# MTH1020 - Analysis of change - 2018

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Coordinator(s)

Dr Daniel Mathews (Semester 1)
Dr Andy Hammerlindl (Semester 2)

Unit guides

Offered

Clayton

• First semester 2018 (On-campus)
• Second semester 2018 (On-campus)

Prerequisites

MTH1010 or VCE Mathematical Methods units 3 and 4 with a study score of at least 25

Prohibitions

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.

## Synopsis

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.

## Outcomes

On completion of this unit students will be able to:

1. Demonstrate basic knowledge of complex numbers, including algebraic manipulations and their various representations;
2. Demonstrate basic knowledge of vectors in two and three-dimensional space, their properties, and geometric applications;
3. Calculate simple limits to describe continuity and behaviour of one-variable real functions near a point and at infinity;
4. Explain how differentiation and integration arise as limits of functions;
5. Calculate derivatives and integrals using a variety of methods;
6. Use calculus methods to analyse function characteristics such as local and global extrema, concavity and points of inflection;
7. Solve differential equations of the separable variables type;
8. Use calculus techniques to solve a variety of problems that can be modelled with functions or with first order differential equations;
9. Demonstrate proficiency in mathematical writing and communication.

## Assessment

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.