Module description
Aims
To learn the theory and practice of numerical problem solving; to learn to use Python notebooks and Mathematica.
Syllabus
Solution of non-linear equations. Approximation of functions by polynomials. Numerical differentiation and integration. Numerical solution of ordinary differential equations, and systems of linear equations. Rates of convergence, and errors. The algorithms developed will be implemented in Python. A short introduction to the modern industrial strength package Wolfram Mathematica will be given.
Teaching arrangements
Three hours of lectures each week and one hour tutorials. In each of the first two weeks there will also be a one-hour computer laboratory session.
Prerequisites
Basic theory of polynomials, linear equations and matrices, calculus, intermediate value theorem, mean value theorem, Taylor’s theorem with remainder.
No previous knowledge of Python or Mathematica is assumed.
Formative Assessment
Exercise sheets will be handed out weekly. For the first two weeks, homework must be submitted electronically (as email attachment). After that, work will not be collected, but solutions to exercises will be discussed during tutorials. Exercise sheets will be placed on the web page, as the module proceeds
Suggested reading/resources (link to My Reading Lists)
Assessment details
2 hour written examination 70%
Class tests 30%
Educational aims & objectives
To learn the theory and practice of numerical problem solving; to learn to use Python notebooks and Mathematica.
Teaching pattern
Three hours of lectures each week
Tutorials and practicals will be in alternative weeks.