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 leastsquares 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, RungeKutta 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, BITSPilani Hyderabad Campus 
2 
Dr. Jaganmohan J 
Department of Mathematics, BITSPilani Hyderabad Campus 
Time Table
Timetable (with names of speakers and tutors):
Day 
Date 
Lecture 1 (9.30–11.00) 
Tea (11.0011.30) 
Lecturer 2 (11.30–1.00) 
Lunch (1.00 
Lecture 3 (2.304.00) 
Tea (4.00 to 
Discussion (4.155.15) 
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.