2nd Semester:
Course Name: Calculus and Analytic Geometry
Course Outline:
Functions & Graphs: Basic concepts of functions, types, graph, shifting of graphs. Limits: Left-hand and right-hand limits, Infinite limits, conditions of continuity. Derivatives: Derivatives and their rules, Implicit differentiation, evaluation of limits using L’ Hopital’s rule, Rolle’s theorem, Mean value theorem, maxima and minima of functions of single, Curve sketching, asymptotes, tangent and normal, Higher order derivatives, Leibnitz theorem, Taylor’s and McLaurin’s series, Limits and continuity, partial derivatives and chain rule, Maxima/minima of function of two variables. Integrations: Indefinite integrals, Riemann sums and definite integrals, Fundamental theorems of integral calculus, Integration by substitution, by parts, by partial fraction and by trigonometric substitution, double integrals, change of order, conversion to polar form, Application in finding area and volume. Vector Algebra: Review of vector algebra, vector product of three and four vectors, volume of parallelepiped and tetrahedron, Parametric equations, Polar coordinates, rectangular coordinates system in three dimensions, Direction cosines, Equations of straight line, Plane.