** 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.