Teaching Responsibility
LJMU Schools involved in Delivery:
Computer Science and Mathematics
Learning Methods
Lecture
Practical
Module Offerings
5103MATHS-JAN-CTY
Aims
To motivate the need to solve problems numerically, and interpret numerical solutions to problems.
To enable students to study and investigate the error of certain numerical methods.
Provide practical experience in the use of numerical methods and appropriate software.
To give students the confidence to solve equations and problems arising in dynamical systems and fractal analysis independently.
Learning Outcomes
1.
Select appropriate methods to obtain numerical solutions to a range of problems.
2.
Classify which numerical methods are both stable and robust, and be able to implement them using mathematical software.
3.
Analyse and interpret numerical solutions to problems.
4.
Identify both abstract and real systems which exhibit chaotic behaviour, and investigate their solution.
5.
Create fractals using simple patterns and replication rules.
Module Content
Outline Syllabus:Decimal search, bisection and linear interpolation.
Fixed point iteration, secant and Newton Raphson methods. Analysis of the methods.
Taylor series and its error term. Error analysis of the above methods.
Numerical integration: mid-point, trapezium, Simpson's rules. Error analysis/order of convergence and applications to Richardson's extrapolation and Romberg integration.
Solution of Ordinary Differential Equations: First and second order, Euler, modified Euler, Runge-Kutta order 4, Taylor methods.
Computations of fixed and periodic points in real and complex dynamic systems. Logistic and Mandelbrot maps.
Construction of iterated function systems using contractive affine maps.
Module Overview:
The aim of this module is to develop an understanding of the need to analyse and interpret numerical solutions to problems. You will study and investigate the error of certain numerical methods and be provided with practical experience in the use of numerical methods and appropriate software.
The aim of this module is to develop an understanding of the need to analyse and interpret numerical solutions to problems. You will study and investigate the error of certain numerical methods and be provided with practical experience in the use of numerical methods and appropriate software.
Additional Information:Acquaint the student with practical methods for solving applied problems, and develop an understanding of the analysis of the methods used.
The fractals and chaos element of the module will enable students to apply advanced mathematical techniques to 3D graphics and the analysis of dynamical systems.