Dr. P. Mahale >>Mathematics I (MAL101)

                                                                 MATHEMATICS-I   (MAL101)                                                             

Differential Calculus:

Functions of single variable:  Limit, continuity and differentiability.  Mean value theorems:   Rolle’s theorem, Lagrange’s theorem, Cauchy’s theorem, Taylor’s theorem with remainders, indeterminate forms,curvature, curve tracing.

Integral Calculus:

Fundamental theorem of Integral calculus, mean value theorems, evaluation of definite integrals, Applications in Area, length, volumes and surface of solids of revolutions, Improper integrals: Beta and Gamma functions, differentiation under integral sign.

Infinite series:

Sequences, Infinite series of real and complex numbers, Cauchy criterion, tests of convergence, absolute and conditional convergence, improper integrals, improper integrals depending on a parameter, uniform convergence, power series, radius of convergence.

Matrices: 

Rank of matrix, consistency of a system of equations, linear dependence  and independence, linear and orthogonal transformations, Eigen values and eigen vectors, Cayley – Hamilton theorem, reduction to diagonal form, Hermitian and skew Hermitian matrices, Quadratic forms.