Differential Calculus:

Abstract

Review: function; limit of a function; continuity and differentiability of functions; successive differentiation; physical applications of first and second order derivatives; Leibnitz‟s theorem; expansion of functions; Rolle‟s theorem; mean value theorem; Taylor‟s theorem and Maclaurins theorem (proof not required); maxima and minima for functions of one and two variables; functions of several variables; partial differentiation; tangent; normal and curvature. Integral Calculus: Review of indefinite integrals; definite integrals; properties of definite integrals; gamma and beta functions; integration by reduction, integrals with several variables; rectification; quadrature; surface areas and volumes of revolution. Matrices: Introduction; transpose of matrix; adjoint and inverse of a matrix; solution of linear equations by matrices; rank of a matrix; symmetric and skew-symmetric matrix; Hermitia