Real numbers: absolute values and inequalities.



Complex numbers: operations on complex numbers, equalities of complex numbers, Argand diagrams and polar form.

Relations and functions: domains and ranges. 1-1 functions, onto functions, composite functions, inverse functions, polynomials, rational functions and transcendental functions.

Limits and continuity: concept of limit, one-sided limits, definition of limit, left-hand limit, right-hand limit, some limit theorems, continuity, continuity at a point, continuity on intervals and pinching/ sandwich theorem.



Differentiation: derivative and some differentiation formulas. d/dx notations, derivatives of higher order, derivative as a rate of change, chain rule, differentiation of trigonometric functions, implicit differentiation, rational powers, rates of change per unit time. Mean value theorem, increasing and decreasing functions, local extreme values, end point and absolute extreme values, some max-min problems, concavity and points of inflection, vertical and horizontal asymptotes, curve sketching.

Integration: area problem, definite integral of a continuous function, function, fundamental theorem of integral calculus, area problems, indefinite integrals, the u-substitution, change of variables, mean value theorems for integrals, integration by parts, powers and products of trigonometric functions, integrals involving ,  ,  , rational functions, partial fractions, area, volume of revolution, centroid, arc length, area of surface of revolution, moment of inertia, hyperbolic functions.



Conic section: circle, parabola, ellipse and hyperbola.



Polar coordinate of a curve and area of region in polar coordinates.



References:

1. Salas, S.L. ,Hille, E. & Etgen G. (2007). Calculus, One and Several Variables. Wiley & Sons.

2. Bradley, G and Smith, K. (1999). Calculus. Prentice Hall.

3. Anton, H. (1988). Calculus with Analytic Geometry. Wiley & Sons.