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 |
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Speaker |
Speaker |
Speaker |
Speaker |
Speaker |
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15-03-2021 Monday |
VDS |
KS |
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16-03-2021 Tuesday |
VDS |
KS |
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17-03-2021 Wednesday |
VDS |
KS |
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18-03-2021 Thursday |
VDS |
KS |
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19-03-2021 Friday |
VDS |
NJ |
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20-03-2021 Saturday |
VDS |
NJ |
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21-03-2021 Sunday |
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DK |
SC |
HC |
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22-03-2021 Monday |
RB |
NJ |
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23-03-2021 Tuesday |
RB |
NJ |
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24-03-2021 Wednesday |
MB |
NJ |
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25-03-2021 Thursday |
RB |
MB |
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26-03-2021 Friday |
RB |
MB |
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27-03-2021 Saturday |
RB |
MB |
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28-03-2021 Sunday |
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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