TEW Mathematics for Engineers (2015)

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.

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

 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