TEW - Differential Equations and its Applications (2021)

Speakers and Syllabus


 

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Prof. V.D. Sharma,

IIT Gandhinagar

6

Method of characteristics and general solution of first order PDEs, Riemann problem, Conservation laws and Burger’s Equations, Cauchy problem for second order PDEs.

First order Ordinary Differential Equations, growth and decay model, Euler’s Equation, Power series solution of a Differential Equation about an ordinary point, Solution about a regular singular point.

Prof. Rashmi Bhardwaj,

GGSIP University Dwarka, New Delhi

5

Non-linear Autonomous systems, Fixed Point, Saddle Point, Hopf Bifurcation, Equilibrium Points and their local stabilities, Cycles, Lyapunov Function, Chaos, Lyapunov Exponent.

Prof. Navneet Jha,

SAU New Delhi

5

Introduction to Radial Basis Functions (RBFs): Thin plate spline, Piecewise smooth RBFs, Generalized Duchon spline, Infinitely smooth RBFs, Gaussian (GA), Multiquadric, Inverse multiquadric, Inverse quadratic. Multi-dimensional scattered mesh generation. Derivative approximations using various RBFs.

 

Computational discretization for the first and second derivatives in one dimension, and two-dimensions. Error analysis and derivation of optimal shape parameters. Convergence theory associated with local RBF method. A convergent radial basis scattered mesh high-resolution compact FDM for boundary layer problems.

Prof. Malay Banerjee,

IIT Kanpur

4

General solution of system of nonlinear equations, Putzer algorithm to calculate exap(At), stable-unstable-center subspaces, stable manifold theorem, Hartman-Grobman theorem.

Local and global bifurcations, normal forms, mathematical criteria for saddle-node, transcritical, pitchfork, Hopf and Bogdanov-Takens bifurcations.

Ordinary differential equation models of single species population growth, two and multi-species interactions.

Application of bifurcation theory to study various dynamics produced by the nonlinear ordinary differential equation models.

Prof. Kapil Sharma,

SAU, New Delhi

4

Evolution of numerical methods for initial value problems: Development and analysis of continuous approximate methods for IVP; Development and analysis of discretization methods, which include single and multi step methods for IVP.

 

Name of the Tutors/Lab Session:

S.N.

Name

Position

Affiliation

1.

Ms. Harindri Chaudhary

Associate Professor

Deshbandhu College, University of Delhi

2.

Ms. Shipra Chauhan

Assistant Professor

Deshbandhu College, University of Delhi

3.

Mr. Dinesh Kumar

Assistant Professor

Deshbandhu College, University of Delhi

 

 


Time Table

 

Date, Days

Lecture 1

5 - 6 PM

Lecture 2

6 - 7 PM

Tutorial 1

2-3 PM

Tutorial 2

3-4 PM

Tutorial 3

04:30-5:30 PM

07:00- 07:30 PM

 

Speaker

Speaker

Speaker

Speaker

Speaker

 

15-03-2021

Monday

VDS

KS

 

 

 

 

16-03-2021

Tuesday

VDS

KS

 

 

 

 

17-03-2021

Wednesday

VDS

KS

 

 

 

 

18-03-2021

Thursday

VDS

KS

 

 

 

 

19-03-2021

Friday

VDS

NJ

 

 

 

 

20-03-2021

Saturday

VDS

NJ

 

 

 

 

21-03-2021

Sunday

 

 

DK

SC

HC

 

22-03-2021

Monday

RB

NJ

 

 

 

 

23-03-2021

Tuesday

RB

NJ

 

 

 

 

24-03-2021

Wednesday

MB

NJ

 

 

 

 

25-03-2021

Thursday

RB

MB

 

 

 

 

26-03-2021

Friday

RB

MB

 

 

 

 

27-03-2021

Saturday

RB

MB

 

 

 

 

28-03-2021

Sunday

 

 

DK

SC

HC

Valedictory Session

VDS: V.D. Sharma
KS: Kapil Sharma
NJ: Navneet Jha
RB: Rashmi Bhardwaj
MB: Malay Banerjee
HC: Harindri Chaudhary
DK: Dinesh Kumar
SC: Shipra Chauhan

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