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Clayton First semester 2007 (Day)

Functions and coordinate geometry: types of functions, composite functions, inverse functions, modelling of periodic phenomena with trigonometric functions. Complex numbers. Differentiation and integration: concepts and techniques, applications to related rate of change and optimization problems, areas, volume, and centre of mass. Vectors in two- and three-dimensional space, application to motion and kinematics.

On completing this unit students will be able to demonstrate understanding of the characteristics of different types of functions and their graphs, composition of functions, and inverse functions; use trigonometric functions to model periodic behaviour; represent complex numbers in cartesian, polar and exponential forms, and on the complex plane; operate with complex numbers, including finding powers and complex roots of polynomials; demonstrate understanding of the concepts of limit, continuity, differentiable and integrable functions; use differentiation rules to find derivatives of implicit and explicit functions; apply differentiation techniques to related rates of change problems and optimization problems; use simple integration techniques to find definite and indefinite integrals, including integration by substitution and integration of rational functions; apply integration techniques to calculate areas, average values, volumes, centres of mass, moment, and work; perform operations with two- and three-dimensional vectors, interpret them geometrically, find vector resolutes, and apply them to motion of a particle; solve kinematics problems, and set up and solve problems involving Newton's laws of motion.

Assignments and test: 30%

Examination (3 hours): 70%.

3 hours lectures, one 2-hour practice class and 7 hours of private study per week

VCE Mathematical Methods 3/4