Course Content


Calculus:Review of the prerequisites such as limits of sequences and functions. Continuity, uniform continuity and differentiability. Rolle's theorem, mean value theorems and Taylor's theorem. Infinite series of real and complex numbers. Cauchy Criterion, test of convergence. Riemann integral and the fundamental theorem of integral calculus. Application to length, area, volume, surface area of revolution.

Linear Algebra:Vector spaces (over the field of real and complex numbers). Matrices and determinants, linear transformations. Systems of linear equations and their solutions. Rank of a matrix. Inverse of a matrix. Bilinear and quadratic forms. Eigenvalues and eigenvectors. Similarity transformations. Diagonalisation ofHermitian matrices.

Differential Equations: First order ordinary differential equations, exactness and integrating factors. Variation of parameters. Picard's iteration. Ordinary linear differential equations of nthorder, solutions of homogeneous and non-homogeneous equations. Operator method. Method of undetermined coefficients and variation of parameters.

Texts / References: 

Calculus:

G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, Narosa, 1985.

T. M. Apostol, Calculus, Volume I, 2nd edition, Wiley, 1967.

Linear Algebra:

K. Hoffman and R. Kunze, Linear Algebra, Prentice Hall, 1996.

T. M. Apostol, Calculus, Volume II, 2nd edition, Wiley, 1969.

Differential Equations:

E. A. Coddington, An Introduction to Ordinary Differential Equations, Prentice Hall, 1995.

S. L. Ross, Differential Equations, 3rd Edition, John Wiley, 1984.

General Text / Reference:

E. Kreyszig, Advanced Engineering Mathematics, 5th/8th Edition,Wiley Eastern/John Wiley, 1983/1999.