To develop the fundamental concepts and basic tools of calculus. To introduce applications of calculus in science and technology. To develop and integrate the basic mathematical skills relevant to technology.

Syllabus

Functions of the Calculus: graphs and functions, domain and range, inverse trigonometric functions, hyperbolic functions. Curve sketching:symmetries, intercepts, restrictions on range, discontinuities, turning points, behaviour for large and small x, asymptotes;Series: sequences, series as sum of sequence, sums of arithmetic and geometric series, infinite series and convergence, ratio and comparison tests, power series, Maclaurin and Taylor series, manipulation of power series, differentiation and integration of power series, use as approximation of a function, limits, l’Hopital’s rule; Integration and applications:indefinite integral as antiderivative, integration of standard functions, definite integral as area, integration by substitution, integration by parts, applications to: area, volumes, surfaces of revolution, numerical integration including Simpson’s rule;Partial derivatives:functions of two variables, partial derivative, definition and examples, differential and total differential, higher partial derivatives, application to small errors.