# ENG1090

## Foundation mathematics ( 6 points, SCA Band 2, 0.125 EFTSL)

Offered:
Clayton First semester 2006 (Day)

Synopsis: 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.

Objectives: 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.

Assessment: Assignments and test: 30% + Examination (3 hours): 70%.

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

Prerequisites: VCE Mathematical Methods 3/4

Prohibitions: ENG1901, MTH1020, MAT1055