Properties of real and complex numbers; algebraic functions and common transcendental functions; modelling change using elementary functions; limits and continuity; rate of change, derivatives, local and global extrema; sums and integrals, anti-derivatives, calculus applications: optimisation, area and volume, introduction to differential equations; Vectors in two- and three- dimensional space.
On completion of this unit students will be able to:
- Demonstrate basic knowledge of complex numbers, including algebraic manipulations and their various representations;
- Demonstrate basic knowledge of vectors in two and three-dimensional space, their properties, and geometric applications;
- Calculate simple limits to describe continuity and behaviour of one-variable real functions near a point and at infinity;
- Explain how differentiation and integration arise as limits of functions;
- Calculate derivatives and integrals using a variety of methods;
- Use calculus methods to analyse function characteristics such as local and global extrema, concavity and points of inflection;
- Solve differential equations of the separable variables type;
- Use calculus techniques to solve a variety of problems that can be modelled with functions or with first order differential equations;
- Demonstrate proficiency in mathematical writing and communication.
Examination (3 hours): 70%
Assignments and tests: 30%
Three 1-hour lectures and one 2-hour support class per week
See also Unit timetable information
MTH1010 or VCE Mathematical Methods units 3 and 4 with a study score of at least 25
ENG1090, ENG1091, ENG1005, MAT1841, MTH1055, MTH1030 and MTH1035. Note that MTH1020 can only be completed prior to MTH1030 or MTH1035 and students who have already completed one of these cannot enrol subsequently in MTH1020.