# TEW Mathematics for Engineers (2015)

Venue: |
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai. |

Dates: |
23^{rd} Nov to 28^{th} Nov 2015 |

Convener(s) |
Speakers, Syllabus and Time table |
Applicants/Participants |

Name |
Parameswaran Sankaran |
K. N Raghavan |

Mailing Address |
Professor, Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113. |
Professor, Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113 |

The week-long workshop was aimed at mathematics teachers at engineering colleges, to enable them to revisit and update content knowledge. The lectures covered some particular topics (see below). Discussion hours offered opportunities to get doubts cleared and work out exercises (both routine and advanced).

** Speakers and subjects****• **Professor Parameswaran Sankaran (IMSc)

Differential and integral calculus of several variables

6 hours of lectures and 2.50 hours of tutorials / discussion

• Professor Kotyada Srinivas (IMSc)

Complex Analysis, Fourier Series, Laplace Transform

6 hours of lectures and 3 hours of tutorials / discussion

• Professor P. Vanchinathan (VIT University, Chennai)

Linear Algebra and Applications

6.25 hours of lectures and 3 hours of tutorials / discussion

** List of topics covered**

• Under Differential and integral calculus:

1. Differential calculus of several variables: Directional derivatives, differentiability, Jacobian, Taylor

formula, applications to extrema, Hessian, constrained extrema, Lagrange multipliers. Exercises.

Reference: Calculus, vol II, by Tom Apostol.

2. Vector calculus: Line integral, integral of vector valued functions with respect to arc length,

Green’s theorem. Surface and volume integral, Stokes’ theorem, divergence theorem. Exercises.

Reference: Calculus by James Stewart.

• Under Linear algebra and applications:

– Linear systems of equations—describing ALL solutions

– A=LU decomposition, its geometric description in two dimensions

– Geometry of linear transformations: shear, rotations, and reflections

– Projections, Gram-Schmidt process

– Matrices and linear transformations

– Solving Legendre’s differential equation; eigenfunctions

– Encyrption using matrices (Hill Cipher)

– Enumerating subsets using total ordering (DISCRETE Mathematics)

• Under Complex Analysis, Fourier Series, Laplace Transform:

– Analytic functions: Cauchy-Riemann equations, examples illustrating their necessity and suffi-

ciency for analyticity of a function; Harmonic functions; Power series; Uniform convergence of

sequences and functions.

– Cauchy’s theorem and its applications; Liouville’s theorem; Cauchy’s Integral formula; Cauchy’s

residue theorem; Evaluation of Integrals.

– Fourier Analysis: Discussion on the Heat equation, the wave equation, the Laplace equation;

Solution of second order ordinary differential equations; Fourier series expansion of a periodic

function; Discussion on the convergence of the Fourier series; Brief discussion of Fourier transform

and Laplace transform.

Actual Participants |

Online registration for the programme was opened about a month in advance. Out of 63 registered, 55 were selected, and 25 of these actually showed up for the programme. Along with 4 who showed up for spot registration, the total number of actual participants was 29. All participants were from within Tamilnadu except for one from Maharashtra who happens to be a long term visitor at IMSc for some other purpose.The weather in Chennai may have played a role in reducing the ratio of the number of those participated to those registered

Sl.No |
SID |
Name |
Affiliation |

1 | 991 | Jothiprakash. SP | Nehru Institute of Engineering and Technology, Anna University, Coimbatore |

2 | 993 | Anbukkarasi. A | IFET College of Engineering, Anna University, Villupuram |

3 | 996 | Rohini | M. Kumarasamy College of Engineering, Anna University,Karur |

4 | 1000 | Girija. L | SAMS College of Engineering and Technology, Anna University, Chennai |

5 | 1001 | Shankar. P | St. Joseph's College of Engineering, Anna University,Chennai |

6 | 1003 | Sivasubramanian. S | University College of Engineering, Anna University,Chennai |

7 | 1004 | Prakash. V | University College of Engineering, Anna University, Tindivanam |

8 | 1007 | Komala Durga. B | Vel Tech University, Chennai |

9 | 1011 | Karuppusamy | Bannari Amman Institute of Technology, Anna University,Erode |

10 | 1012 | Sivachandran. Y. L | Bannari Amman Institute of Technology, Anna University, Erode |

11 | 1014 | Parimala. M | Bannari Amman Institute of Technology,Anna University, Sathyamangalam |

12 | 1019 | Perumal | S.R.M University, Chennai |

13 | 1020 | Arul Joseph | S.R.M University, Chennai |

14 | 1021 | Prabhavathi. K | Bannari Amman Institute of Technology, Anna University, Erode |

15 | 1025 | Mohana. V | M Kumarasamy College of Engineering, Anna University,Karur |

16 | 1026 | Ravi Gopal Allamsetty | Indira Gandhi Centre For Atomic Research, Kalpakkam, Tamil Nadu |

17 | 1030 | Jaganathan. B | V.I.T University Chennai Campus, Chennai |

18 | 1035 | Thilagavathi. K | M.Kumarasamy College of Engineering, Anna University,Karur |

19 | 1040 | Gajendran. P | M.Kumarasamy College of Engineering, Anna University, Karur |

20 | 1041 | Swarnagowri | Jawahar Engineering College, Anna University,chennai |

21 | 1043 | Jeevarathinam. V | Karpaga Vinayaga College of Engineering and Technology, Anna University,Chennai |

22 | 1044 | Sathyavathy. M | M.Kumarasamy College of Engineering, Anna University,Karur |

23 | 1045 | Venkatachalam. A | M. Kumarasamy College of Engineering, Anna University, Karur |

24 | 1047 | Veeramalai. G | M.Kumarasamy College of Engineering, Anna University,Karur |

25 | 1050 | Sadiq Basha | Anna University, Chennai |

26 | Raja. N | Velammal Polytechnique College, Chennai | |

27 | Usha Sangale | S.R.T.M University,Nanded, Maharashtra | |

28 | Saravanan. M | St. Joseph's College of Engineering, Anna University,Chennai | |

29 | Arunachala Boopathy. G | S.R.M University, Chennai |

**How to Reach **

** **Welcome to Chennai neé Madras, and to IMSc, the Institute of Mathematical Sciences. Here is some information on getting to the Institute. Our 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 campus-like 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.

**Special note on weather in Chennai during the workshop**

Chennai experienced a record rainfall in November 2015 resulting in flooding in many parts of the city including within IMSc campus and the road leading up to it. During the week of the programme, however, there was not too much rain, and the programme was not affected, except perhaps to the extent that it was the cause for many of those registered to not show up.