MTH1030 · Techniques for modelling

Overview

This unit develops a comprehensive understanding of basic linear algebra and advanced calculus, equipping you with versatile techniques and skills applicable within the natural sciences, engineering, computer science, economics and many other disciplines. The first half of the unit is dedicated to linear algebra. Topics covered include: solution of systems of linear equations, Gauss-Jordan algorithm, reduced row echelon form, matrix operations, inverses and determinants, linear independence, subspaces, linear transformations, eigenvectors and eigenvalues, diagonalization of matrices, Cayley-Hamilton theorem and various applications of linear algebra. The second half of the unit is dedicated to calculus. Topics covered include: limits and continuity, L’Hôpital’s rule, infinite sequences and series, Taylor and general power series, solution of various types of differential equations such as separable and linear first and second order differential equations.

Areas of study: Applied mathematics Astrophysics Climate and atmospheric science Computational science Financial and insurance mathematics Mathematical statistics Mathematics Physics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Requisites

Learning outcomes

1. Demonstrate a deep conceptual understanding of fundamental linear algebra and calculus;
2. Solve basic and complex mathematical problems involving linear algebra and calculus techniques;
3. Model practical scenarios using linear algebra and calculus, identify relevant solution strategies and communicate solutions effectively through written presentations;
4. Collaborate and communicate effectively in small groups to analyse, discuss, and solve mathematical problems;
5. Utilise proficiently the advanced computer algebra Mathematica to perform complex mathematical computations, symbolic algebraic manipulations, and visualisation tasks.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7.5 hours of independent study per week.

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