TEW Workshop for Mathematics Teachers of Engineering Colleges (2016)
Venue: 
The Institute of Mathematical Sciences, Chennai 
Dates: 
21^{st} to 26^{th} Nov, 2016 
Convener(s)  Speakers, Syllabus and Time table  Applicants/Participants 
Name  Prof. Parameswaran Sankaran  Prof. K Srinivas 
Mailing Address  The Institute of Mathematical Sciences C I T Campus Chennai 600 113 
The Institute of Mathematical Sciences C I T Campus Chennai 600 113 
1. Complex Analysis by Sushmita Venugopalan:
The topics covered in the complex analysis course include:
 holomorphicity of complex functions,
 power series and their discs of convergence
 Cauchy’s integral formula and
 classification of isolated singularities of holomorphic functions.
The course consisted of six lectures and two tutorial sessions, In the tutorial sessions, teachers were given a problem sheet, and they came up to the board to solve the problems in the sheet.A geometric and visual approach was adopted throughout the course, with the hope of augmenting the teachers’ understanding of the topics. The course started o↵ with a detailed discussion of the concept of derivative for multivariable functions. This was then used to explain complex linearity of derivative. Thus the link between the CauchyRiemann equations and its geometric consequence of conformality was explained. After this, the study of the transformations of the complex plane defined by various holomorphic functions, like linear functions, powers of z, followed by the exponential and logarithm functions were discussed. An entire lecture was spent in conveying a geometric intuition of the exponentialfunction, explaining why the log function cannot be defined on all of the complex plane, and why the log function can be defined on a spiral ramp that is a covering space of the complex plane minus the origin. The concept of analyticity was explained as being a source of rigidity in complex functions. An example of a smooth real function that is not analytic to explain the contrast, was then discussed. The tutorial problem sheets contained many examples of computations of power series and their radius of convergences. These examples were used to illustrate the fact that the disc of convergence was the largest possible disc that was contained in the domain on which the function can be defined holomorphically. Examples of the log function, and noninteger powers of z were discussed from this point of view. A visual proof of the Cauchy integral formula was presented. Various examples on the application of the Cauchy integral formula were discussed in the tutorial and the lecture. Using the geometric discussions of the log function, the integral of 1/z on the unit circle was evaluated. The final part of the course dealt with the types of isolated singularities using various examples.
2. Laplace transforms by Indrava Roy:
In this course standard material concerning Laplace transforms were covered comprising of the following topics:
 Background and definition of Laplace Transforms with definition
 Computing basic examples involving elementary functions for illustration
 Integral transforms
 Properties of Laplace transforms
 Computations involving special functions
 Limiting behaviour Initial and Final value theorems
 Inverse Laplace transform and the Bromwich integral; use of residue theorem
 Applications to solve linear ordinary and partial di↵erential equations with constant coefficients
Some nonstandard material was also covered, which helped bring out technical subtleties and richness of the theoretical aspects as well as applications in realworld problems of Laplace transforms. These include:
 Convergence issues for improper Riemann integrals
 Criteria for exchanging limits and integrals; Dominated convergence theorem for improper integrals
 Applications of Laplace transform to physical systems; examples of damped oscillations and bending of beams were illustrated
 Applications to solve integral and integrodi↵erential equations; example of Abel’s solution for the tautochrone problem and PID controllers in control system engineering were mentioned.
 Applications to solve recurrence relations, e.g. Fibonacci sequence.
3. Vector Calculus by Parameswaran Sankaran
Dot and cross product of vectors. Work done by a force–rotation and angular velocity. Moment of a force about a point acting on a body. Gradient of a vector field. Geometric and physical significance. Scalar potential. Constrained extrema–Lagrange multipliers. Line integral. Work done by a force field along a path. Divergence of a vector field. Surface integral. Flux of a vector field across a surface. Curl of a vector field. Green’s theorem, Stokes’ theorem, divergence theorem.
Name of the Speaker with affiliation 
Detailed Syllabus 
Sushmita Venugopalan IMSc Chennai 
Complex analysis 
Indrava Roy IMSc Chennai 
Laplace transform 
P Sankaran IMSc, Chennai 
Vector calculus 
Monday  Tuesday  Wednesday  Thursday  Friday  Saturday  
09:00 10:00  09:30  11:00 Vector calculus P Sankaran 
09:30  11:00 Vector calculus P Sankaran 
09:30  11:00 Vector calculus P Sankaran 
09:30  11:00 Vector calculus P Sankaran 
09:30  11:00 Complex analysis Sushmita V 
09:30  10:30 Complex analysis Sushmita V 10:30  11:30 Laplace transform Indrava Roy 
11:00  Coffee/Tea  Coffee/Tea  Coffee/Tea  Coffee/Tea  Coffee/Tea  
12:00 
11:30  13:00 
11:30  13:00 Complex analysis Sushmita V 
11:30  13:00 Laplace transform Indrava Roy 
11:30  13:00 Laplace transform Indrava Roy 
11:30  13:00 Laplace transform Indrava Roy 
Coffee/Tea 11:45  12:45 Vector calculus P Sankaran 
13:00  Lunch  Lunch  Lunch  Lunch  Lunch  Lunch 
14:00  14:00  15:00 Laplace transform Indrava Roy 
14:00  15:00 Laplace transform Indrava Roy 
14:00  15:00 Complex analysis Sushmita V 
14:00  15:00 Complex analysis Sushmita V 
14:00  15:00 Vector calculus P Sankaran 

15:00  Coffee/Tea  Coffee/Tea  Coffee/Tea  Coffee/Tea  Coffee/Tea  
16:00  15:15  16:45 Discussion Time 
15:15  16:45 Discussion Time 
15:15  16:45 Discussion Time 
15:15  16:45 Discussion Time 
15:15  16:45 Discussion Time 

17:00  Snacks  Snacks  Snacks  Snacks  Snacks 
Actual Participants 
Sr.  SID  Full Name  Gender  Affiliation  Position in College/ University  University / Institute M.Sc. / M.A.  Year of Passing M.Sc./ M.A  Ph.D. Deg Date 
1  9750  Mr. Ramesh Babu Thangavadivel  Male  Mepco Schlenk Engineering College, Sivakasi  Asst. Prof.  School of Mathematics, Madurai Kamaraj University  2010  
2  9756  Dr. C Arun Kumar  Male  Mepco Schlenk Engineering College , Sivakasi.  Asst. Prof.  Jamal Mohamed College, Trichy  2008  1/17/2014 
3  9757  Dr S. Priyan  Male  Mepco Schlenk Engineering College  Asst. Prof.  Thiagarajar College of Engineering, Madurai.  2010  12/28/2015 
4  9758  Dr Nagarajan Murugesan  Male  NEHRU INSTITUTE OF TECHNOLOGY  Asst. Prof.  Bharathiar University  2007  8/11/2014 
5  9771  Ms Gk Revathi  Female  VIT University  Asst. Prof.  Sri sarada college for women, Autonomous, Salem  2007  2/5/2013 
6  9773  Prof Mohana Natarajan  Female  VIT University  Asst. Prof.  M.Sc.  2007  
7  9775  Dr M Palanivel  Male  M. Kumarasamy College of Engineering  Asst. Prof.  The Gandhigram Rural Institute  Deemeed University  2010  6/27/2016 
8  9781  Dr. Manivannan Annamalai  Male  VIT University  Chennai Campus  Asst. Prof.  M.Sc., Pachaiyappa's College, University of Madras  2007  6/19/2015 
9  9782  Ms. S Gowri  Female  M.Kumarasamy College Of Engineering  Asst. Prof.  Bharathiyar  2013  
10  9783  Ms M Suganya  Female  M.Kumarasamy College Of Engineering  Asst. Prof.  bharathidasan  2013  
11  9788  Mr. Karunagaran K  Male  Bharath University  Asst. Prof.  S.I.V.E.T COLLEGE  2013  
12  9795  Dr Parthiban Venugopal  Male  Vit University  Chennai Campus  Asst. Prof.  Bharathiar University, Coimbatore  2008  8/16/2013 
13  9796  Mr E. Balaji Easwaran  Male  NEHRU INSTITUTE OF TECHNOLOGY  Asst. Prof.  ERODE ARTS COLLEGE, ERODE  2006  
14  9809  Mr Balamurugan P  Male  M.Kumarasamy College Of Engineering, Karur  Asst. Prof.  Bharathidasan University  2010  
15  9816  Mr A Arul Dass  Male  M.Kumarasamy College Of Engineering  Asst. Prof.  St.Josephs College,Trichy  2012  
16  9835  Dr. Vembarasan V  Male  Sri Sivasubramaniya Nadar College of Engineering  Asst. Prof.  Gandhigram Rural Institute  2009  1/22/2014 
17  9844  Dr. Yugesh S  Male  SSN College of Engineering, Kalavakkam603110  Asst. Prof.  Anna University/ College of Engineering  2011  
18  9849  Ms Priya Natarajan Sukumar  Female  sri venkateswara college of engineering  Asst. Prof.  M.Sc  2011  
19  9855  Dr. Raj Umadevi  Female  Sri Venkateswara College of Engineering  Asst. Prof.  Madurai Kamaraj University  2004  11/11/2011 
20  9856  Mrs. Krishnamoorthy Vijayalakshmi  Female  Sri Venkateswara College of Engineering  Asst. Prof.  Annamalai University  2005  
21  9867  Mrs. G Saravanan Sathish  Female  Vel tech Technical university  Asst.Prof  Bharathidasan university/A.V.V.M SPC Poondi  2004  5/26/2016 
22  9869  Professor M. Eswaramurthi  Male  Velalar College of Engineering and Technology  Professor  M.Sc  1987  1/2/2009 
23  9870  Dr Madan Lakshmanan  Male  AcSIR  Asst. Prof.  Delft University of Technology, Netherlands  2006  11/21/2011 
24  9873  Mr Saravanan G  Male  Veltech Dr.RR & Dr.SR University  Asst. Prof.  Madras University/S.I.V.E.T. COLLEGE  2014  
25  9876  Mr Naresh Kumar Jothi  Male  Vel tech Dr RR Dr SR University  Asst. Prof.  M.Sc  2006  
26  9885  Mr. M Regan Murugesan  Male  Veltech Dr.RR & Dr.SR University  Asst. Prof.  Govt.Arts College,Kumbakonam  2009  
27  9887  Mr. K Sathish Kumar  Male  Veltech Dr.RR & Dr.SR University  Asst.Prof  Pachayappas College,Chennai  2011  
28  9902  Dr Prabhu S  Male  Sri Venkateswara College of Engineering  Asst. Prof.  M.Sc  2006  2/20/2015 
29  9914  Mr Subramanian R  Male  Sri Sairam Engineering College  Asst.prof  Bharathidasan University  2005  
30  9915  Mr. Manikanda Prabhu S  Male  St.Joseph's College Of Engineering  Asst. Prof.  The Madura College  2012  
31  9917  Dr V.Vijaya Bharathi  Female  National Institute of Technology  Asst. Prof.  Bharathidasan  2008  1/8/2016 
32  9922  Ms. Methini M  Female  St.Joseph's College Of Engineering  Asst. Prof.  University Of Madras  2009  
33  9926  Mr. Murugan J  Male  St.Joseph's College Of Engineering  Asst. Prof.  University Of Madras  2007  
34  9927  Dr Nirmala Venkatachalam  Female  University College of Engineering  Asst.Prof  Bharahtidasan University  1996  11/5/2014 
35  9940  Mr. Meiyanathan M  Male  SRI SAIRAM ENGINEERING COLLEGE  Asst. Prof.  H.H.THE RAJAH'S COLLEGE PUDUKKOTTAI  2005  
36  9966  Mr. Josephrobinson Michealraj  Male  T.J.S Engineering College  Asst.Prof  Bharathidasan University  2005  
37  9967  Mr Satheesh Subramani  Male  T.J.S Engineering College  Asst.Prof  Anna University  2007  
38  9991  Mrs Geetha S  Female  National Engineering College  Asst. Prof.  Bishop Heber College, Trichirapalli  1995  
39  9996  Ms. Sandhiya A  Female  TJS Engineering College  Asst. Prof.  Madras univeristy  2009  
40  9998  Mr Loganathan M  Male  TJS Engineering College  Asst. Prof.  University Of Madras  2009  
41  9999  Mrs Anusuya K.V  Female  TJS Engineering College  Asst. Prof.  University Of Madras  2008  
42  10005  Mrs Meenadevi P  Female  SRI SAIRAM ENGINEERING COLLEGE  Asst. Prof.  V.V.Vanniaperumal College For Women  2004  
43  10012  Mr Vidhurankumar Moorthy  Male  TJS Engineering College  Asst. Prof.  Thiruvalluvar University  2008  
44  10016  Mr. Karthikeyan .D  Male  Podhigai College of Engineering and Technology  Asst. Prof.  Bharathiar University, Coimbatore  2005  
45  10019  Dr Poornima T  Female  Vit University, Chennai Campus  Asst. Prof.  Sri Padmavathi Mahila Viswavidyalayam,Tirupati  2005  3/13/2014 
46  10024  Mr Siluvai Dasan  Male  Tagore Engineering College  Asst. Prof.  ST.JOSEPH'S COLLEGE  2009  
47  10025  Mr. Mayavel P  Male  GKM college of Engineering and technology  Asst.Professor  Bharathidasan university  2013  
48  10028  Dr. Athithan Singaram  Male  SRM University  Asst. Prof.  University of Madras/AM Jain College M.Sc.  2007  1/11/2016 
49  10036  Dr. Sheeja G  Female  SRM University  Asst. Prof.  M.Sc  2002  1/10/2012 
50  10038  Mr Jegan S  Male  SRM University  Asst. Prof.  Loyola College,Chennai  2011  
51  10042  Dr. Mayilvaganan Subramanian  Male  SRM University  Asst. Prof.  Sacred heart college  2005  11/15/2015 
52  9772  Mrs. Radha Sundarrajan  Female  Vit University Chennai Campus  Asst.Professor  Kongu Nadu Arts and Science college, Coimbatore  1998  
53  9778  Ms Vasanthika S  Female  VIT University  Asst.Professor  Anna University Chennai – 600 025.  
54  9997  Mr Laksmikaanth Devi  Male  T.J.S ENGINEERING COLLEGE  ASSOCIATE PROFESSOR  UNIVERSITY OF MADRAS  1998  
55  9776  Mr Sundaram Dhanasekar  Male  VIT University  Asst.Professor  University of Madras  1998  
56  9768  Mrs. J.Deepa Lakshmi  Female  Mepco Schlenk Engg. College  Senior Grade Asst.Professor  M.sc  2001  
57  Usha Sangale  SRTM University, Naned  Asst.Professor  
58  Thilakaraj E  IMSc, Chennai  
59  Karthikeyan M  Panimalar Engineering College  Asst.Professor  
60  Raja N  VPT SRM  Asst.Professor  
61  Manirathnam D  Panimalar Engineering College  Asst.Professor  
62  Jeevarathinam V  Karpaga Vinayaga College of Engineering Technology  Asst.Professor  
63  Dhanasekar S  VIT UNIVERSITY, CHENNAI CAMPUS  Asst.Professor  
64  Logu S  Presidency College Chennai  PhD student 
How to reach
The Chennai neé Madras, and to IMSc, the Institute of Mathematical Sciences. Here is some information on getting to the Institute. Address and phone numbers are
THE INSTITUTE OF MATHEMATICAL SCIENCES
C I T CAMPUS, TARAMANI, CHENNAI 600 113
Telephone Numbers
Here are some maps to give you a rough idea of the layout of Madras and the area around the Institute.
 A simplified schematic map of Madras, showing the major roads and Hotels and marking the area in which the CIT Campus is located.
 A postscript version of this figure if you want to download it to print at your end.
 A detailed Madras map.
 A gzipped postscript version of this figure
 A schenatic map of the location of IMSc within CIT Campus and its environs
 Detailed map of the location of IMSc within CIT Campus and other landmarks in the Greater Adyar area.
The Institute of Mathematical Sciences is located in a campuslike area variously known as the ``CIT Campus'' or the ``CPT Campus''. Many people in Madras may not have heard of the Institute, but almost everyone would have heard of the M.G.R. Film City and Tidel Park which are further down in the same campus area. IMSc has two complexes. One houses the main Institute building, the library building and the new building. The other has the students' hostel and Guest House. These two complexes are across the road from each other.