This unit introduces students to numerical and approximate techniques to solving applied mathematical problems and the application of current problem-solving tools such as CAS calculators. Computational methods are a core technique for analysing and explaining patterns: both naturally-occurring and arising in industrial and scientific applications. While applied mathematics can provide many "aha!" moments with recognising connections between two seemingly different topics, computational methods are also highly satisfying to teach. As with all mathematics, this unit requires demonstration of logical rigour and application to problem solving. Pre-service teachers will see how to introduce students to its relevance, applications, and intrinsic simplicity. In order to illustrate conventional teaching methods for solving such applied mathematical problems, this unit is divided into five discrete modules:
- non-linear equations;
- solving systems of linear equations;
- interpolation and extrapolation;
- numerical calculus, including integration (quatrature) and differentiation;
- numerical solution of ordinary differential equations.
Although the modules are discrete, they are scaffolded to the extent that later modules assume material and techniques from previous modules.
- non-linear equations;
- solving systems of linear equations;
- interpolation and extrapolation;
- numerical calculus, including integration (quatrature) and differentiation;
- numerical solution of ordinary differential equations.
Although the modules are discrete, they are scaffolded to the extent that later modules assume material and techniques from previous modules.
Unit details
Location:
Study level:
Undergraduate
Credit points:
12
Unit code:
RCM3711
Prerequisites
NEM1001 - Algebra and Calculus and
RCM2713 - Modelling for Decision Making
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Learning Outcomes
| 1. | Analyse the errors inherent in numerical processes. | ||
| 2. | Select and evaluate computational techniques appropriate to solving a wide range of problems chosen from the field of numerical analysis. | ||
| 3. | Implement appropriate numerical techniques using a computer algebra system. | ||
| 4. | Critically review the use of technology in the secondary mathematics classroom. |
Assessment
| Assessment type | Description | Grade |
|---|---|---|
| Assignment | Assignment 1 - covering topics 1 and 2 (approximately 6 pages of mathematics) | 30% |
| Assignment | Assignment 2 - covering topics 3, 4 and 5 (approximately 9 pages of mathematics) | 50% |
| Essay | Short essay on a topic based on school mathematics and technology (500 words) | 20% |
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