103. Mathematics


FIRST TERM:
Integral Calculus:
	Riemann integrals upper and lower sums,
	definite integral as the limit of a sum, 
	fundamental theorem integral calculus, mean value theorems, 
	evaluation of definite integrals reduction formula, 
	convergence of improper integrals tests of convergence, 
	beta and gamma function elementary properties,
	differentiation under integral sign, 
	differentiation of integrals with variable limits 
	Lei-bnitz; rule, integrals dependent on a parameter applications
	Rectification, double and triple integrals
	Jacobians of transformations, 
	integrals dependent on parameter application.

SECOND TERM:
Vector Calculus:
	Scalar and vector fields, level surfaces, directional derivative, 
	gradient curl, divergence, laplacian, line and surface integrals, 
	theorem of Green, Gauss and stokes orthogonal curvilinear coordinates, 
	Infinite series: sequence and series - their convergence and 
	divergence tests of convergence, 
	power series - uniform and absolute convergence: 
	Fourier series its convergence, Dirichlet, conditions half range series. 

Matrices: 
	Algebra of Matrices, vector space linear dependence of vectors, 
	rank and inverse of a matrix, 
	solution of algebraic equations consistency conditions
	eigen-values and eigen vectors, 
	similarity transformations reduction to a diagonal matrix.

Texts / References