. Prof. Prabhat Upadhyay KJ Somaiya College of Science and Commerce
5. Prof. Anoop Varghese SIES College of Arts, Science and Commerce

Time Table

 

 

Day
&
Date

Lecture 1

(9.30–10.30)

Tea

(10.35-10.55)

Lecturer 2

(11.00–12.00)

Lecture 3

(12.00–1.00)

Lunch

(1.00 
to
2.20)

Lecture 4

(2.30-3.30)

Tea

(3.35
to
3.55)

Discussion

(4.00-500)

Snacks

(5.05
to
5.35)

Monday

Jan 15,2024

 

JVP

 

 

JVP

 

VSK

 

 

HH

 

 

AV/SA

 

Tuesday

Jan 16,2024

VSK

  

VSK

SGS

 

 

SGS

 

HH/RK

 

Wednesday

Jan 17,2024

SGS

 

SGS

HH

 

HH

 

MN/AV/RK

 

Thursday

Jan 18,2024

JVP

 

SGS

SGS

 

HH

 

HH/PU

 

Friday

Jan 19,2024

KS

 

VSK

KS

 

NS

 

PU/AV

 

Saturday

Jan 20,2024

KS

 

JVP

KS

 

JVP

 

JVP

 

Full forms for the abbreviations of speakers and tutors:

  • JVP: Prof. Jyotshana V. Prajapat
  • VSK:Prof. Vinayak S. Kulkarni
  • KS:  Prof. K. Sandeep
  • SGS: Prof. Sivaji Ganesh Sista
  • HH:  Prof. Harsha Hutridurga
  • NS:  Nikhil Sonawane (MATLAB)
  • MN: Prof. Makarand Niphadkar
  • PU: Prof. Prabhat Upadhyay
  • AV: Prof. Anoop Varghese
  • SA: Prof. Sudha Agarwal
  • RK: Prof. Reema Khanna
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