MTH1020 · Analysis of change

Overview

This unit develops critical thinking generally as well as a comprehensive understanding of several important areas of mathematics, equipping you with versatile techniques and skills applicable within specific disciplines, for example the natural sciences, engineering, computer science, and economics. The unit is broken up into three areas. First, the focus is on logic and proofs, which are fundamental to mathematical reasoning. Topics covered include proof by induction and proof by contradiction. Second, vectors and complex numbers are covered. Topics covered include: definitions and properties of vectors; dot and cross product; lines and planes in 3-dimensional space; definitions and properties of complex numbers; Cartesian and exponential forms of complex numbers; powers and roots of complex numbers. Third, the unit delves into calculus. Topics covered include: rates of change and derivatives; local and global extrema; optimisation and related rates; anti-derivatives and integrals; applications of integrals to calculating areas and volumes.

Areas of study: Applied mathematics Astrophysics Climate and atmospheric science Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Demonstrate a deep conceptual understanding of mathematical proofs, vectors, complex numbers, and differential and integral calculus;
2. Solve basic and complex mathematical problems involving proofs, vectors, complex numbers, and calculus techniques;
3. Model practical scenarios using vectors, complex numbers, and calculus, identify relevant solution strategies and communicate solutions effectively through written presentations;
4. Use calculus methods to analyse function characteristics such as local and global extrema, concavity, and points of inflection;
5. Collaborate and communicate effectively in small groups to analyse, discuss, and solve mathematical problems.

Workload

• Two1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 8 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.