Computational Methods

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 learn how to introduce students to the relevance of computational methods, relevant technology and applications. This unit will consist of:

• error analysis & propagation;
  
• use of technology (CAS Calculators & Desktop Tools)
  
• solving non-linear equations;
  
• solving systems of linear equations;
  
• interpolation and extrapolation;
  
• numerical calculus, including integration (quadrature) and differentiation;
  
  Although the modules are discrete, they are scaffolded to the extent that later modules assume material and techniques from previous modules.