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)
- First semester 2018 (On-campus)
- Second semester 2018 (On-campus)
- October intake 2018 (On-campus)
Mathematical Methods (CAS)
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