Calculus

What you’ll study

Differential Calculus: functions and their graphs (polynomial, rational, logarithmic, exponential, trigonometric and hyperbolic functions). Limits of functions, continuity and algebra of continuous functions. Differentiation — tangent lines and rates of change, rules of differentiation, successive differentiation, Leibnitz theorem, related rates, linear approximations and differentials. Rolle's theorem, Lagrange's and Cauchy's mean value theorems, extrema of functions, maxima and minima, concavity and points of inflection. Taylor's theorem and series, indeterminate forms, L'Hospital's rule. Integral Calculus: anti-derivatives and indefinite integrals, techniques of integration, definite integration using Riemann sums, fundamental theorems of calculus, integration by reduction, applications — plane areas, solids of revolution, arc length and surface of revolution, improper integrals, Gamma and Beta functions, graphing in polar co-ordinates.