Units
Computational Mathematics 2
Unit code: MAN420
Contact hours: 4 per week
Credit points: 12
Information about fees and unit costs
This unit provides you with the opportunity to employ a number of the skills that you have developed in the disciplines of computational mathematics and linear algebra, combining them in a coherent manner for resolving topical and relevant real world problems. You will become familiar with the methodologies for developing numerical algorithms that can be employed for either the direct solution or the iterative solution of large, sparse linear systems.
Availability
| Semester | Available |
|---|---|
| 2013 Semester 2 | Yes |
Sample subject outline - Semester 2 2013
Note: Subject outlines often change before the semester begins. Below is a sample outline.
Rationale
An essential skill for applied mathematicians, statisticians and engineers is the implementation of computational techniques for the efficient solution of large, sparse matrix systems. Through the investigation of specific case studies, the analysis of numerical techniques, the investigation of suitable data structures to accommodate sparse matrix systems, the implementation of efficient algorithms and the visualisation of the simulation results, you will develop an understanding of the value of computational mathematics. The subject matter is not only intellectually challenging, but successful completion of this unit should enable you to apply the underlying theory and concepts to many of the advanced mathematics units offered within this school.
Aims
This unit provides you with the opportunity to employ a number of the skills that you have developed in the disciplines of computational mathematics and linear algebra, combining them in a coherent manner for resolving topical and relevant real world problems. You will become familiar with the methodologies for developing numerical algorithms that can be employed for either the direct solution or the iterative solution of large, sparse linear systems.
Objectives
On satisfactory completion of this unit, you should be able to:
1. Demonstrate an understanding of direct and iterative methods for solving linear systems and the special data structures and techniques used to handle sparse matrices.
2. Define matrix and vector norms and understand their application and implications in error analysis.
3. Use MATLAB to implement the algorithms discussed throughout the unit and apply them to solve real world problems.
4. Engage critical, analytical and communication skills through a combination of report writing, individual problem-solving and computer programming.
Content
Topics will be selected from the following sections:
Direct methods for solving systems of linear equations:
Triangular decomposition methods, pivoting.
Solution Methods for Special Matrix systems:
Data structures and algorithms for storing banded matrices, sparse matrices. A brief discussion on node reordering.
Vector and Matrix Norms:
Basic theory and definitions of matrix and vector norms. Error Bounds for direct methods, condition numbers.
Iterative methods for solving systems of linear equations:
General form of iterative schemes including Jacobi, Gauss-Seidel, Successive Over-Relaxation; A discussion of convergence issues. Conjugate gradient method.
Approaches to Teaching and Learning
You are expected to attend lectures (3 hours per week) in which the course content will be presented and the computational techniques will be demonstrated. You are also expected to attend a practical session (1 hour per week) where the MATLAB programming language will be used to implement the techniques discussed in lectures.
This unit is being taught concurrently with an undergraduate offering of the same subject. University policy permits that postgraduate and undergraduate students attend the same lectures. Separate practical/discussion groups will be provided for postgraduate student where numbers allow.
Assessment
You will be expected to undertake a number of assessments related to the learning outcomes of this unit (see below).Feedback will be made available to students and consultation with unit coordinator is avaiable on request.
Assessment name:
Problem Solving Task
Description:
There will be several problem solving tasks. Each will be based on implementing the techniques discussed in lectures using MATLAB.
Relates to objectives:
1-4
Weight:
50%
Internal or external:
Internal
Group or individual:
Group with Individual Component
Due date:
Throughout semester
Assessment name:
Examination (Theory)
Description:
The end of semester examination will assess you on your knowledge and ability in all sections of unit contentas well as your ability to apply this knowledge to solve new problems.
Relates to objectives:
1-4.
Weight:
50%
Internal or external:
Internal
Group or individual:
Individual
Due date:
Exam period
Academic Honesty
QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.
A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.
Resource materials
There is no set text for this unit.
Risk assessment statement
There is no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.hrd.qut.edu.au/healthsafely/healthsafe/index.jsp
Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.
Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.
Last modified: 03-May-2012
