MZB125 Introductory Engineering 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: | MZB125 |
|---|---|
| Antirequisite(s): | EGD125, MXB100 |
| Equivalent(s): | MAB125, MAB100, MAB120 |
| Assumed Knowledge: | Grade of at least Sound Achievement in Senior Mathematics B (or equivalent) or MAB105 or MZB101 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 1 2024, Gardens Point, Internal
| Unit code: | MZB125 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB125, MAB100, MAB120 |
| Assumed Knowledge: | Grade of at least Sound Achievement in Queensland Mathematical Methods / Senior Mathematics B (or equivalent) or MAB105 or MZB101 is assumed knowledge |
| Anti-requisite: | EGD125, MXB100 |
| Coordinators: | Pascal Buenzli | pascal.buenzli@qut.edu.au |
Overview
Professional engineers have a "conceptual understanding of the mathematics, numerical analysis, statistics, and computer and information sciences which underpin the engineering discipline" (Engineers Australia Stage 1 Competency Standard for Professional Engineer). This unit will serve as the transition from high school mathematics to university, particularly if you have not studied Queensland Specialist Mathematics (formerly called Senior Mathematics C) or equivalent. You will learn about elementary functions, their derivatives and integrals, the algebra of complex numbers, and vectors and matrices. Mathematical techniques and problem solving skills are employed in a range of mathematical exercises and contextualised problems, illustrating how these concepts and techniques are used in engineering systems. In future units you will continue to apply the mathematical knowledge and skills you have learned in this unit to increasingly complex problems.
Learning Outcomes
On successful completion of this unit you will be able to:
- Apply mathematical concepts and ideas relevant to engineering at an introduced level.
- Utilise technical notation and correct techniques to solve mathematical problems relevant to engineering at an introduced level.
- Interpret, translate and solve real world problems relevant to engineering using mathematical methods at an introduced level.
- Communicate effectively in mathematical formats to specialist Engineering audiences at an introduced level.
Content
- Elementary functions including polynomial, trigonometric, logarithmic and exponential functions. Their properties, the principle of composite functions, inverse functions, and the use of functions as representations of data are emphasised.
- Introduction to the processes of differentiation and integration of elementary functions as ways to model simple problems for functions of one variable, including those defined parametrically. Techniques such as implicit differentiation, product and chain rules, integration by substitution, and integration by parts are all employed to solve mathematical and applied problems.
- Introduction to vectors and matrices and arithmetic operations on vectors and matrices (cross products, dot products as well as matrix multiplication and addition), with applications to problems relevant to engineering, including solving systems of linear equations.
- The algebra of complex numbers, of vectors, and of matrices, illustrating how each may be used in representations of systems in real-world applications.
Learning Approaches
- In this unit, you will be provided with learning resources including readings and videos that you can access flexibly to prepare for your timetabled learning activities. Timetabled activities will be in the form of interactive lectures and workshops. These activities are an important opportunity for you to interact directly with the teaching team, to familiarise yourself with best practice, and to ask for help or clarification where needed.
- Learning resources will introduce you to theoretical background and concepts in fundamental engineering mathematics, along with example problems and real-world applications;
- Interactive lectures will discuss important concepts and work through example problems relevant for your assessment;
- In the workshops, you will solve a range of example problems, from purely mathematical exercises to contextualised problems. You will work both individually and in groups, allowing you to develop your group problem solving and oral communication skills.
You will be expected to:
- Prepare for timetabled classes and activities by engaging with the learning resources available from the unit website.
- Engage with timetabled activities and ask questions.
- Work on a wide variety of exercises and problems in your own time to consolidate material from timetabled activities.
- Engage with your peers in a learning community to practise problem solving and then work independently to complete your assessment tasks.
The total expected volume of learning for MZB125, as per the Australian Qualifications Framework, is 150 hours. As a guide, a breakdown for these hours might typically be:
- 26 lecture contact hours (2 hours x 13 weeks)
- 26 workshop contact hours (2 hours x 13 weeks)
- 78 hours self-guided independent study including worksheets and regular portfolio submission (6 hours x 13 weeks)
- 20 hours independent end of semester revision, consolidation and exam preparation
Feedback on Learning and Assessment
During workshops, you will share your formative ideas around problem solving and receive feedback from demonstrators. You are encouraged to view your workshop group as a learning community and to share and discuss challenges and strategies for learning. You will receive formative feedback by completing in-semester assignments. Each assessment submission will be graded against criteria and standards which will be shared with you through Assessment Task Descriptions and Marking Rubrics. Marked assessment will include written feedback from markers against the criteria.
Assessment
Overview
The assessment in this unit is designed to assess your learning against the unit learning outcomes. The portfolio supports you to progress in developing your competency in the application of fundamental methods as well as the development of problem-solving skills that will allow you to tackle more complex and open problems in your future career. Consistent practice in mathematical techniques and problem solving at the workshops will support your success in the summative tasks.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Portfolio
Each of the 6 topics of this unit has two worksheets (2x functions, 2x vectors, 2x matrices, 2x differentiation, 2x integration, and 2x complex numbers). You will complete and hand in a prescribed set of exercises from 8 out of 12 worksheets in total, including at least one set per topic. Exercises to be handed in are similar to those illustrated at the lecture. They will first be discussed at the workshops by your instructors, who will demonstrate similar examples. After the workshops, you will have one week to hand in your handwritten worked solution to the prescribed set of exercises. These exercises will comprise short questions with an emphasis on determining level of competency in the use of fundamental mathematical techniques, as well as contextualised problems that require the synthesis of more than one mathematical technique for their solution. You will be expected to communicate clearly and effectively the detailed working of all answers and utilise appropriate technical notation and correct techniques.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination
You will be required to solve problems requiring coherent mathematical solutions.
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
Open-access Textbooks:
- OpenStax College, Precalculus, 2020, CC-BY 4.0 https://openstax.org/details/books/precalculus
- OpenStax College, Calculus Vol. 1, 2020, CC-BY-NC_SA 4.0, https://openstax.org/details/books/calculus-volume-1
Other resources:
- Rattan, KS, Klingbeil, NW, Introductory Mathematics for Engineering Applications, 2015, John Wiley & Sons.
- Mallet DG, Pettet GJ & Farr AC. Introductory Algebra and Calculus, 2012, Pearson.
- Bird J, Engineering Mathematics, 2007 (5th Ed) – 2017 (8th Ed), Elsevier
There are numerous suitable reference texts for this unit, many of which can be located in the library. You should also make use of suitable online resources such as video instructions for specific problems. Additional resources, including audio and video recordings of appropriate segments of the lectures will be made available via the QUT Canvas site for this unit.
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in lecture theatres and small group tutorial rooms. Emergency exits and assembly areas will be made apparent to all attending students. 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: Portfolio, Examination
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.EN01 Bachelor of Engineering (Honours)
- Engage stakeholders professionally and communicate the outcomes of your work effectively to expert and non-expert audiences using appropriate modes.
Relates to: ULO4, Portfolio, Examination - Demonstrate coherent knowledge and skills of physical, mathematical, statistical, computer, and information sciences that are fundamental to professional engineering practice.
Relates to: ULO1, ULO2, ULO3, Portfolio, Examination
EN29 Bachelor of Engineering Studies
- Evidence of engaging stakeholders professionally and communicating the outcomes of your work effectively to expert and non-expert audiences.
Relates to: ULO4, Portfolio, Examination - Evidence of engaging with and applying regulatory requirements relating to safety, risk management and sustainability in professional engineering practice.
Relates to: ULO2, ULO3 - Evidence of demonstrating coherent knowledge and skills of physical, mathematical, statistical, computer and information science.
Relates to: ULO1, Portfolio, Examination
EV01 Bachelor of Engineering (Honours)
- Engage stakeholders professionally and communicate the outcomes of your work effectively to expert and non-expert audiences using appropriate modes.
Relates to: Portfolio - Demonstrate coherent knowledge and skills of physical, mathematical, statistical, computer, and information sciences that are fundamental to professional engineering practice.
Relates to: Portfolio, Examination
Unit Outline: Semester 2 2024, Gardens Point, Internal
| Unit code: | MZB125 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB125, MAB100, MAB120 |
| Assumed Knowledge: | Grade of at least Sound Achievement in Queensland Mathematical Methods / Senior Mathematics B (or equivalent) or MAB105 or MZB101 is assumed knowledge |
| Anti-requisite: | EGD125, MXB100 |
| Coordinators: | Nicholas Buttle | n.buttle@qut.edu.au |
Overview
Professional engineers have a "conceptual understanding of the mathematics, numerical analysis, statistics, and computer and information sciences which underpin the engineering discipline" (Engineers Australia Stage 1 Competency Standard for Professional Engineer). This unit will serve as the transition from high school mathematics to university, particularly if you have not studied Queensland Specialist Mathematics (formerly called Senior Mathematics C) or equivalent. You will learn about elementary functions, their derivatives and integrals, the algebra of complex numbers, and vectors and matrices. Mathematical techniques and problem solving skills are employed in a range of mathematical exercises and contextualised problems, illustrating how these concepts and techniques are used in engineering systems. In future units you will continue to apply the mathematical knowledge and skills you have learned in this unit to increasingly complex problems.
Learning Outcomes
On successful completion of this unit you will be able to:
- Apply mathematical concepts and ideas relevant to engineering at an introduced level.
- Utilise technical notation and correct techniques to solve mathematical problems relevant to engineering at an introduced level.
- Interpret, translate and solve real world problems relevant to engineering using mathematical methods at an introduced level.
- Communicate effectively in mathematical formats to specialist Engineering audiences at an introduced level.
Content
- Elementary functions including polynomial, trigonometric, logarithmic and exponential functions. Their properties, the principle of composite functions, inverse functions, and the use of functions as representations of data are emphasised.
- Introduction to the processes of differentiation and integration of elementary functions as ways to model simple problems for functions of one variable, including those defined parametrically. Techniques such as implicit differentiation, product and chain rules, integration by substitution, and integration by parts are all employed to solve mathematical and applied problems.
- Introduction to vectors and matrices and arithmetic operations on vectors and matrices (cross products, dot products as well as matrix multiplication and addition), with applications to problems relevant to engineering, including solving systems of linear equations.
- The algebra of complex numbers, of vectors, and of matrices, illustrating how each may be used in representations of systems in real-world applications.
Learning Approaches
- In this unit, you will be provided with learning resources including readings and videos that you can access flexibly to prepare for your timetabled learning activities. Timetabled activities will be in the form of interactive lectures and workshops. These activities are an important opportunity for you to interact directly with the teaching team, to familiarise yourself with best practice, and to ask for help or clarification where needed.
- Learning resources will introduce you to theoretical background and concepts in fundamental engineering mathematics, along with example problems and real-world applications;
- Interactive lectures will discuss important concepts and work through example problems relevant for your assessment;
- In the workshops, you will solve a range of example problems, from purely mathematical exercises to contextualised problems. You will work both individually and in groups, allowing you to develop your group problem solving and oral communication skills.
You will be expected to:
- Prepare for timetabled classes and activities by engaging with the learning resources available from the unit website.
- Engage with timetabled activities and ask questions.
- Work on a wide variety of exercises and problems in your own time to consolidate material from timetabled activities.
- Engage with your peers in a learning community to practise problem solving and then work independently to complete your assessment tasks.
The total expected volume of learning for MZB125, as per the Australian Qualifications Framework, is 150 hours. As a guide, a breakdown for these hours might typically be:
- 26 lecture contact hours (2 hours x 13 weeks)
- 26 workshop contact hours (2 hours x 13 weeks)
- 78 hours self-guided independent study including worksheets and regular portfolio submission (6 hours x 13 weeks)
- 20 hours independent end of semester revision, consolidation and exam preparation
Feedback on Learning and Assessment
During workshops, you will share your formative ideas around problem solving and receive feedback from demonstrators. You are encouraged to view your workshop group as a learning community and to share and discuss challenges and strategies for learning. You will receive formative feedback by completing in-semester assignments. Each assessment submission will be graded against criteria and standards which will be shared with you through Assessment Task Descriptions and Marking Rubrics. Marked assessment will include written feedback from markers against the criteria.
Assessment
Overview
The assessment in this unit is designed to assess your learning against the unit learning outcomes. The portfolio supports you to progress in developing your competency in the application of fundamental methods as well as the development of problem-solving skills that will allow you to tackle more complex and open problems in your future career. Consistent practice in mathematical techniques and problem solving at the workshops will support your success in the summative tasks.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Portfolio
Each of the 6 topics of this unit has two worksheets (2x functions, 2x vectors, 2x matrices, 2x differentiation, 2x integration, and 2x complex numbers). You will complete and hand in a prescribed set of exercises from 8 out of 12 worksheets in total, including at least one set per topic. Exercises to be handed in are similar to those illustrated at the lecture. They will first be discussed at the workshops by your instructors, who will demonstrate similar examples. After the workshops, you will have one week to hand in your handwritten worked solution to the prescribed set of exercises. These exercises will comprise short questions with an emphasis on determining level of competency in the use of fundamental mathematical techniques, as well as contextualised problems that require the synthesis of more than one mathematical technique for their solution. You will be expected to communicate clearly and effectively the detailed working of all answers and utilise appropriate technical notation and correct techniques.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination
You will be required to solve problems requiring coherent mathematical solutions.
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
Open-access Textbooks:
- OpenStax College, Precalculus, 2020, CC-BY 4.0 https://openstax.org/details/books/precalculus
- OpenStax College, Calculus Vol. 1, 2020, CC-BY-NC_SA 4.0, https://openstax.org/details/books/calculus-volume-1
Other resources:
- Rattan, KS, Klingbeil, NW, Introductory Mathematics for Engineering Applications, 2015, John Wiley & Sons.
- Mallet DG, Pettet GJ & Farr AC. Introductory Algebra and Calculus, 2012, Pearson.
- Bird J, Engineering Mathematics, 2007 (5th Ed) – 2017 (8th Ed), Elsevier
There are numerous suitable reference texts for this unit, many of which can be located in the library. You should also make use of suitable online resources such as video instructions for specific problems. Additional resources, including audio and video recordings of appropriate segments of the lectures will be made available via the QUT Canvas site for this unit.
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in lecture theatres and small group tutorial rooms. Emergency exits and assembly areas will be made apparent to all attending students. 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: Portfolio, Examination
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.EN01 Bachelor of Engineering (Honours)
- Engage stakeholders professionally and communicate the outcomes of your work effectively to expert and non-expert audiences using appropriate modes.
Relates to: ULO4, Portfolio, Examination - Demonstrate coherent knowledge and skills of physical, mathematical, statistical, computer, and information sciences that are fundamental to professional engineering practice.
Relates to: ULO1, ULO2, ULO3, Portfolio, Examination
EN29 Bachelor of Engineering Studies
- Evidence of engaging stakeholders professionally and communicating the outcomes of your work effectively to expert and non-expert audiences.
Relates to: ULO4, Portfolio, Examination - Evidence of engaging with and applying regulatory requirements relating to safety, risk management and sustainability in professional engineering practice.
Relates to: ULO2, ULO3 - Evidence of demonstrating coherent knowledge and skills of physical, mathematical, statistical, computer and information science.
Relates to: ULO1, Portfolio, Examination
EV01 Bachelor of Engineering (Honours)
- Engage stakeholders professionally and communicate the outcomes of your work effectively to expert and non-expert audiences using appropriate modes.
Relates to: Portfolio - Demonstrate coherent knowledge and skills of physical, mathematical, statistical, computer, and information sciences that are fundamental to professional engineering practice.
Relates to: Portfolio, Examination