Computer Algebra and Dynamical Systems module (MA21002)

Computer algebra involves the use of algorithms and software to perform symbolic mathematical computations. It allows for exact solutions to mathematical problems. This is unlike numerical methods which provide approximate answers. This can help solve complex equations, simplify expressions, and develop mathematical models.

Dynamical systems is the study of systems that evolve over time according to a set of rules. These systems can be found in nature, engineering, economics, and more. Understanding dynamical systems helps in predicting future behaviour, analysing stability, and controlling systems.

Studying these topics equips students with powerful tools for mathematical modelling and problem-solving. It enhances analytical skills and fosters a deeper understanding of mathematical theory.

What you will learn

In this module, you will:

• learn the syntax and structure of the Maple Computer-Algebra software package
• learn key results from dynamical system theory. including Newton's laws, Keplerian motion, and oscillator theory
• learn how to use Maple to solve dynamic systems problems and interpret the results

By the end of this module, you will be able to Use the Maple Computer-Algebra software package to:

• plot functions, solve equations, manipulate expressions, and plot trajectories of solutions
• solve differential equations arising from various oscillator problems
• carry out matrix-vector calculations

Assignments / assessment

• coursework (40%)
• final computer-based exam using Maple software package (60%)

Teaching methods / timetable

• three one-hour lectures weekly
  • key points of the week's content will be discussed
  • lecture notes covering the full module content will be available before classes
  • use of Maple will be demonstrated live in class
  • in-class time will be prioritised for interactive discussion
• two hours of computer labs weekly
  • solve problems individually and in groups
  • support with difficulties will be provided by your lecturers and peers