Numerical Linear Algebra and Differential Equations

Convener(s)

 
Name: Dr. Manoj Sahni Dr. Chandra Shekhar Nishad
Mailing Address: Professor in affiliation
Department of Mathematics,
School of Technology
Pandit Deendayal Energy University,
Gandhinagar,
Gujarat - 382426.		 Assistant Professor (Grade I)
Department of Science and Mathematics
International Institute of Information Technology,
Naya Raipur,
Chhattisgarh – 493661
Email: manoj.sahni at sot.pdpu.ac.in,
manojsahani117 at gmail.com		  chandrashekhar at iiitnr.edu.in

In this course, we will cover the essential concepts of Numerical linear algebra, mastering vectors, matrices,eigenvalues, and eigenvectors. Explore the dynamics of real-world systems through ordinary and partial differential equations, gaining insights into their applications in Physics and Engineering, and try to cover the basics like consistency, stability and convergence. The participants will elevate their knowledge of problem-solving skills and lay a robust foundation for understanding and tackling complex mathematical challenges.

The topic Numerical Linear Algebra and Differential Equations delves into the essential elements of constructing mathematical models using two key pillars of mathematics: linear algebra and differential equations. This interdisciplinary approach provides a solid groundwork for understanding and solving real world problems across various fields. Linear algebra serves as a powerful tool for representing and manipulating systems of equations, while differential equations offer a framework for describing the dynamic changes within these systems. The integration of these two mathematical branches equips learners with the skills to create and analyze models that capture complex phenomena. This topic is pivotal for students and professionals seeking a comprehensive understanding of mathematical modeling and its practical applications. In addition, we intend to have many tutorials/problem sessions to supplement the lectures. This program will have a considerably positive effect on students in many colleges and universities.

Please note that TEW is meant only for the local college teachers. The lectures in this workshop covers specific topics which are relevant for the teachers' classroom instructions. The usual length of the TEW is 5/6 days. An important component of this programme is the discussion hour during which the teachers will have opportunities to get their doubts cleared.

Dates: 

Friday, August 23, 2024 - 19:00 to Wednesday, August 28, 2024 - 19:00

Venue: 

Venue Address: 

Pandit Deendayal Energy University (PDEU) Gandhinagar

Venue State: 

Venue City: 

PIN: 

38246

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:

 

Selected Applicants: 

The last date for confirmation of the selected participants is 8th Aug 2024 send your confirmation to the  mail id manojsahani117@gmail.com

Sr.n SID Full name Gender Affiliation Position in College/University University/Institute M.Sc./M.A. Year of Passing M.Sc./M.A Ph.D. Degree Date
1 57920 Ms. Seema Bano Aluddin Shah Female S.N. Patel Institute of technology and Research center, Bardoli Assistant Professor B.K.M.Science college, Valsad 2018  
2 57952 Mr. Sumit Singh Male Indian Institute of Technology Madras PhD University of Gour Banga 2020  
3 58034 Ms Gopika K V Female National Institute Of Technology Puducherry PhD Pondicherry University 2021  
4 58048 Mr Govinda Raju R Male Vidyavardhaka College of Engineering Assistant Professor University of Mysore 2018  
5 58066 Mr. Gnanasekaran S Male SRM Easwari Engineering College Assistant Professor Bharathiar University / University Department 2015 7 Aug 23
6 58070 Dr. Bhavini Maheshbhai Pandya Female Sardar Vallabhbhai Patel Institute of Technology, Vasad Associate Professor M.S.University 2000 23 Feb 17
7 58078 Dr. Neeru Bala Female Dayanand College Assistant Professor Guru Jamheshwar University, Hisar 2002 27 Jun 11
8 58110 Mr Ritabrata Banibrata Mukhopadhyay Male SAC-ISRO,Indus University JRF Institute of Advanced Research Gandhinagar 2021  
9 58124 Mrs Sonali Mandar Narsale Female MES Wadia College Of Engineering Pune Assistant professor M.Sc Mathematics 2006  
10 58165 Mr Mukesh Chandra Karmi Male DA-IICT GANDHINAGAR PhD NIT ROURKELA 2020  
11 58173 Mr. Manoj Kumar Male Aligarh Muslim University PhD student Aligarh Muslim University 2019  
12 58179 Dr. Saurabh Kumar Male Gautam Buddha University Assistant Professor M.A. 2016 8 Sep 23
13 58322 Mr. Dharmendra Kumar Chaurasia Male Banaras Hindu University PhD University of Allahabad 2019  
14 58326 Dr. Parth Dinesh Mehta Male Symbiosis Institute of Business Management, Bengaluru, Symbiosis International Assistant Professor Kadi Sara Vishwavidyalaya 2015 21 Nov 20
15 58336 Dr. Meghna M Parikh Female Lj university Assistant professor Kadi sarva vishvidhyalaya 2013 25 Nov 22
16 58337 Prof. Shruti R. Rathod Female LDRP Institute of Technology and Research Assistant Professor Veer Narmad South Gujarat University 2007  
17 58396 Dr. Muneer Nabi Male Karnavati University Assistant Professor Jamia Millia Islamia /M.Sc. 2015 21 Jun 23
18 58407 Dr. Rashmi Prasad Female Amrita Vishwa Vidyapeetham Assistant Professor Central University of South Bihar 2017 23 Jun 23
19 58415 Mr. Chandra Prakash Male Shivaji College Assistant Professor M.Sc. 2008 10 May 24
20 58431 Mr. Akash Panwar Male The LNM Institute of Information Technology PhD Student The LNM Institute of Information Technology 2021  
21 58442 Dr Lakshmi Rani Basumatary Female Zakir Husain Delhi College, University of Delhi, Delhi Assistant Professor Gauhati University 2012 24 Feb 22
22 58465 Dr. Shashikant Kumar Male Amity University Madhya Pradesh Assistant Professor Visvesvaraya National Institute of Technology Nagpur, Maharashtra 2017 20 Sep 23
23 58550 Prof Ajender Kumar Malik Male UP Rajarshi Tandon Open University Professor Gurukul Kangri Vishvidhalaya Haridwar 2005 12 Feb 11
24 58552 Dr. Ritu Sahni Female Kaushaliya - The Skill University Assistant Professor Dayalbagh Educational Institute, Agra 2003 20 Jun 13
25 58570 Dr. Sonu Rani Female Government College for Girls Kairu Assistant Professor MDU Rohtak 2011 20 Oct 21
26 58607 Mr. Jatin Bansal Male Central University of Punjab Research Scholar Panjab University Chandigarh 2019  
27 58626 Mr. Sandeep Wankhade Male Parul University Assistant Professor The Maharaja Sayajirao University of Barod 2014  
28 58632 Mr. Dharamikkumar Bharatkumar Chauhan Male PDEU, Gandhinagar JRF Indian Institute of Teacher Education 2023  
29 58664 Ms. Priya Tak Female Chaudhary Charan Singh Haryana Agricultural University(CCS HAU) Scholar South Asian University/M.Sc(applied Mathematics) 2019  
30 58665 Ms Kritika Gupta Female NIT kurukshetra PhD Kurukshetra University, Kurukshetra, 136119 Appeared / Awaiting Result  
31 58666 Ms Amisha Rani Female National institute of technology PhD Kurukshetra University , kurukshetra Haryana 2021  
32 58673 Dr Palanisamy Lakshmanan Male SRMInstitute Of Science And Technology Assistant Professor M.Sc., 2006 28 Dec 22
33 58679 Mr. Ram Kishan Male Birla Institute of Technology And Science, Pilani PhD University Of Rajasthan 2022  
34 58716 Dr. Sanjeev Kumar Singh Male V. S. S. D. College, Kanpur Assistant Professor Banaras Hindu University, Varanasi 2015 24 Nov 22
35 58719 Mr. Vikendra Singh Male Janki Devi Memorial College Asst. Prof. South Asian University 2015  
Waiting list      
1 58096 Dr Umamaheswari Palanivel Female Dr. N.G.P Arts and Science College, Coimbatore Assistant Professor Department of Mathematics, Bharathiar University, Coimbatore, Tamil Nadu 2014 4 Apr 19
2 58164 Dr. Bishnu Pada Ghosh Male Jagannath University Associate Professor University of Dhaka 2004 9 Nov 21
3 58171 Dr. Jogendra Kumar Male DIT University Associate Professor Banaras Hindu University 2005 20 Oct 11
4 58172 Mrs Vinitha M Female Dr.N.G.P. Arts and Science College Assistatnt Professor Dr.N.G.P. Arts and Science College 2018  
5 58208 Miss Shakshi Sharma Female Pt. Ravishankar Shukla University Msc student      
6 58209 Miss Tanya Verma Female Pt. Ravishankar Shukla University MSc Student Pt. Ravishankar Shukla University Appeared  
7 58401 Dr. Muthukumar Palanisamy Male Assistant Professor, Department of Mathematics
The Gandhigram Rural Institute (Deemed to be University), Gandhigram		 Assistant Professor Bharathiar University, Coimbatore, Tamilnadu 2002 5 Nov 09
8 58612 Ms. Nandani Jayeshbhai Viradiya Female Pandit Deendayal Energy University MSc student Pandit Deendayal Energy University Appeared  
9 58633 Dr. Sowrirajan R Male Dr. N. G. P Arts and Science College Assistant Professor and Head Bharathiar University/ Sri Ramakrishna Mission Vidyalaya College of Arts and Science 2003 27 Mar 09
10 58646 Mr. Bhavik Dhirubhai Chauhan Male Pandit Deendayal Energy University M.Sc. Pandit Deendayal Energy University Appeared  
11 58648 Mr. Jenishkumar Kanjibhai Zala Male Pandit Deendayal Energy University | MSc Pandit Deendayal Energy University Appeared  
12 58687 Mr. Jay Jani Male PDEU MSc Student PDEU Appeared  
13 58717 Dr. Rajasekar S P Male Government Arts College for Women, Nilakottai Associate Professor Pondicherry University 2004 30 Sep 20

 

 

School Short Name: 

nlade

Last Date Application: 

Monday, August 15, 2022

School Type: 

TEW

Separate faculty form: 

0