Limit of functions. Theorems on limits. Continuous functions. The derivative of a function. Rules for finding derivatives. The chain rule. Increments and differentials. Implicit differentiation. Newton's method. Local extrema of functions. Rolle's theorem and the mean value theorem. The first derivative test. Concavity and the second derivative test. Related rates.
Antiderivatives. Definite integral. The mean value theorem. The Newton-Leibniz theorem. Methods of integrations, i.e. by parts, by substitution etc. Integration of special types of functions. Indefinite integral. Area. Solids of revolution. Arc length. Other applications. Exponential and logarithm functions. Trigonometric functions and their inverses. Hyperbolic functions. Differentiation and integration of these functions.
Infinite Sequences. Absolute convergence. Power series Taylor and MacLaurin series. The binomial series. Conic sections. Plain curves. Polar equations of curves. Areas in polar coordinates. Length of curves. Surfaces of revolution. Vector valued functions. Limits, derivatives, integrals. Motion. Curvatures.
Multiple integrals, applications, vector calculus, line integrals, surface integrals, Green's Theorem, Stokes' Theorem.