units

MTH1020

Faculty of Science

# Undergraduate - UnitMTH1020 - Analysis of change

This unit entry is for students who completed this unit in 2014 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

## 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, or view unit timetables.

 Level Undergraduate Faculty Faculty of Science Organisational Unit School of Mathematical Sciences Offered Clayton First semester 2014 (Day)Gippsland First semester 2014 (Day)Gippsland First semester 2014 (Off-campus)Clayton Second semester 2014 (Day) Coordinator(s) Dr Daniel Mathews (Clayton); Dr Andrew Percy (Gippsland)

### 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;

1. Demonstrate basic knowledge of vectors in two and three-dimensional space, their properties, and geometric applications;

1. Calculate simple limits to describe continuity and behaviour of one-variable real functions near a point and at infinity;

1. Explain how differentiation and integration arise as limits of functions;

1. Calculate derivatives and integrals using a variety of methods;

1. Use calculus methods to analyse function characteristics such as local and global extrema, concavity and points of inflection;

1. Solve differential equations of the separable variables type;

1. Use calculus techniques to solve a variety of problems that can be modelled with functions or with first order differential equations;

1. Demonstrate proficiency in mathematical writing and communication.

### Assessment

Examination (3 hours): 60%
Assignments and tests: 40%
Students must pass the examination to be awarded a pass grade.