MXB105 Calculus and Differential Equations
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: | MXB105 |
|---|---|
| Antirequisite(s): | PVB201 |
| Equivalent(s): | MAB121, PVB200 |
| 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 1 2024, Gardens Point, Internal
| Unit code: | MXB105 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB121, PVB200 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Anti-requisite: | PVB201 |
| Coordinator: | Maria Kleshnina | maria.kleshnina@qut.edu.au |
Overview
Calculus and differential equations are used ubiquitously throughout mathematics, statistics and operations research. In this unit, you will build upon the foundations of calculus established in high school or in earlier university mathematics study, to greatly enhance your repertoire of theory and practice in these areas. The application of calculus and differential equations in the description and modelling of real-world problems will also be considered. This unit will extend your problem-solving skills, range of knowledge and use of techniques in differential and integral calculus. These theoretical concepts and their applications will be pursued further in MXB202 Advanced Calculus.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of foundational differential and integral calculus concepts, notation and techniques.
- Construct and solve mathematical and real-world problems using the techniques of single and multivariable calculus.
- Critically select and apply appropriate tools to analyse and solve ordinary differential equations.
- Communicate mathematical arguments and results effectively.
- Collaborate in a team environment to achieve an outcome.
Content
Differentiability by definition, implicit differentiation, mean value theorem. Taylor and Maclaurin series. Techniques of integration. Fundamental theorem of calculus. Functions of several variables, limits, partial derivatives, gradient. Introductions to multivariable chain rule, multivariable optimisation. Double and triple integrals. Vector-valued functions, limits, continuity, derivatives, curve parameterisation. First and second order ordinary differential equations, terminology, classification and basic solution methods.
Learning Approaches
This unit is available for you to study in either on-campus or online mode. You will be provided with learning resources including pre-recorded videos, readings and formative quizzes that you can access flexibly to prepare for your timetabled learning activities. The pre-recorded videos will provide you with theoretical background and concepts applied in problem solving processes, and the formative quizzes are for you to check your understanding of the new concepts.
The timetabled sessions are an important opportunity for you to interact directly with the teaching team and ask for help or clarification when needed. The timetabled interactive lecture sessions will emphasise important concepts and work through additional example problems relevant for your assessment. In the timetabled workshops you will solve a range of example problems, from purely mathematical exercises to real-world applications. You will work in groups, allowing you to develop your group problem solving and oral communication skills.
Feedback on Learning and Assessment
Automated formative feedback will be provided regularly throughout the unit via online quizzes designed to check your understanding of key concepts. Opportunities for peer feedback is provided through the group assessment task.
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece or informal interview.
Summative feedback will be provided throughout the semester with progressive release of results for in-semester assessment items.
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: Timed Online Assessment
Part-way through the semester you will have the opportunity to submit your solutions to a number of problems that arise from or extend the material presented in lectures.
The late submission period does not apply, and no extensions are available. if you can’t attend this exam due to special circumstances, you may apply to sit a deferred exam.
Assessment: Portfolio
You will work in a group to submit solutions to problems that extend the material presented in lectures. These extension topics will in some cases require you to use appropriate mathematical software. You will also be required to individually reflect on how effectively your group worked together as a team.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
Written examination requiring the demonstration of mathematical techniques, problem solving, and understanding of mathematical concepts, through performing mathematical exercises of a similar nature as those demonstrated in the unit lectures and workshops.
The examination will require attendance 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 local 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 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.
Resource Materials
Recommended text(s)
Anton H, Bivens I & Davis S. Calculus: Early Transcendentals, John Wiley & Sons Inc.
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: Timed Online Assessment, Portfolio, Examination (invigilated)
2: Engineering Application Ability
Relates to: Portfolio
Relates to: Portfolio, Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Portfolio, Examination (invigilated)
Relates to: Portfolio
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.ST01 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Timed Online Assessment, Portfolio, Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO2, ULO3, Timed Online Assessment, Portfolio, Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO3, Portfolio, Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Timed Online Assessment, Portfolio, Examination (invigilated) - Work autonomously and collaboratively with others in an inclusive and professional manner and use critical reflection for personal and professional growth.
Relates to: ULO5, Portfolio
SV02 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Timed Online Assessment, Portfolio, Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO2, ULO3, Timed Online Assessment, Portfolio, Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO3, Portfolio, Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Timed Online Assessment, Portfolio, Examination (invigilated) - Work autonomously and collaboratively with others in an inclusive and professional manner and use critical reflection for personal and professional growth.
Relates to: ULO5, Portfolio
Unit Outline: Semester 1 2024, Online
| Unit code: | MXB105 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB121, PVB200 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Anti-requisite: | PVB201 |
Overview
Calculus and differential equations are used ubiquitously throughout mathematics, statistics and operations research. In this unit, you will build upon the foundations of calculus established in high school or in earlier university mathematics study, to greatly enhance your repertoire of theory and practice in these areas. The application of calculus and differential equations in the description and modelling of real-world problems will also be considered. This unit will extend your problem-solving skills, range of knowledge and use of techniques in differential and integral calculus. These theoretical concepts and their applications will be pursued further in MXB202 Advanced Calculus.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of foundational differential and integral calculus concepts, notation and techniques.
- Construct and solve mathematical and real-world problems using the techniques of single and multivariable calculus.
- Critically select and apply appropriate tools to analyse and solve ordinary differential equations.
- Communicate mathematical arguments and results effectively.
- Collaborate in a team environment to achieve an outcome.
Content
Differentiability by definition, implicit differentiation, mean value theorem. Taylor and Maclaurin series. Techniques of integration. Fundamental theorem of calculus. Functions of several variables, limits, partial derivatives, gradient. Introductions to multivariable chain rule, multivariable optimisation. Double and triple integrals. Vector-valued functions, limits, continuity, derivatives, curve parameterisation. First and second order ordinary differential equations, terminology, classification and basic solution methods.
Learning Approaches
This unit is available for you to study in either on-campus or online mode. You will be provided with learning resources including pre-recorded videos, readings and formative quizzes that you can access flexibly to prepare for your timetabled learning activities. The pre-recorded videos will provide you with theoretical background and concepts applied in problem solving processes, and the formative quizzes are for you to check your understanding of the new concepts.
The timetabled sessions are an important opportunity for you to interact directly with the teaching team and ask for help or clarification when needed. The timetabled interactive lecture sessions will emphasise important concepts and work through additional example problems relevant for your assessment. In the timetabled workshops you will solve a range of example problems, from purely mathematical exercises to real-world applications. You will work in groups, allowing you to develop your group problem solving and oral communication skills.
Feedback on Learning and Assessment
Automated formative feedback will be provided regularly throughout the unit via online quizzes designed to check your understanding of key concepts. Opportunities for peer feedback is provided through the group assessment task.
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece or informal interview.
Summative feedback will be provided throughout the semester with progressive release of results for in-semester assessment items.
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: Timed Online Assessment
Part-way through the semester you will have the opportunity to submit your solutions to a number of problems that arise from or extend the material presented in lectures.
The late submission period does not apply, and no extensions are available. if you can’t attend this exam due to special circumstances, you may apply to sit a deferred exam.
Assessment: Portfolio
You will work in a group to submit solutions to problems that extend the material presented in lectures. These extension topics will in some cases require you to use appropriate mathematical software. You will also be required to individually reflect on how effectively your group worked together as a team.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
Written examination requiring the demonstration of mathematical techniques, problem solving, and understanding of mathematical concepts, through performing mathematical exercises of a similar nature as those demonstrated in the unit lectures and workshops.
The examination will require attendance 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 local 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 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.
Resource Materials
Recommended text(s)
Anton H, Bivens I & Davis S. Calculus: Early Transcendentals, John Wiley & Sons Inc.
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: Timed Online Assessment, Portfolio, Examination (invigilated)
2: Engineering Application Ability
Relates to: Portfolio
Relates to: Portfolio, Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Portfolio, Examination (invigilated)
Relates to: Portfolio
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.ST01 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Timed Online Assessment, Portfolio, Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO2, ULO3, Timed Online Assessment, Portfolio, Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO3, Portfolio, Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Timed Online Assessment, Portfolio, Examination (invigilated) - Work autonomously and collaboratively with others in an inclusive and professional manner and use critical reflection for personal and professional growth.
Relates to: ULO5, Portfolio
SV02 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Timed Online Assessment, Portfolio, Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO2, ULO3, Timed Online Assessment, Portfolio, Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO3, Portfolio, Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Timed Online Assessment, Portfolio, Examination (invigilated) - Work autonomously and collaboratively with others in an inclusive and professional manner and use critical reflection for personal and professional growth.
Relates to: ULO5, Portfolio
Unit Outline: Semester 2 2024, Gardens Point, Internal
| Unit code: | MXB105 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB121, PVB200 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Anti-requisite: | PVB201 |
| Coordinators: | Michael Dallaston | michael.dallaston@qut.edu.au Vivien Challis | vivien.challis@qut.edu.au |
Overview
Calculus and differential equations are used ubiquitously throughout mathematics, statistics and operations research. In this unit, you will build upon the foundations of calculus established in high school or in earlier university mathematics study, to greatly enhance your repertoire of theory and practice in these areas. The application of calculus and differential equations in the description and modelling of real-world problems will also be considered. This unit will extend your problem-solving skills, range of knowledge and use of techniques in differential and integral calculus. These theoretical concepts and their applications will be pursued further in MXB202 Advanced Calculus.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of foundational differential and integral calculus concepts, notation and techniques.
- Construct and solve mathematical and real-world problems using the techniques of single and multivariable calculus.
- Critically select and apply appropriate tools to analyse and solve ordinary differential equations.
- Communicate mathematical arguments and results effectively.
- Collaborate in a team environment to achieve an outcome.
Content
Differentiability by definition, implicit differentiation, mean value theorem. Taylor and Maclaurin series. Techniques of integration. Fundamental theorem of calculus. Functions of several variables, limits, partial derivatives, gradient. Introductions to multivariable chain rule, multivariable optimisation. Double and triple integrals. Vector-valued functions, limits, continuity, derivatives, curve parameterisation. First and second order ordinary differential equations, terminology, classification and basic solution methods.
Learning Approaches
This unit is available for you to study in either on-campus or online mode. You will be provided with learning resources including pre-recorded videos, readings and formative quizzes that you can access flexibly to prepare for your timetabled learning activities. The pre-recorded videos will provide you with theoretical background and concepts applied in problem solving processes, and the formative quizzes are for you to check your understanding of the new concepts.
The timetabled sessions are an important opportunity for you to interact directly with the teaching team and ask for help or clarification when needed. The timetabled interactive lecture sessions will emphasise important concepts and work through additional example problems relevant for your assessment. In the timetabled workshops you will solve a range of example problems, from purely mathematical exercises to real-world applications. You will work in groups, allowing you to develop your group problem solving and oral communication skills.
Feedback on Learning and Assessment
Automated formative feedback will be provided regularly throughout the unit via online quizzes designed to check your understanding of key concepts. Opportunities for peer feedback is provided through the group assessment task.
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece or informal interview.
Summative feedback will be provided throughout the semester with progressive release of results for in-semester assessment items.
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
Part-way through the semester you will have the opportunity to submit your solutions to a number of problems that arise from or extend the material presented in lectures.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Portfolio
You will work in a group to submit solutions to problems that extend the material presented in lectures. These extension topics will in some cases require you to use appropriate mathematical software. You will also be required to individually reflect on how effectively your group worked together as a team.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
Written examination requiring the demonstration of mathematical techniques, problem solving, and understanding of mathematical concepts, through performing mathematical exercises of a similar nature as those demonstrated in the unit lectures and workshops.
The examination will require attendance 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 local 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 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.
Resource Materials
Recommended text(s)
Anton H, Bivens I & Davis S. Calculus: Early Transcendentals, John Wiley & Sons Inc.
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: Problem Solving Task, Portfolio, Examination (invigilated)
2: Engineering Application Ability
Relates to: Portfolio
Relates to: Portfolio, Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Portfolio, Examination (invigilated)
Relates to: Portfolio
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.ST01 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Problem Solving Task, Portfolio, Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO2, ULO3, Problem Solving Task, Portfolio, Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO3, Portfolio, Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Problem Solving Task, Portfolio, Examination (invigilated) - Work autonomously and collaboratively with others in an inclusive and professional manner and use critical reflection for personal and professional growth.
Relates to: ULO5, Portfolio
SV02 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Problem Solving Task, Portfolio, Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO2, ULO3, Problem Solving Task, Portfolio, Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO3, Portfolio, Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Problem Solving Task, Portfolio, Examination (invigilated) - Work autonomously and collaboratively with others in an inclusive and professional manner and use critical reflection for personal and professional growth.
Relates to: ULO5, Portfolio
Unit Outline: Semester 2 2024, Online
| Unit code: | MXB105 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB121, PVB200 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Anti-requisite: | PVB201 |
Overview
Calculus and differential equations are used ubiquitously throughout mathematics, statistics and operations research. In this unit, you will build upon the foundations of calculus established in high school or in earlier university mathematics study, to greatly enhance your repertoire of theory and practice in these areas. The application of calculus and differential equations in the description and modelling of real-world problems will also be considered. This unit will extend your problem-solving skills, range of knowledge and use of techniques in differential and integral calculus. These theoretical concepts and their applications will be pursued further in MXB202 Advanced Calculus.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of foundational differential and integral calculus concepts, notation and techniques.
- Construct and solve mathematical and real-world problems using the techniques of single and multivariable calculus.
- Critically select and apply appropriate tools to analyse and solve ordinary differential equations.
- Communicate mathematical arguments and results effectively.
- Collaborate in a team environment to achieve an outcome.
Content
Differentiability by definition, implicit differentiation, mean value theorem. Taylor and Maclaurin series. Techniques of integration. Fundamental theorem of calculus. Functions of several variables, limits, partial derivatives, gradient. Introductions to multivariable chain rule, multivariable optimisation. Double and triple integrals. Vector-valued functions, limits, continuity, derivatives, curve parameterisation. First and second order ordinary differential equations, terminology, classification and basic solution methods.
Learning Approaches
This unit is available for you to study in either on-campus or online mode. You will be provided with learning resources including pre-recorded videos, readings and formative quizzes that you can access flexibly to prepare for your timetabled learning activities. The pre-recorded videos will provide you with theoretical background and concepts applied in problem solving processes, and the formative quizzes are for you to check your understanding of the new concepts.
The timetabled sessions are an important opportunity for you to interact directly with the teaching team and ask for help or clarification when needed. The timetabled interactive lecture sessions will emphasise important concepts and work through additional example problems relevant for your assessment. In the timetabled workshops you will solve a range of example problems, from purely mathematical exercises to real-world applications. You will work in groups, allowing you to develop your group problem solving and oral communication skills.
Feedback on Learning and Assessment
Automated formative feedback will be provided regularly throughout the unit via online quizzes designed to check your understanding of key concepts. Opportunities for peer feedback is provided through the group assessment task.
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece or informal interview.
Summative feedback will be provided throughout the semester with progressive release of results for in-semester assessment items.
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
Part-way through the semester you will have the opportunity to submit your solutions to a number of problems that arise from or extend the material presented in lectures.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Portfolio
You will work in a group to submit solutions to problems that extend the material presented in lectures. These extension topics will in some cases require you to use appropriate mathematical software. You will also be required to individually reflect on how effectively your group worked together as a team.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
Written examination requiring the demonstration of mathematical techniques, problem solving, and understanding of mathematical concepts, through performing mathematical exercises of a similar nature as those demonstrated in the unit lectures and workshops.
The examination will require attendance 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 local 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 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.
Resource Materials
Recommended text(s)
Anton H, Bivens I & Davis S. Calculus: Early Transcendentals, John Wiley & Sons Inc.
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: Problem Solving Task, Portfolio, Examination (invigilated)
2: Engineering Application Ability
Relates to: Portfolio
Relates to: Portfolio, Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Portfolio, Examination (invigilated)
Relates to: Portfolio
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.ST01 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Problem Solving Task, Portfolio, Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO2, ULO3, Problem Solving Task, Portfolio, Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO3, Portfolio, Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Problem Solving Task, Portfolio, Examination (invigilated) - Work autonomously and collaboratively with others in an inclusive and professional manner and use critical reflection for personal and professional growth.
Relates to: ULO5, Portfolio
SV02 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Problem Solving Task, Portfolio, Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO2, ULO3, Problem Solving Task, Portfolio, Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO3, Portfolio, Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Problem Solving Task, Portfolio, Examination (invigilated) - Work autonomously and collaboratively with others in an inclusive and professional manner and use critical reflection for personal and professional growth.
Relates to: ULO5, Portfolio