MXB202 Advanced Calculus
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: | MXB202 |
|---|---|
| Prerequisite(s): | MXB105 and MXB106 |
| Equivalent(s): | MAB311 |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
Unit Outline: Semester 2 2027, Gardens Point, Internal
| Unit code: | MXB202 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | MXB105 and MXB106 |
| Equivalent: | MAB311 |
| Coordinators: | Pascal Buenzli | pascal.buenzli@qut.edu.au Maria Kleshnina | maria.kleshnina@qut.edu.au |
Overview
Advanced calculus introduces you to new skills and methodologies in multivariable and vector calculus that are essential to more advanced study in applied mathematics, such as partial differential equations and advanced mathematical modelling, as well as in related quantitative disciplines in science and technology, such as physics, physical chemistry, and engineering. This unit builds on your introductory calculus and linear algebra skills developed in MXB105 Calculus and Differential Equations and MXB106 Linear Algebra, and will further develop your ability to decompose complex problems into smaller components, resolve these smaller components and hence solve the original problem. You will also use advanced calculus techniques to explore aspects of Indigenous culture including boomerang design, and waterway desertification due to tectonic movement, with associated stories of adaptation in changing environments, and early Indigenous Australian funerals.
Learning Outcomes
On successful completion of this unit you will be able to:
- Communicate mathematics and problem solutions clearly and consistently both in written and oral forms.
- Recognise, construct and solve problems, both in abstract and real world contexts, using the critical thinking and the mathematical theory of advanced calculus.
- Decompose complex problems into smaller components, resolve these smaller components and hence the original problem.
Content
Multivariable calculus: multivariable functions, limits and continuity, partial derivatives, higher-order derivatives, the chain rule, linear approximations and differentiability, differentials, gradients and directional derivatives, implicit functions, Taylor series and approximations, extreme values, double integrals, triple integrals, change of variables in multiple integrals, applications of multiple integrals.
Vector calculus: vector and scalar fields, conservative fields, line integrals, surfaces and surface integrals, oriented surfaces and flux integrals, gradient, divergence and curl.
Learning Approaches
This unit involves 2 hours of lectures each week where theory and concepts will be presented and discussed, and where you will be exposed to the processes required to solve problems using the methods of this unit. There will also be 2 hours of workshop activities each week.
The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios. The emphasis will be on learning by doing, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning.
In workshops and lectures, you will engage in collaborative activity with peers, tutors and lecturers. You will work with experts and peers to develop effective methods/approaches for communicating, retrieving, evaluating and presenting information.
You will present for assessment and feedback, solutions to problems set throughout the semester in the workshops.
You are expected to work in any lecture/workshop session times allocated, but also in your own private study time. That is, you are expected to consolidate the material presented during class by working a wide variety of exercises, problems and online learning activities in your own time.
Feedback on Learning and Assessment
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 and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
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.
QUT’s extension policy may not apply to all assessment items in this unit. The extension policy pertaining to each assessment item can be found on the unit Canvas site.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Problem Solving Task 1
Assessment: Problem Solving Task 2
This assessment will consist of problem-solution based exercises to demonstrate your understanding of theoretical concepts and their application. You will submit hand-written worked solutions.
This assignment will allow you to demonstrate the authentic mathematical practice of decomposing complex problems into smaller components, resolving these smaller components and hence the original problem.
The ethical and responsible use of generative artificial intelligence (GenAI) tools is authorised in this assessment. See the relevant assessment details in Canvas for specific guidelines.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
You will be required to complete a formal, end of semester examination where you will demonstrate your skills, techniques and problem solving abilities. The exam may include short and long answer type questions.
The use of generative artificial intelligence (GenAI) tools is prohibited during this assessment.
The examination will require attendance on QUT campus.
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
There are several reference texts for this unit. 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, 9th edition, John Wiley & Sons Inc
Reference book(s)
Adams RA & Essex C (2010) Calculus: a Complete Course, 7th edition, Pearson Education Canada Inc
Kaplan W (2003) Advanced Calculus, 5th edition, Addison-Wesley Higher Mathematics
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit.
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
2: Engineering Application Ability
Relates to: Problem Solving Task 2
Relates to: Problem Solving Task 1, Problem Solving Task 2, Examination (invigilated)
3: Professional and Personal Attributes
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.MS01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Problem Solving Task 1, Problem Solving Task 2, Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Problem Solving Task 1, Problem Solving Task 2, Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Problem Solving Task 1, Problem Solving Task 2 - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Problem Solving Task 1, Problem Solving Task 2, Examination (invigilated)
MV01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Problem Solving Task 1, Problem Solving Task 2, Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Problem Solving Task 1, Problem Solving Task 2, Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Problem Solving Task 1, Problem Solving Task 2 - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Problem Solving Task 1, Problem Solving Task 2, Examination (invigilated)
ST20 Bachelor of Science Advanced (Honours)
- Articulate advanced and coherent knowledge and understanding of at least one scientific discipline
Relates to: Problem Solving Task 1, Problem Solving Task 2, Examination (invigilated) - Critically evaluate and apply advanced scientific principles to design experiments, and collect, record, analyse and interpret data using appropriate scientific methodologies, and critical thinking, judgment and deduction to solve complex problems
Relates to: Problem Solving Task 1, Problem Solving Task 2, Examination (invigilated)