TEW - Partial Differential Equations (2022)
Speakers and Syllabus
|
Name of the Speaker with affiliation |
No. of Lectures (each of 1.5 hours) |
Detailed Syllabus |
|
Veerappa Gowda G. D., Former Professor, TIFR-Centre for Applicable Mathematics, Bengaluru |
4 |
Introduction to PDE. Solving linear, semi-linear, quasilinear and fully non-linear first order equations by using the method of characteristics. Conservation laws: Weak Solutions, concept of entropy solution and Riemann problems. Examples with their applications in various fields. |
|
Prof. Ujjwal Koley (UK) , Associate Professor at TIFR-CAM |
4 |
Laplace equation: Fundamental solution, mean-value property, strong maximum principle. Introduction to Sobolev spaces, notion of weak derivatives. Poisson equation: Notion of weak solution, Lax-Milgram Lemma, existence and uniqueness of the weak solution for Dirichlet as well as Neumann problems. |
|
Joseph K.T., Former Professor, TIFR-Centre for Applicable Mathematics, Bengaluru |
4 |
Wave equation:Geometrical and symmetry properties of the wave operator, properties of the fundamental solution, the well-posedness and properties of the solution such as , energy conservation, loss of regularity in the solution, finite speed of propagation and Huygen's principle. Second order linear hyperbolic equations with variable coefficients: Existence, uniqueness of the solution and its continuous dependence on the data. Regularity results and the finite speed of propagation property. |
|
Venky Krishnan, TIFR-Centre for Applicable Mathematics, Bengaluru |
4 |
Heat Equation: Introduction to the heat equation and derivation of the fundamental solution. Solution to the homogeneous problem and solution to the non-homogeneous problem by Duhamel's principle. Regularity of the solution in bounded domains and explanation of the infinite speed propagation. Heat mean value formula. Weak and strong maximum principles. Energy methods to prove the uniqueness and backward uniqueness of the solution. |
References:
(1) Evans, L.C., Partial differential equations, Rhode Island: AMS, Providence.
(2) Folland, G.B., Introduction to partial differential equations,2nd ed., Princeton University Press.
(3) John, F., Partial Differential equations, Springer verlag.
(4) Jurgen Jost, Partial differential equations, Springer
(5) McOwen, R.C., Partial differential equations:Methods and Applications, 2nd ed.,Pearson Education.
Name of the tutors:
|
S. No. |
Name |
Affiliation |
|
1 |
Joseph K.T. |
Former Professor, TIFR-Centre for Applicable Mathematics, Bengaluru |
|
2 |
Ujjwal Koley |
Associate Professor at TIFR-CAM |
|
3 |
Veerappa Gowda G. D. |
Former Professor, TIFR-Centre for Applicable Mathematics, Bengaluru |
|
4. |
Venky Krishnan |
TIFR-Centre for Applicable Mathematics, Bengaluru |
Time Table
Week-1, February (17,18,19,20)
|
Lecture-1 |
Lecture-2 |
Lecture-3 |
Lecture-4 |
Tutorial-1 |
Tutorial-2 |
|
|
Date |
Thursday 17-02-2022 |
Friday 18-02-2022 |
Saturday 19-02-2022 |
Saturday 19-02-2022 |
Sunday 20-02-2022 |
Sunday 20-02-2022 |
|
Time |
18:00-19:30 |
18:00-19:30 |
16:00-17:30 |
18:00-19:30 |
16:30-17:30 |
18:00-19:00 |
|
Speaker |
GDVG |
UK |
GDVG |
UK |
GDVG |
UK |
Week-2, February (24,25,26,27)
|
|
Lecture-1 |
Lecture-2 |
Lecture-3 |
Lecture-4 |
Tutorial-1 |
Tutorial-2 |
|
Date |
Thursday 24-02-2022 |
Friday 25-02-2022 |
Saturday 26-02-2022 |
Saturday 26-02-2022 |
Sunday 27-02-2022 |
Sunday 27-02-2022 |
|
Time |
18:00-19:30 |
18:00-19:30 |
16:00-17:30 |
18:00-19:30 |
16:30-17:30 |
18:00-19:00 |
|
Speaker |
UK |
GDVG |
UK |
GDVG |
UK |
GDVG |
Week-3, March (3,4,5,6)
|
|
Lecture-1 |
Lecture-2 |
Lecture-3 |
Lecture-4 |
Tutorial-1 |
Tutorial-2 |
|
Date |
Thursday 03-03-2022 |
Friday 04-03-2022 |
Saturday 05-03-2022 |
Saturday 05-03-2022 |
Sunday 06-03-2022 |
Sunday 06-03-2022 |
|
Time |
18:00-19:30 |
18:00-19:30 |
16:00-17:30 |
18:00-19:30 |
16:30-17:30 |
18:00-19:00 |
|
Speaker |
KTJ |
VK |
KTJ |
VK |
KTJ |
VK |
Week-4, March (10,11,12,13)
|
|
Lecture-1 |
Lecture-2 |
Lecture-3 |
Lecture-4 |
Tutorial-1 |
Tutorial-2 |
|
Date |
Thursday 10-03-2022 |
Friday 11-03-2022 |
Saturday 12-03-2022 |
Saturday 12-03-2022 |
Sunday 13-03-2022 |
Sunday 13-03-2022 |
|
Time |
18:00-19:30 |
18:00-19:30 |
16:00-17:30 |
18:00-19:30 |
16:30-17:30 |
18:00-19:00 |
|
Speaker |
VK |
KTJ |
VK |
KTJ |
VK |
KTJ |
Full forms for the abbreviations of speakers and tutors:
UK:Ujjwal Koley
KTJ: Joseph K.T.
VK: Venky Krishnan
GDVG: Veerappa Gowda G D