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
2:30

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:

 

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