IST - Differential Equations - Theory, Methods and Applications

Speakers and Syllabus


Name of the Speaker with affiliation No. of Lectures Detailed Syllabus
A Adimurthi, Professor, TIFR CAM (AA) 4 Elliptic partial differential equations: Gauss-Green theorem, Integration by parts formula, fundamental solution for Laplace equation, solving Poisson equation in Rn, Harnack’s inequality, Green’s functions, representation formula for the solution of boundary value problem by using Green’s function. Green’s functions for a ball and for an upper half plane.
Girija Jayaraman, Former Professor, IIT Delhi (GJ) 4 Physico-Biological models: modelling perspective and history, Initial/Boundary value problems and their applications in Physics and Biology, forced and free oscillations, Mathematics of Diffusion, Diffusion in Biology. Physiological applications involving wave propagation, Ecological applications using nonlinear dynamical systems, challenges with multi-scales.
G D V Gowda, Professor, TIFR CAM (GDVG) 4 First order nonlinear equations: First order partial differential equations: Introduction to PDE, solving linear, semilinear, quasilinear and fully nonlinear first order equations by using the method of characteristics. Examples and their applications in various fields.
P Kandaswamy, Former Professor, Bharathiar University (PK) 4 Applications of IBVPs: ode model - human immune system, system of equations, phase plane analysis and interpretation, two extreme cases. pde models - gravity waves and their occurrence in atmosphere, critical levels and their significance, the energy and momentum transfer; double diffusive convection and its solutions, finger and other instabilities.
P G Siddheshwar, Professor, Bangalore University (PGS) 4 Numerics for ordinary differential equations (IVPs and BVPs): Initial Value problems: Euler' s method, Higher order Taylor' s method, Runge-Kutta method, stability and convergence. Boundary value problems with or without eigenvalues: shooting method for nonlinear problems, finite difference methods for boundary value problems, etc.
S Sundar, Professor, IIT Madras (SS) 4 Meshfree methods: Boundary value problems: meshfree method, 2D incompressible Navier-Stokes Equations, solution for applications involving Coutte flow, Poiseuelle flow, driven cavity flow, broken dam free surface flow, etc.

 Names of the tutors with their affiliation and status:

1. A Srinivasan, Post Doc, TIFR CAM (AS)
2. R Kumar, Post Doc, TIFR CAM (RK)


Time Table

 

Day Date

Lecture 1
(9.30–11.00)

Tea
(11.05– 11.25)
Lecture 2
(11.30–1.00)
Lunch
(1.05– 2.25)
Tutorial 1
(2.30–3.30)
Tea
(3.35- 3.55)
Tutorial 2
(4.00-5.00)
Snacks
5.05- 5.30
Mon 18 Nov ‘19 PGS   PGS   PGS+AS   PGS+AS  
Tues 19 Nov ‘19 PGS   PGS   PGS+AS   PGS+AS  
Wed 20 Nov ‘19 PK   PK   PK+AS   PK+AS  
Thu 21 Nov ‘19 AA   GDVG   AA+AS   GDVG+AS  
Fri 22 Nov ‘19 GDVG   AA   GDVG+AS   AA+AS  
Sat 23 Nov ‘19 AA   GDVG   AA+AS   GDVG+AS  
    Sunday : Off      
Mon 25 Nov ‘19 GDVG   AA   GDVG+RK   AA+ RK  
Tue 26 Nov ‘19 GJ   GJ   GJ+ RK   GJ+ RK  
Wed 27 Nov ‘19 GJ   GJ   GJ+ RK   GJ+ RK  
Thur 28 Nov ‘19 PK   PK   PK+ RK   PK+ RK  
Fri 29 Nov ‘19 SS   SS   SS+ RK   SS+ RK  
Sat 30 Nov ‘19 SS   SS   SS+ RK   SS+ RK  
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