TEW - Linear Algebra and Differential Equations (2025)

Speakers and Syllabus

 

Name of the Speaker with affiliation No. of Lectures Detailed Syllabus
Dr. Sreenivasa Rao Y
Assistant Professor Department of Mathematics,
National Institute of Technology Warangal		 8+1 Vector spaces, linear dependence and independence of vectors, basis and dimension. Eigenvalues and eigenvectors, Diagonalizability, Orthogonal matrices, Symmetric matrices, Unitary matrices, Similar matrices, Change-of-basis, Orthonormal basis, Spectral theorem, Schur’s unitary triangularization, full and reduced QR Factorization, GramSchmidt Orthogonalization, Rank-nullity theorem, Existence of eigenvalues and eigenvectors.
Prof. Subrahmanya Sastry Challa
Professor,
Dept. of Mathematics, IIT Hyderabad		 6+2 Modelling with the system of equations, General first-order systems, Linear systems, linear homogeneous systems, The Eigen-analysis Method for x′ = Ax, Jordan Form and Eigen- analysis, Nonhomogeneous Linear Systems. Existence and uniqueness of Singular Value Decomposition (SVD), SVD as a change of basis, Low-rank approximation, Power Method for Computing the SVD.
Prof. Raja Sekhar G P Professor (HAG) Department of Mathematics, IIT Kharagpur 6+2 ODEs and Dynamical Systems. Existence of Solutions, Uniqueness of Solutions, Picard-Lindelöf Theorem, Intervals of Existence, Dependence on Parameters, Constant Coeffi- cient Linear Equations. Single step methods and multi-step methods for solving IVPs, convergence and stability.
Numerical solution to Parabolic PDE (1D-Heat Conduction equation): Explicit methods, Implicit Methods, Convergence and Stability; Hyperbolic PDE (Wave Equation): Explicit, Implicit methods, Method of characteristics, Convergence
and stability.
Prof. Kasi Viswanadham K N S, Professor
Department of Mathematics, National Institute of
Technology Warangal		 4+1 Concept of weak formulation; Lax-Milgram Theorem for existence and uniqueness of linear operators.
Basic concepts of the Finite Element Method (FEM), examples; Applications of FEM in fluid flows.

References:

  1. Linear Algebra and its Applications. by Gilbert Strang, Wellesley-Cambridge Press.
  2. Linear Algebra, Hoffman and Kunze, Pearson publications.
  3. Algebra, M. Artin, Pearson Publications.
  4. Numerical Solution of Partial Differential Equations: Finite Difference Methods (Oxford Applied Mathematics & Computing Science Series), G. D. Smith
  5. Numerical Solution of Ordinary Differential Equations (Wiley), Kendall E. Atkinson, Weimin Han, David E. Stewart
  6. Numerical Methods for Scientific and Engineering Computation (New Age International) M K Jain, S R K Iyengar, R K Jain.

Time Table

 

Day

Date

Lecture 1
(9.30
to
10.30)

Tea
(10.35
to
10.55)

Lecture 2

(11.00
to
12.00)

Lecture 3
(12.00
to
1.00)

Lunch (1.00
to
2.20)

Lecture 4
(2.30
to
3.30)

Tea (3.35
to
3.55)

Discussion (4.00
to
500)

Snacks (5.05
to
5.30)

 

 

(Speaker’s name)

 

(Speaker’s name)

(Speaker’s
name)

 

(Speaker’s
name)

 

(Tutor’s
name)

 

Mon

21.04.2025

S1

 

S1

S2

 

S2

 

T1,T2, S2

 

Tue

22.04.2025

S1

 

S2

S1

 

S2

 

T1,T2, S2

 

Wed

23.04.2025

S1

 

S2

S1

 

S2

 

T1,T2, S3

 

Thu

24.04.2025

S1

 

S1

S3

 

S3

 

T1,T2, S3

 

Fri

25.04.2025

S3

 

S3

S4

 

S4

 

T1,T2, S4

 

Sat

26.04.2025

S3

 

S3

S4

 

S4

 

T1,T2, S4

 

 Full forms for the abbreviations of speakers and tutors:

S. No.

Name

Affiliation

1

Dr.Y.Sreenivasa Rao(S1)

Dept.of Mathematics, NIT Warangal

2

Prof.Subrahmanya Sastry Challa(S2)

Dept.of Mathematics ,IIT Hyderabad

3

Prof.Raja Sekhar GP (S3)

Dept.of Mathematics ,IIT Kharagpur

4

Prof.Kasi Viswanadham K (S4)

Dept.of Mathematics ,NIT Warangal

 Name of the tutors:

S. No.

Name

Affiliation

1

Dr.Y.Sreenivasa Rao (T1)

Dept.of Mathematics, NIT Warangal

2

Dr.Satyanarayana Engu (T2)

Dept.of Mathematics, NIT Warangal
File Attachments: