TEW - Differential Equations and its Applications (2025)
Speakers and Syllabus
| Name of the Speaker with affiliation | No. of Lectures | Detailed Syllabus |
| Prof. Manas Ranjan Sahoo, NISER Bhubaneswar | 4 (each one 1.5 hr) |
Theory of first order and higher order ordinary differential equations, Existence, uniqueness and continuous dependence. Systems of first order ODE and higher order ordinary differential equations with applications. Applications: Application to brachistochrone problem, Pursuit curve, Population model, Lotka-Volterra model etc. |
| Prof. Debajyoti Choudhuri, IIT Bhubaneswar | 4 (each one 1.5 hr) |
First order partial differential equations: Introduction to PDE, the method of characteristics to solve linear, semi- linear, quasilinear and fully nonlinear first order equations. Classification of second order partial differential equations, Laplace equation, Wave equation and Heat equation. Applications: Elastic Wave Propagation/Continuum Mechanics. |
| Prof. Bivudutta Mishra, BITS Pilani Hyderabad Campus | 4 (each one 1.5 hr) |
Applications of differential equations in finding Riemannian metric tensor, affine connection, Weitzen- bock connection, contortion tensor and super potential. Over all the use of ordinary and partial differential equations in the derivation of curvature and torsion based gravitational theories would be discussed. |
References:
1. Ross, Differential equations, John Wiley.
2. Y. Pinchover and J. Rubinstein, Introduction to partial differential equations, Cambridge press.
3. Barbara Ryden, Introduction to Cosmology.
4. P. M. Shearer, Introduction to Seismology, Cambridge University Press.
Name of the tutors:
| S. No. | Name | Affiliation |
| 1 | Dr. Tapas Ranjan Panigrahi | Department of Mathematics, GIET University, Gunupur |
| 2 | Dr. Dipan Jyoti Mohanty | Department of Mathematics, GIET University, Gunupur |
| 3 | Dr. Pratik Premadarsi Ray | Department of Mathematics, VIT, Amaravati, Andhra Pradesh. |
Time Table
| Day | Date | Lecture 1 (9.30– 11.00) |
Tea (11.00 - 11.30) |
Discussion (11.30– 12.30) |
Lunch (1.00 to 2.30) |
Lecture 3 (2.00- 3.30) |
Tea (3.30-3.45) |
Discussion (3.45- 4.45) |
Snacks (4.45 –5.15) |
| Mon | 07.04.25 | ODE(L1), MS |
ODE(T1) MS, TP |
ODE(L2) MS | ODE(T2) MS, TP |
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| Tue | 08.04.25 | ODE(L3), MS |
ODE(T3), MS, TP |
ODE(L4), MS | ODE(T4), MS, TP |
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| Wed | 09.04.25 | PDE(L1), DC |
PDE(T1), DC, DM |
PDE(L2), DC | PDE(T2), DC, DM |
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| Thu | 10.04.25 | PDE(L3) | PDE(T3) DC, DM |
PDE(L4) | PDE(T4), DC, DM |
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| Fri | 11.04.25 | Application’s (L1), BM |
Application’s (T1), BM, PR |
Application’s (L2), BM |
Application’s (T2), BM, PR |
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| Sat | 12.04.25 | Application’s (L3), BM |
Application’s (T3), BM, PR |
Applicatio n’s (L4), BM |
Applicatio n’s (T4), BM, PR |