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 | $493 |
| Domestic tuition unit fee | $3,348 |
| International unit fee | $4,008 |
Unit Outline: Semester 1 2021, Gardens Point, Internal
| Unit code: | MXB105 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB121 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Anti-requisite: | PVB201, PVB200 |
| Coordinator: | Scott McCue | scott.mccue@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 Linear 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 utilises an inquiry-based approach where you will engage in collaborative activity with peers, tutors and lecturers and will learn how to work effectively within teams. Throughout the semester, you will be exposed to a broad range of learning activities requiring both written and oral communication.
Lectures will provide you with theoretical background and concepts applied in problem solving processes. Workshop activities will give direction to your inquiry and will require you to retrieve, evaluate and present information. The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios.
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.
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.
Assessment: Examination (written)
If campus access is restricted at the time of the central examination period/due date, an alternative, which may be a timed online assessment, will be offered. Individual students whose circumstances prevent their attendance on campus will be provided with an alternative assessment approach.
Exposition of techniques and problem solving, with a distribution of short and long answers required.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
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.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
Anton H, Bivens I & Davis S. Calculus: Early Transcendentals, John Wiley & Sons Inc.
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.
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
Unit Outline: Semester 1 2021, Online, External
| Unit code: | MXB105 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB121 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Anti-requisite: | PVB201, PVB200 |
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 Linear 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 utilises an inquiry-based approach where you will engage in collaborative activity with peers, tutors and lecturers and will learn how to work effectively within teams. Throughout the semester, you will be exposed to a broad range of learning activities requiring both written and oral communication.
Lectures will provide you with theoretical background and concepts applied in problem solving processes. Workshop activities will give direction to your inquiry and will require you to retrieve, evaluate and present information. The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios.
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.
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.
Assessment: Examination (written)
If campus access is restricted at the time of the central examination period/due date, an alternative, which may be a timed online assessment, will be offered. Individual students whose circumstances prevent their attendance on campus will be provided with an alternative assessment approach.
Exposition of techniques and problem solving, with a distribution of short and long answers required.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
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.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
Anton H, Bivens I & Davis S. Calculus: Early Transcendentals, John Wiley & Sons Inc.
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.
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
Unit Outline: Semester 2 2021, Gardens Point, Internal
| Unit code: | MXB105 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB121 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Anti-requisite: | PVB201, PVB200 |
| Coordinators: | 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 Linear 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.
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.
Assessment: Examination (written)
If campus access is restricted at the time of the central examination period/due date, an alternative, which may be a timed online assessment, will be offered. Individual students whose circumstances prevent their attendance on campus will be provided with an alternative assessment approach.
Exposition of techniques and problem solving, with a distribution of short and long answers required.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
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.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
Anton H, Bivens I & Davis S. Calculus: Early Transcendentals, John Wiley & Sons Inc.
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.
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
Unit Outline: Semester 2 2021, Online, External
| Unit code: | MXB105 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB121 |
| Assumed Knowledge: | Sound achievement in Senior Mathematics C (or equivalent) or MXB100 is assumed knowledge. |
| Anti-requisite: | PVB201, PVB200 |
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 Linear 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.
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.
Assessment: Examination (written)
If campus access is restricted at the time of the central examination period/due date, an alternative, which may be a timed online assessment, will be offered. Individual students whose circumstances prevent their attendance on campus will be provided with an alternative assessment approach.
Exposition of techniques and problem solving, with a distribution of short and long answers required.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
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.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
Anton H, Bivens I & Davis S. Calculus: Early Transcendentals, John Wiley & Sons Inc.
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.
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