TEC1803 · Differential equations and numerical methods

Overview

This unit introduces the fundamental concepts of ordinary differential equations (ODEs) and numerical methods, with a focus on technology-driven applications. You will learn analytical methods for solving first- and second-order ODEs, including Laplace transform techniques, and apply them to dynamic systems, electrical circuits, thermal responses, and control processes. The unit also covers numerical methods such as root-finding, interpolation, numerical differentiation and integration, matrix algebra, and numerical solutions for initial-value and boundary-value problems. In addition, you will be introduced to the finite difference method for approximating solutions to partial differential equations (PDEs) in engineering contexts such as heat transfer, fluid flow, and electrodynamics. Through theoretical study and computational exercises, this unit develops the mathematical understanding and problem-solving skills needed for the modelling, simulation, and optimisation of real-world technological systems.

Areas of study: E2000 Bachelor of Technology

Offerings

Assessment

The Handbook lists an examination for this unit.

Continuous assessment: 60% Final assessment: 40% Assessment in this unit includes competency hurdle assessment task/s. The consequence of not achieving a competency hurdle is a fail grade (NH) and a maximum mark of 45 for the 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. Formulate and solve ordinary differential equations (first- and second-order) analytically and numerically using appropriate methods, including separation of variables, integrating factors, characteristic equations, Laplace transforms, and selected numerical techniques.
2. Apply numerical methods to analyse mathematical models, including root finding, interpolation, differentiation, and integration, and interpret approximate solutions in technology-based contexts.
3. Use matrix operations and numerical techniques to formulate and solve linear systems arising in engineering and technological applications.
4. Solve partial differential equations and interpret solutions in the context of thermal, fluid, structural, and electrical systems relevant to engineering practice.

Workload

The minimum total expected workload to achieve the learning outcomes for this unit is 144 hours per semester typically comprising a mixture of 3-6 hours of scheduled learning activities and 6-9 hours of independent study per week. Scheduled activities may include a combination of teacher-directed learning, peer-directed learning and online engagement. Independent study may include associated readings, assessment and preparation for scheduled activities.

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