Functions and graphs; limit and continuity; applications of derivative and integral. Conics; Polar coordinates; Convergence of sequence and series. Maclaurin and Taylor series. Partial derivatives. Vector calculus in Rn; vector analysis; theorems of Green, Gauss and Stokes. Complex numbers, analytic functions, Cauchy? s theorms; elementary functions; series expansions; calculus of residues and applications. Vector space; basis and dimension; linear transformation; range and kernel of a linear transformation; row deduction method and application to linear system of equations.
Probability spaces; conditional probability and independence; random variables and probability distributions; marginal and conditional distributions; independent random variables; mathematical expectation; mean and variance; binomial, Poisson? s and normal distributions; sum of independent random variables; law of large numbers; central limit theorem, sampling distribution and test for mean using normal and students t-distribution; test of hypothesis; correlation and linear regression.