TEW - Numerical Linear Algebra and Differential Equations
Speakers and Syllabus
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
Dr. Akshaa Vatwani, IIT Gandhinagar
|
6 |
Inner product spaces, Gram-Schmidt Process, Eigenvalues and Eigenvectors, Spectral theorem for normal matrices and its applications. Definition and properties of matrix norms. |
Prof. J.K. Verma, IIT Bombay |
6 |
Singular Value Decomposition and its applications, Polar decomposition QR Decomposition, Moore Penrose inverse and its applications |
Dr. Manoj Sahni, PDEU Gandhinagar |
6 |
Theory of first-order ordinary differential equations. The existence and uniqueness theorem for IVP. Systems of first-order ODE and higher-order ordinary differential equations with applications. Numerics for ordinary differential equations (IVPs and BVPs): Euler's method, Modified Euler’s method, 4th order Runge-Kutta method, Stability and convergence, Finite difference methods for boundary value problems. |
Dr. Rohit Kumar Mishra, IIT Gandhinagar |
6 |
Introduction to first-order Partial Differential Equations, Method of characteristics to solve linear, semi-linear, quasilinear, and fully non-linear first-order equations. Introduction to Second Order Partial Differential Equations (PDEs): Definition and Classification of PDEs. Linear Second Order PDEs: Classification and Characteristics, Canonical Forms: Elliptic, Parabolic, and Hyperbolic Equations, Analytical Solutions and Boundary Value Problems. |
References:
1. Gilbert Strang, Introduction to Linear Algebra, 6th Edition, 2023
2. Kenneth Hoffman, Linear Algebra, 2nd Edition, Prentice Hall India Learning Private Limited, 2015.
3. David Watkins, Fundamentals of matrix computations, 2nd Edition, John Wiley & Sons, 2002.
4. Ward Cheney and David Kincaid, Linear Algebra: Theory and Application, 1st Edition, 2008.
5. L. N. Trefethen and David Bau, Numerical Linear Algebra, SIAM, 1997.
6. B. N. Datta, Numerical Linear Algebra and Applications, 2nd Edition, SIAM, 2010.
7. S.L. Ross, Differential Equations, 3rd Edition, 2007.
8. Francois Treves, Basic Linear Partial Differential Equations, 2013.
Time Table
Time-table (with names of speakers and tutors):
Date, Days |
Lecture 1 9:30-10:30 |
10:30 11:00 |
Lecture 2 11:00-12:00 |
Tutorial 1 12:00-12:45 |
12:45 |
Lecture 3 2:30-3:30 |
3:30 – 4:00 |
Lecture 4 4:00-5:00 |
Tutorial 2 5:00-5:45 |
5:45-6:15 |
|
(Speaker’s name) |
Tea |
(Speaker’s name) |
(Tutor’s name) |
Lunch |
(Speaker’s name) |
Tea |
(Speaker’s name) |
(Tutor’s name) |
Snacks |
23-08-2024 Friday |
AV |
|
AV |
AV, MS, CSN |
|
MS |
|
MS |
MS, CSN |
|
24-08-2024 Saturday |
AV |
|
AV |
AV, MS, CSN |
|
MS |
|
MS |
MS, CSN |
|
25-08-2024 Sunday |
AV |
|
AV |
AV, MS, CSN |
|
RKM |
|
RKM |
RKM, MS, CSN |
|
26-08-2024 Monday |
RKM |
|
RKM |
RKM, MS, CSN |
|
JKV |
|
JKV |
JKV, MS, CSN |
|
27-08-2024 Tuesday |
RKM |
|
RKM |
RKM, MS, CSN |
|
JKV |
|
JKV |
JKV, MS, CSN |
|
28-08-2024 Wednesday |
MS |
|
MS |
MS, CSN |
|
JKV |
|
JKV |
JKV, MS, CSN |
Valedictory Session followed by Snacks |
Full forms for the abbreviations of speakers and tutors:
- Prof. J.K. Verma (JKV) https://www.math.iitb.ac.in/~jkv/
- Dr. Akshaa Vatwani, (AV) https://iitgn.ac.in/faculty/maths/fac-akshaa
- Dr. Rohit Kumar Mishra (RKM) https://iitgn.ac.in/faculty/maths/fac-rohit
- Dr. Manoj Sahni (MS) https://scholar.google.co.in/citations?user=iDrxNGwAAAAJ&hl=en
- Dr. Chandra Shekhar Nishad (CSN) https://scholar.google.co.in/citations?user=iDrxNGwAAAAJ&hl=en