Courses Taught

**Bachelor in Technology (B. Tech.) Courses at IIT, Bombay**

·
MA 102- Calculus of
Several Variables and Linear Algebra (called now MA-104,
Mathematics -II)

·
MA 103- Calculus (Mathematica -I)

·
MA 203- Ordinary Differential
Equations (Mathematics-III)

·
MA 210- Introduction to Numerical
Methods Course at Colorado School of Mines

·
MACS 332-Linear Algebra (Fall
Semester, 1998).

·
**Master in Science (M. Sc. ) Courses
at IIT, Bombay**

·
Ordinary Differential Equations

·
Partial Differetial Equations

·
Operator Theory

·
Functional Analysis

·
Numerical Analysis II

·
Finite Element Methods

·
Finite Element and Finite Difference Methods for PDEs

·
Mathematical Modeling

·
Mathematical Methods-I

·
Second Order Elliptic PDEs

**Ph. D. level Courses at IIT, Bombay**

·
Modern Partial Differential
Equations

·
Advanced Analysis

·
Advanced Numerical Analysis

·
Mathematical Aspects of Finite
Element Methods

·
Variational Inequalities

·
Spectral Methods for PDEs

·
Functional Analysis

*Some of the above advanced level
courses were developed and taught by me*

during last 11 years. The Ordinary Differential Equation & Partial Differential equation are appropriately modified by me to put emphasis on the basic theory of these subjects.

- Presently,
we (with one of my colleague Prof. M.C. Joshi) are developing and also
collecting some teaching-ware packages to teach the existing computational
mathematics courses in a more meaningful way (that is alongwith theory,
hands in computers will be emphasised with the help of existing software
packages like Mathematica, Matlab, Public domain Packages (ODEPACK,
LINPACK, HOMPACK) etc.).

Both development of algorithms as well as use of public domain packages for large scale computation are the main focus. Further, we are preparing Lab Note Books for the Lab components attached to the courses like Numerical Analysis, Optimization, Finite Difference and Finite Element Methods, Mathematical Modeling and also for Scientific Computing Lab in our M. Sc. (ASI) programme. We have been conducting these experiments in some scientific computing courses for the last few years. Specially, a course on Indroduction to Numerical Methods for Engineering Students was taught by me a couple of times with emphasis on the following:

·
Motivate each modules (Linear
Solver, Nonlinear Solver, Data Fitting (Interpolation, Least Square), Numerical
Integrations, and ODE Solvers) through a Case Study.

·
Discuss Mathematical Techniques
with examples.

·
Revisit Case Study to give a feel
for the method.

Based on these features, Lecture
Note ([5] under Proceedings Edited, Books and Lecture Notes) has been prepared
by me.

- I have made
another experiment in a course on ` Mathematical Modeling'. Software
packages like Mathematica, Matlab, ODE Solvers are used as a black box to
solve the required problems in that course. In subsequent semesters, the
mathematical techniques on Numerical Methods, Optimizations are introduced
with advantages and disadvantages and practical utilities of the
computational techniques. This experiment is working reasonably well as
the Motiva tion has already been laid by the modeling course.

- In master's level course on PDE, starting with a brief
historical note, I pose some questions in the begining of this course.
Then through out the course, I try to provide answers to these questions.
A similar experiment was done for a course on finite element methods. A
lecture note has been prepared by me on this topic ( ref. [6] under
Proceedings Edited, Books and Lecture Notes)