MXB103 Introductory Computational Mathematics
To view more information for this unit, select Unit Outline from the list below. Please note the teaching period for which the Unit Outline is relevant.
| Unit code: | MXB103 |
|---|---|
| Equivalent(s): | MAB220 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
| CSP student contribution | $555 |
| Domestic tuition unit fee | $3,324 |
| International unit fee | $4,296 |
Unit Outline: Semester 2 2024, Gardens Point, Internal
| Unit code: | MXB103 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB220 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Coordinators: | Qianqian Yang | q.yang@qut.edu.au Elliot Carr | elliot.carr@qut.edu.au Megan Farquhar | me.farquhar@qut.edu.au |
Overview
Many real world phenomena are modelled by mathematical models whose solutions cannot be found analytically. To solve these problems in practice, it is necessary to develop computational methods, algorithms and computer code. This unit will introduce you to numerical methods for addressing foundational problems in computational mathematics such as solving nonlinear ordinary differential equations, finding roots of nonlinear functions, constructing interpolating polynomials of data sets, computing derivatives and integrals numerically and solving linear systems of equations. This is an introductory unit providing foundational skills in computational methods and their practical implementation using relevant computational software. This unit will be essential throughout the remaining parts of your degree. MXB226 Computational Methods 1 builds on this unit by extending your computational and programming skills to more challenging problems and more sophisticated algorithms.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of concepts, derivations, limitations and theory underlying key foundational techniques of computational mathematics
- Apply appropriate computational techniques to calculate computational solutions to problems
- Use MATLAB programming skills to implement computational techniques and computational solutions to problems
- Identify and correct errors in MATLAB code implementing foundational computational techniques
- Communicate in writing the assumptions, outcomes and interpretation of results of computational modelling investigations.
- Work independently and collaboratively in groups to solve a range of problems.
Content
- Measuring and quantifying errors, roundoff and truncation errors, floating point arithmetic.
- Ordinary differential equations: Euler's method, modified Euler method, Taylor methods, introduction to Runge-Kutta methods.
- Interpolation: Lagrange polynomials, divided differences, forward differences.
- Roots of nonlinear functions: bisection method, fixed point iteration, Newton's method, secant method.
- Numerical differentiation and integration: first and second order difference quotients, trapezoidal rule, Simpson's rule.
- Numerical methods for linear systems: substitution, Gaussian elimination, factorisation methods.
- Programming computational algorithms with MATLAB.
Learning Approaches
This unit is available for you to study in either on-campus or online mode. This unit utilises a technology-enhanced learning approach consisting of:
- Pre-recorded lectures and online activities, where you will learn the fundamentals of computational techniques, and witness these ideas come to life in the form of problem solving and demonstrations in MATLAB.
- Timetabled lectures (online or on-campus) will discuss important lecture concepts and work through example problems and provide you with the opportunity to ask the lecturer questions.
- Practicals (online or on-campus), where you will have the opportunity to further explore lecture concepts and hone both your problem-solving and programming skills in MATLAB.
- Communication channel, designed to facilitate communication with your peers and teaching staff outside of scheduled classes.
You can expect to spend an average of 10-15 hours per week engaging in the online lecture activities, preparing for and attending all scheduled practicals, completing assessment tasks, and undertaking your own independent study to consolidate your learning.
All techniques and algorithms will be motivated by drawing upon real-world applications for which computational skills are essential for obtaining solutions. Ultimately, you will learn how to synthesise many of these techniques into a holistic solution approach to more complex problems.
You will work with peers and the teaching team to develop effective methods/approaches for communicating, retrieving, evaluating and presenting information, and you will learn how to work effectively within groups with consideration for cultural differences.
Feedback on Learning and Assessment
Feedback in this unit is provided to you in the following ways:
- Ongoing formative feedback will be provided by the teaching team during the practicals and consultation sessions.
- Feedback on all assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required will be available.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Problem Solving Task
There will be a number of problem solving tasks administered online via Canvas. They will consist of small problems similar to those demonstrated in lectures and practicals.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Project (applied)
The project will give you the opportunity to combine the many skills you have learned in a coherent fashion in order to solve a real-world problem. You will use your computational model and solution to perform investigations, and communicate your findings in writing.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
This final invigilated examination will assess your learning over the course of the entire semester.
The examination will be at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide testing centre information.
Academic Integrity
Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.
Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.
Resources
There is no set text for this unit.
There are many reference texts for this unit, many of which can be located in the library. There are also many online resources such as lecture notes and some e-books that can be found online. Example reference texts are listed below.
Resource Materials
Reference book(s)
Bradie, A Friendly Introduction to Numerical Analysis
Burden and Faires, Numerical Analysis
Gilat, Numerical methods for engineers and scientists: an introduction with applications using MATLAB
Mathworks, MATLAB Primer. Available online: https://www.mathworks.com/help/pdf_doc/matlab/getstart.pdf
Moler, Numerical Computing with MATLAB. Available online: http://www.mathworks.com/moler/chapters.html
Risk Assessment Statement
There are 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.mopp.qut.edu.au/A/A_09_01.jsp
Standards/Competencies
This unit is designed to support your development of the following standards\competencies.
Engineers Australia Stage 1 Competency Standard for Professional Engineer
1: Knowledge and Skill Base
Relates to: Project (applied)
Relates to: Problem Solving Task, Project (applied), Examination (invigilated)
Relates to: Problem Solving Task, Project (applied)
2: Engineering Application Ability
Relates to: Problem Solving Task, Project (applied), Examination (invigilated)
Relates to: Problem Solving Task, Project (applied), Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Problem Solving Task, Project (applied), Examination (invigilated)
Relates to: Project (applied)
Relates to: Project (applied)
Unit Outline: Semester 2 2024, Online
| Unit code: | MXB103 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB220 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
Overview
Many real world phenomena are modelled by mathematical models whose solutions cannot be found analytically. To solve these problems in practice, it is necessary to develop computational methods, algorithms and computer code. This unit will introduce you to numerical methods for addressing foundational problems in computational mathematics such as solving nonlinear ordinary differential equations, finding roots of nonlinear functions, constructing interpolating polynomials of data sets, computing derivatives and integrals numerically and solving linear systems of equations. This is an introductory unit providing foundational skills in computational methods and their practical implementation using relevant computational software. This unit will be essential throughout the remaining parts of your degree. MXB226 Computational Methods 1 builds on this unit by extending your computational and programming skills to more challenging problems and more sophisticated algorithms.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of concepts, derivations, limitations and theory underlying key foundational techniques of computational mathematics
- Apply appropriate computational techniques to calculate computational solutions to problems
- Use MATLAB programming skills to implement computational techniques and computational solutions to problems
- Identify and correct errors in MATLAB code implementing foundational computational techniques
- Communicate in writing the assumptions, outcomes and interpretation of results of computational modelling investigations.
- Work independently and collaboratively in groups to solve a range of problems.
Content
- Measuring and quantifying errors, roundoff and truncation errors, floating point arithmetic.
- Ordinary differential equations: Euler's method, modified Euler method, Taylor methods, introduction to Runge-Kutta methods.
- Interpolation: Lagrange polynomials, divided differences, forward differences.
- Roots of nonlinear functions: bisection method, fixed point iteration, Newton's method, secant method.
- Numerical differentiation and integration: first and second order difference quotients, trapezoidal rule, Simpson's rule.
- Numerical methods for linear systems: substitution, Gaussian elimination, factorisation methods.
- Programming computational algorithms with MATLAB.
Learning Approaches
This unit is available for you to study in either on-campus or online mode. This unit utilises a technology-enhanced learning approach consisting of:
- Pre-recorded lectures and online activities, where you will learn the fundamentals of computational techniques, and witness these ideas come to life in the form of problem solving and demonstrations in MATLAB.
- Timetabled lectures (online or on-campus) will discuss important lecture concepts and work through example problems and provide you with the opportunity to ask the lecturer questions.
- Practicals (online or on-campus), where you will have the opportunity to further explore lecture concepts and hone both your problem-solving and programming skills in MATLAB.
- Communication channel, designed to facilitate communication with your peers and teaching staff outside of scheduled classes.
You can expect to spend an average of 10-15 hours per week engaging in the online lecture activities, preparing for and attending all scheduled practicals, completing assessment tasks, and undertaking your own independent study to consolidate your learning.
All techniques and algorithms will be motivated by drawing upon real-world applications for which computational skills are essential for obtaining solutions. Ultimately, you will learn how to synthesise many of these techniques into a holistic solution approach to more complex problems.
You will work with peers and the teaching team to develop effective methods/approaches for communicating, retrieving, evaluating and presenting information, and you will learn how to work effectively within groups with consideration for cultural differences.
Feedback on Learning and Assessment
Feedback in this unit is provided to you in the following ways:
- Ongoing formative feedback will be provided by the teaching team during the practicals and consultation sessions.
- Feedback on all assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required will be available.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Problem Solving Task
There will be a number of problem solving tasks administered online via Canvas. They will consist of small problems similar to those demonstrated in lectures and practicals.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Project (applied)
The project will give you the opportunity to combine the many skills you have learned in a coherent fashion in order to solve a real-world problem. You will use your computational model and solution to perform investigations, and communicate your findings in writing.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
This final invigilated examination will assess your learning over the course of the entire semester.
The examination will be at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide testing centre information.
Academic Integrity
Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.
Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.
Resources
There is no set text for this unit.
There are many reference texts for this unit, many of which can be located in the library. There are also many online resources such as lecture notes and some e-books that can be found online. Example reference texts are listed below.
Resource Materials
Reference book(s)
Bradie, A Friendly Introduction to Numerical Analysis
Burden and Faires, Numerical Analysis
Gilat, Numerical methods for engineers and scientists: an introduction with applications using MATLAB
Mathworks, MATLAB Primer. Available online: https://www.mathworks.com/help/pdf_doc/matlab/getstart.pdf
Moler, Numerical Computing with MATLAB. Available online: http://www.mathworks.com/moler/chapters.html
Risk Assessment Statement
There are 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.mopp.qut.edu.au/A/A_09_01.jsp
Standards/Competencies
This unit is designed to support your development of the following standards\competencies.
Engineers Australia Stage 1 Competency Standard for Professional Engineer
1: Knowledge and Skill Base
Relates to: Project (applied)
Relates to: Problem Solving Task, Project (applied), Examination (invigilated)
Relates to: Problem Solving Task, Project (applied)
2: Engineering Application Ability
Relates to: Problem Solving Task, Project (applied), Examination (invigilated)
Relates to: Problem Solving Task, Project (applied), Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Problem Solving Task, Project (applied), Examination (invigilated)
Relates to: Project (applied)
Relates to: Project (applied)