TEW Linear Algebra & Multivariable Calculus (2019)

Venue:	Mepco Schlenk Engineering College, Sivakasi, Tamil Nadu
Date:	13th, May 2019 to 18th, May 2019

School Convener(s)
Name	K.N Raghavan	R.Ratha Jeyalakshmi
Mailing Address	Professor, IMSc, C. I. T. Campus Chennai 600 113	Head, Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi, Tamilnadu - 626005

Speakers with their affiliations:

Name of the speaker	Position	Affiliation
Anirban Mukhopadhyay		IMSc, Chennai
K. N. Raghavan	Professor	IMSc, Chennai
S. Sundar		IMSc, Chennai

Syllabus:

The topics covered:

Anirban Mukhopadhyay

Differential forms, following chapter 10 of baby Rudin:

Definition, examples, basic form, standard presentation, addition and multiplication.
Differentiation of forms, examples, differentiation of product of forms.
Change of variables.
Transformation properties.
Oriented simplices and their boundaries.
Stokes’ theorem
Applications: Green’s theorem, Gauss’ theorem; gradient, divergence, and curl; area and volume computation.

K. N. Raghavan

Linear Algebra, following notes (https://www.imsc.res.in/~knr/past/linalg_ed.pdf) copies of which were distributed. Emphasis was laid on problem solving and the utility of raising questions. Much time was devoted to discussion of the exercise sets in the notes.

Row reduced echelon forms: existence and uniqueness, properties and uses.
Equality of row and column ranks; various spaces associated with a matrix and relations between them.
Solving linear equations; geometry of the solution set.
Orthogonal projections; approximate solution to an over-determined system of linear equations; application to the line of best fit.
Spectral theorem for real symmetric matrices; positive definite and semi-definite matrices.
Singular value decomposition.

S. Sundar

Multivariate Calculus

Basics of metric spaces, norms induced by inner products, Cauchy Schwarz inequality, equivalence of norms on finite dimensional vector spaces.
Derivative as a linear map, examples from first principles, chain rule, directional derivative and partial derivative, examples.
Sufficient condition for existence of total derivative, equality of mixed partial derivatives, Taylor’s theorem up to second order and applications to maxima and minima.
Diagonalising a symmetric operator, min max theorem, application to the proof of Sylvester’s criterion (for positive definiteness).

Time Table

Time	09:30 to 11:00		11:15 to 12: 45		14:00 to15:30		15:45 to 16:45
Mon 13th	KNR	T E A	SS	L U N C H	AM	T E A	Tutorials (KNR & SS)	S N A C K S
Tue 14th	AM		KNR		SS		Tutorials (AM & SS)
Wed 15th	KNR		AM		SS		Tutorials (KNR & SS)
Thur 16th	KNR		SS		AM		Tutorials (SS & AM)
Fri 17th	KNR		AM		AM		Tutorials (KNR & AM)
Sat 18th	KNR		AM		KNR		Tutorials (AM & KNR)

KNR - K.N.Raghavan
AM - Anirban Mukhopadhyay
SS - S.Sundar

List of actual Participants

Sr.	SID	Full Name	Gender	Affiliation	Position in College /Univ.	Univ. / Instit. M.Sc./M.A.	Year of Passing M.Sc./ M.A	Ph.D. Deg Date
1	23713	Mrs Mala P	Female	Kamaraj College of Engineering and Technology	Assistant Professor	Ayya Nadar Janaki Ammal College, Sivakasi	2008
2	23722	Dr Mallika A	Female	Sadakathullah Appa College (Autonomous)	Assisistant Professor	M.Sc	2010	10/13/2017
3	23741	Dr. Anantha Kumar Ramasamy	Male	MEPCO Schlenk Engineering College	Assistant Professor	Ayyanadar Janakiammal Collge(Autonomous), Sivakasi	2005	10/27/2014
4	23746	Dr M Palanivel	Male	Mepco Schlenk Engineering College (Autonomous)	Assistant Professor	Gandhigram Rural Institute Deemed University	2010	06/26/2016
5	23749	Dr. C Arun Kumar	Male	MEPCO SCHLENK ENGINEERING COLLEGE (Autonomous), SIVAKASI	Assistant Professor	JAMAL MOHAMED COLLEGE, TRICHY	2006	01/17/2014
6	23750	Dr. Lakshmanan Ramaraj	Male	MEPCO SCHLENK ENGINEERING COLLEGE (Autonomous), SIVAKASI	Assistant Professor	AYYA NADAR JANAKI AMMAL COLLEGE, SIVAKASI		09/24/2014
7	24042	Dr. Manimaran Thiruvudayan	Male	Ramco Institute of Technology Rajapalayam	Associate Professor	M.Sc	1996	19/08/2017
8	24164	Mrs. Vetri Selvi	Female	S.F.R. College For Women	Assistant Professor	S.F.R.College For Women, Sivakasi	1991
9	24309	Dr. Virendra Kumar	Male	CENTRAL UNIVERSITY OF TAMIL NADU THIRUVARUR	Assistant Professor	HNB GARHWAL UNIVERSITY SRINAGAR (GARHWAL)	2007	07/26/2013
10	24338	Mrs Rega Ramesh Babu	Female	BHARATHIDASAN UNIVERSITY	PhD	ALAGAPPA UNIVERSITY	2009
11	24367	Mrs Sankari Chandrasekaran	Female	A.V.V.M Sri Pushpam College (Autonomous)	PhD	Madurai Kamarajar University	2013
12	24400	Mrs. Geetha M	Female	Kamaraj college of Engg and Technology	Assistant Professor	VVV College for women	2007
13	24410	Dr Jamal Fathima	Female	Sadakathullah Appa College	Assistant Professor	Manonmaniam Sundaranar University	2010
14	24427	Dr T Kavaskar	Male	Central University of Tamil Nadu	Assistant Professor	Annamalai University	2005	08/06/2011
15	24443	Dr Renukadevi V	Female	Ayya Nadar Janaki Ammal College	Asst. Prof.	Kamaraj College, Thoothukudi	1998	06/06/2007
16	24451	Mr. Jeshua Rajan	Male	St. John's College	Asst. Prof.	St. John's College, Palayamkottai	2016
17	24546	Mrs Sankari Alias Deepa	Female	Rajapalayam rajus college	Assistant professor	A.k.D.R womens college	2015
18	24934	Mr. Vignesh K	Male	AYYA NADAR JANAKI AMMAL COLLEGE	M.SC., STUDENT	M.Sc.	Appeared / Awaiting Result
19	25246	Ms. P Vijaya Shanthi	Female	Ayya Nadar Janaki Ammal College	Ph.D Student	MADURAI KAMARAJ UNIVERSITY	2015
20	25996	Mr. L. David Raj Kumar	Male	The American College	Assistant Professor	The American College	2006
21	26086	Dr. Abirami Subburaj	Female	Sri S Ramasamy Naidu Memorial College	Assistant Professor	Madurai Kamaraj University	2008	06/08/2018
22	26425	Mr Sowndrarajan Selvaraj	Male	Raja Doraisingam Government Arts College	Asst. Professor	IIT Madras	2011
23	26865	Mr Gnanasekaran S S	Male	MADURAI KAMARAJ UNIVERSITY		BHARATHIDASAN UNIVERSITY	2017
24	27008	Mr. Anandasrinivasan S	Male	The Madura College	Assistant Professor	The Madura College	2015
25	27019	Mr Manivannan P	Male	Mepco Schlenk Engineering College, Sivakasi	Assistant Professor	Bharathidasan University, Trichy	2007
26	27021	Mr. Rajesh Kannan Alagarsamy	Male	Mepco Schlenk Engineering College, Sivakasi	Assistant Professor	Madurai Kamaraj University, Madurai	2001
27	27088	Dr. Saravanakumar K	Male	The Madura College	Assistant Professor	THE MADURA COLLEGE, TN	2011	23/02/2018
28	27362	Mrs. Muthumari U	Female	THE STANDARD FIREWORKS RAJARATNAM COLLEGE FOR WOMEN	Asst. prof.	Ayya Nadar Janaki Ammal College, Sivakasi	2010
29	27428	Ms Karthika Muthusamy	Female	Bannari Amman Institute of technology, sathyamangalam	Asst. Prof	P.K.R Arts College for Women	2013
30	27431	Dr Selvaraj Ganesan	Male	Ramco institute of Technology	Asst. Prof	Gandhigram Rural Insitute DU	2011	28/09/2017
31	27442	Mrs. Sathikala Subramanian	Female	Ramco Institute of Technology	Associate Professor	Madurai Kamaraj University	1995	19/02/2016
32	27452	Dr. I Rani	Female	Anna University Regional Campus -Tirunelveli	Asst. Prof.	Sarah Tucker College for Women	1994	01/23/2010
33	27469	Dr Kamatchi N	Male	KAMARAJ COLLEGE OF ENGINEERING AND TECHNOLOGY	Asso. Prof.	Ayya Nadar Janaki Ammal College, Sivakasi	2003	09/14/2013
34	27500	Dr Vennila R		Kongu Engineering College
35	27501	Mr. Selvaganesh T	Male	RAMCO INSTITUTE OF TECHNOLOGY	Assistant Professor	AYYA NADAR JANAKI AMMAL COLLEGE, SIVAKAI	2009
36	27519	Mrs. Subasini R	Female	Pollachi Institute of Engineering and Technology	Assistant Professor	NGM College M.Sc.,	2000
37	27528	Mrs Akila Saravanakumar	Female	The Standard Fireworks Rajaratnam College for Women	Assistant Professor	mother teresa university	2007
38	27530	Ms. G Petchiammal	Female	VHNSN COLLEGE (AUTONOMOUS)	Assistant Professor	MADURAI KAMARAJ UNIVERSITY	2012
39	27543	Dr. Chandra Guru Sekar R	Male	Mepco Schlenk Engineering College, Sivakasi	Assistant Professor	College of Engineering, Guindy	2014	10/24/2017
40	27622	Mrs Mydeen Bibi A	Female	The Standard Fireworks Rajaratnam College For Women	Assistant Professor	Lady Doak College, Madurai	2004	11/10/2013
41	27664	Dr. N. Annamalai	Male	Central University of Tamil Nadu	Assistant Professor	Bharathidasan University/ M.Sc	2011	02/26/2019
42	27765	Dr. Santhi P	Female	The Standard Fireworks Rajaratnam College for Women, Sivakasi	Assistant Professor	M.Sc	1996	23/06/2017
43	27772	Dr. K Pattabiraman	Male	Government Arts College(Autonomous)	Assistant Professor	Annamalai University	2004	11/11/2012
44	27791	Dr Karpagavalli Ramasamy	Female	Vidhyaa Giri College of Arts & Science	Associate Professor	M.Sc	2004	09/11/2015
45	27798	Dr. S. Kalai Selvi	Female	S.F.R. College For Women	Assistant Professor	Annamalai University	2004	11/11/2012
46	27807	Dr. Muthuselvi A	Female	The Standard Fireworks Rajaratnam College for Women	Assitant Professor	The Standard Fireworks Rajaratnam College for Women, Sivakasi	2013	24/08/2018
47	27823	Mrs Tamil Selvi	Female	Ayya Nadar Janaki Ammal College	phD	Ayya Nadar Janaki Ammal College, Sivakasi	2016
48	27829	Mrs Anandha Selvam	Female	The American college	Assistant Professor	Lady Doak college Madurai	1998
49	27992	Mr Subramanian Krishnamoorthy	Male	RAMCO INSTITUTE OF TECHNOLOGY	Assistant Professor	AYYA NADAR JANAKI AMMAL COLLEGE	2006

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