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.

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.

Define the domain and range of a function and define and plot simple inverse trigonometric and hyperbolic functions. Sketch curves using properties such as symmetry, intercepts, discontinuities, turning points and asymptotic behaviour. Sum arithmetic, geometric and telescoping series; test series for convergence; find the Maclaurin series of a function; manipulate power series; use lHopitals rule. Integrate standard functions using substitution and parts; Apply to calculation of areas and volumes. Integrate numerically using Simpsons rule. Find partial derivatives of functions of two variables as well as higher partial derivatives; apply to analysis of small errors.

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Normal lecture and tutorial mode of delivery. Examples used should be simple and technologically relevant as far as practicable.