MTH1035 · Techniques for modelling (Advanced)

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. This unit is the advanced stream of MTH1030.

Areas of study: Applied mathematics Astrophysics Climate and atmospheric science Financial and insurance mathematics Mathematical statistics 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

Learning outcomes

1. Demonstrate advanced 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;
6. Demonstrate proficiency in proving mathematical theorems.

Workload

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

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