Applied Mathematics Course in IIT Roorkee

Can you provide me the Syllabi of Core courses for Integrated M. Sc. (Applied Mathematics) offered by IIT or Indian Institute of Technology Roorkee?

[shikha]

The Syllabi of Core courses for Integrated M. Sc. (Applied Mathematics) offered by IIT or Indian Institute of Technology Roorkee are as follows:

Course Title: Mathematics I

1. Matrix Algebra: Elementary operations and their use in getting the Rank, Inverse
of a matrix and solution of linear simultaneous equations. Orthogonal, Symmetric,
Skew-symmetric, Hermitian, Skew-Hermitian, Normal & Unitary matrices and
their elementary properties. Eigen-values and Eigenvectors of a matrix, CayleyHamilton theorem, Diagonalization of a matrix.

2. Differential Calculus: Limit, Continuity and differentiability of functions of two
variables, Euler’s theorem for homogeneous equations, Tangent plane and normal.
Change of variables, chain rule, Jacobians, Taylor’s Theorem for two variables,
Error approximations. Extrema of functions of two or more variables,
Lagrange’s method of undetermined multipliers

3. Integral Calculus:
Review of curve tracing and quadric surfaces, Double and Triple integrals,
Change of order of integration. Change of variables. Gamma and Beta functions.
Dirichlet’s integral. Applications of Multiple integrals such as surface area,
volumes, centre of gravity and moment of inertia..

4. Vector Calculus: Differentiation of vectors, gradient, divergence, curl and their
physical meaning. Identities involving gradient, divergence and curl. Line and
surface integrals. Green’s, Gauss and Stroke’s theorem and their applications