IST - Differential Equations - Theory and Applications (2022)
Speakers and Syllabus
Syllabus to be covered :
Name of the Speaker with affiliation | Lectures No.of | Detailed Syllabus |
Ali Hyder, Reader, TIFR CAM (AH) | 4 | Laplace equation: Method of separation of variables, fundamental solution for Laplace equation, mean value properties, maximum principles, solution to the Poisson equation, regularity of solutions to the Laplace equation, analyticity of solutions to the Laplace equation, Harnack inequality, Green function, explicit computation in certain domains, representation formula for the boundary value problem for Laplace equation using Green function, energy methods for the Laplace equation. |
Girija Jayaraman, Former Professor, IIT Delhi (GJ) | 4 | Models in Physics and Natural Sciences: Modelling perspective and history of model develolpment using differential equations, Initial/Boundary value problems in Physics and Natural Sciences, forced and free oscillations, Physiological applications involving wave/pulse propagation, Mathematics of Diffusion, Diffusion in Ecology, Ecological applications using nonlinear dynamical systems, Challenges in solving Pysico- Biological models with multi-scales. |
G D Veerappa Gowda, Professor, TIFR CAM (GDVG) | 4 | First order PDEs: Transport equation, solving linear, semilinear, quasilinear and fully nonlinear first order equations by the method of characteristics. Physical and real-world applications of these PDEs. |
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 S Datti, Former Professor, TIFR CAM (PSD) | 4 | Wave equation: d'Alembert formula (dimension n=1), spherical means and Euler- Poisson-Darboux equation, explicit construction of the solution in odd dimensions, and for even dimensions by the method of descent, energy methods, explanation of finite speed of propagation for solution to the wave equation. |
Venky Krishnan, Associate Profesor, TIFR CAM (VK) | 4 | Heat equation: Introduction to the heat equation and derivation of the fundamental solution using Fourier transforms, finding a solution to the standard homogeneous initial value problem with appropriate initial conditions as well as solution to the non-homogeneous problem by Duhamel's principle, regularity of solution to the heat equation in bounded domains and explanation of the infinite speed propagation, Space analyticity of solutions to the heat equation, counterexample describing lack of space-time analyticity for solutions to the heat equation, heat mean value formula, weak and strong maximum principles, energy methods |
Names of the tutors with their affiliation:
- Divyansh Agrawal, TIFR CAM (DA)
- Dr N Raja, KPR College of Engineering (NR)
- Dr S Meenasaranya, PSG Arts College (SM)
- Soumen Senapati, TIFR CAM (SS)
- Swaraj Paul, TIFR CAM (SP)
Time Table
Tentative time-table:
Day | Date | FN Session 1 (9.30–11.00) |
FN Session 2 (11.30–1.00) |
AN Session 1 (2.30–3.30) |
AN Session 2 (4.00-5.00) |
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Tue s | 16 Aug ‘22 | Lecture GJ | Lecture PK | L | Tutorial GJ+SM+NR | Tutorial PK+SM+NR | S | ||
Wed | 17 Aug ‘22 | Lecture GDVG | T | Lecture GJ | U | Tutorial GDVG+DA+SS | T | Tutorial GJ+SM+NR | N |
Thu | 18 Aug ‘22 | Lecture PK | E | Lecture GDVG | N | Tutorial PK+SM+NR | E | Tutorial GDVG+DA+SS | A |
Fri | 19 Aug ‘22 | Lecture GJ | A | Lecture PK | C | Tutorial GJ+SM+NR | A | Tutorial PK+SM+NR | C |
Sat | 20 Aug ‘22 | Lecture GDVG | Lecture GJ | H | Tutorial GDVG+DA+SS | Tutorial GJ+SM+NR | K | ||
Sunday : Off | |||||||||
Mon | 22 Aug ‘22 | Lecture PK | Lecture GDVG | Tutorial PK+SM+NR | Tutorial GGDVG+DA+SS | S | |||
Tue | 23 Aug ‘22 | Lecture AH | Lecture VK | L | Tutorial AH+DA+SS | Tutorial VK+SS+DP | N | ||
Wed | 24 Aug ‘22 | Lecture PSD | T | Lecture AH | U | Tutorial PSD+SS+SP | T | Tutorial AH+DA+SS | A |
Thu | 25 Aug ‘22 | Lecture VK | E | Lecture PSD | N | Tutorial VK+SS+SP | E | Tutorial PSD+SS+SP | C |
Fri | 26 Aug ‘22 | Lecture AH | A | Lecture VK | C | Tutorial AH+SS+SP | A | Tutorial VK+SS+SP | K |
Sat | 27 Aug ‘22 | Lecture PSD | Lecture AH | H | Tutorial PSD+SS+SP | Tutorial AH+SS+SP | S | ||
Sunday : Off | |||||||||
Mon | 29 Aug ‘22 | Lecture VK | Lecture PSD | Tutorial VK+SS+SP | Tutorial PSD+SS+SP |