TEW - Linear Algebra, Differential Equations and its Applications (2023)
Speakers and Syllabus
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Dr. Pratysha Chattopadhyay BITS Pilani Hyderabad Campus |
3 (each one 1.5 hr) |
Basics of vector spaces: Basis and dimensions, Subspaces, Dimension Theorem, Inner product spaces, QR decomposition, Linear least-squares problem, |
|
Dr. S Kumaresan Retd, Professor, University of Hyderabad |
3 (each one 1.5 hr) |
Eigenvalue problem, Diagonalization, Canonical forms, Spectral Theorem, Matrix norms, Condition number, Singular value decomposition and its applications. |
|
Prof. B. Mishra BITS Pilani Hyderabad Campus |
3 (each one 1.5 hr) |
Theory of first order ordinary differential equations: Existence, uniqueness and continuous dependence. Systems of first order ODE and higher order ordinary differential equations with applications. |
|
Prof. N. Kishore Kumar BITS Pilani Hyderabad Campus |
3 (each one 1.5 hr ) |
Numerics for ordinary differential equations (IVPs and BVPs): Euler's method, Higher order Taylor's method, Runge-Kutta method, stability and convergence., finite difference methods for boundary value problems, etc. |
|
Dr. G. Murali Mohan Reddy BITS Pilani Hyderabad Campus
|
3 (each one 1.5 hr) |
First order partial differential equations: Introduction to PDE, the method of characteristics to solve linear, semilinear, quasilinear and fully nonlinear first order equations |
|
Dr. G. Murali Mohan Reddy BITS Pilani Hyderabad Campus |
3 (each one 1.5 hr) |
Classification of second order partial differential equations Theory of elliptic partial differential equations: Mean value formula, Maximum and minimum principles, Uniqueness and regularity of the Dirichlet problem. |
References:
1. Ross, Differential equations, John Wiley.
2. Y. Pinchover and J. Rubinstein, Introduction to partial differential equations, Cambridge press.
3. Gilbert Strang, Introduction to Linear Algebra.
4. Bradie, A friendly introduction to Numerical Analysis, Perason.
Name of the tutors:
|
S. No. |
Name |
Affiliation |
|
1 |
Dr. Rohit Gupta |
Department of Mathematics, BITS-Pilani Hyderabad Campus |
|
2 |
Dr. Jaganmohan J |
Department of Mathematics, BITS-Pilani Hyderabad Campus |
Time Table
Time-table (with names of speakers and tutors):
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.00-11.30) |
Lecturer 2 (11.30–1.00) |
Lunch (1.00 |
Lecture 3 (2.30-4.00) |
Tea (4.00 to |
Discussion (4.15-5.15) |
Snacks (5.15 |
|
Mon |
09.01.23 |
PC |
|
BM |
|
GM |
|
PC,DP,RG |
|
|
Tue |
10.01.23 |
PC |
|
BM |
|
GM |
|
PC,DP,RG |
|
|
Wed |
11.01.23 |
PC |
|
BM |
|
GM |
|
BM,JJ,BG |
|
|
Thu |
12.01.23 |
SK |
|
NK |
|
GM |
|
NK, JJ,BG |
|
|
Fri |
13.01.23 |
SK |
|
NK |
|
GM |
|
GM,JJ,BG |
|
|
Sat |
14.01.23 |
SK |
|
NK |
|
GM |
|
GM,JJ,BG |
|
Full forms for the abbreviations of speakers and tutors:
PC: Pratyusha Chattopadhyay
SK: S. Kumaresan
GM: G. Murali Mohan Reddy
BM: B. Mishra
NK: N. Kishore Kumar
DP: Deepika
RG: Rohit Gupta
BG: Bhargav Kumar
JJ: Jaganmohan J.