6 points, SCA Band 2, 0.125 EFTSL
Undergraduate - Unit
Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
Associate Professor Michael Page (Clayton)
Associate Professor Rajendran Parthiban (Malaysia)
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 optimisation problems, areas, volume, and centre of mass. Vectors in two- and three-dimensional space, application to motion and kinematics.
On successful completion of this unit, students will be able to:
- Demonstrate understanding of the properties of common functions and their graphs, use 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.
- Perform arithmetic and algebra on complex numbers, including finding powers and complex roots of polynomials.
- Demonstrate understanding of the concepts of limit, continuity, differentiable and integrable functions.
- Evaluate limits of piecewise functions, and of rational functions at infinity.
- Use differentiation rules to find derivatives of implicit and explicit functions.
- Apply differentiation techniques to related rates of change problems and optimisation problems.
- Use simple integration techniques to find definite and indefinite integrals, including by substitution and partial fractions.
- Apply integration techniques to calculate areas, average values, volumes, and centres of mass or moment.
- Perform operations with two and three-dimensional vectors, interpret them geometrically, calculate dot products, 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.
- Express and explain mathematical techniques and arguments clearly in words.
Weekly assignments or quizzes: 40%
Final examination (3 hours): 60%
Students are required to achieve at least 45% in the total continuous assessment component and at least 45% in the final examination component and an overall mark of 50% to achieve a pass grade in the unit. Students failing to achieve this requirement will be given a maximum of 45% in the unit.
Three 1 hour lectures ( or equivalent), one 2 hour practice class and 7 hours of private study per week
See also Unit timetable information
Mathematical Methods (CAS)