68108 Calculus 3
Warning: The information on this page is indicative. The subject outline for a
particular session, location and mode of offering is the authoritative source
of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.
Subject handbook information prior to 2024 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 68106 Mathematics for Secondary Education Calculus 1
These requisites may not apply to students in certain courses.
There are course requisites for this subject. See access conditions.
Anti-requisite(s): 37335 Differential Equations
Description
In this subject students develop familiarity with the theory of functions of several variables extended to include the following topics: line integrals, integrals over vector paths, systems of linear ordinary differential equations, applications of this theory and some of the main computational techniques used in the solution of linear systems of ordinary differential equations. Technology tools such as Mathematica ( wolfram alpha ) and Python are used to model real world scenarios using systems of linear ordinary differential equations. Applications in biology, chemistry, physics, statistics and engineering rely heavily on the use of such design tools. Examples and applications are introduced throughout the subject.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | model real world problems using mathematical tools and resources |
|---|---|
| 2. | use formal mathematical terminology and also informal (lay) language to express the concepts presented in the subject |
| 3. | demonstrate a high level of skill in the mathematical techniques covered in the subject |
| 4. | demonstrate understanding of the theoretical results which justify the use of these techniques |
| 5. | communicate mathematical knowledge clearly, logically and critically |
| 6. | use appropriate mathematical software packages to perform calculations and explore ideas relevant to the subject content |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Analyse: Demonstrate critical engagement with mathematical knowledge in the secondary classroom context. (1.1)
- Analyse: Critically evaluate information in the investigation of mathematical and pedagogical problems. (2.1)
- Analyse: Demonstrate an understanding of health and safety requirements, ethical conduct, and risk management, in the context of teaching mathematics. (3.1)
- Analyse: Derive innovative solutions to complex mathematical and educational problems. (4.1)
- Analyse: critique approaches for communicating with students, parents, peers, mathematicians, educationalists, and the public. (5.1)
Contribution to the development of graduate attributes
This subject contributes to the following Faculty of Science Graduate Attributes:
Graduate Attribute 1 - Disciplinary Knowledge
An understanding of the nature, practice & application of the chosen science discipline,
Graduate Attribute 2 - Research, Inquiry and Critical Thinking
An understanding of the scientific method of knowledge acquisition. Encompasses problem solving, critical thinking and analysis attributes, and the ability to discover new understandings.
Graduate Attribute 3 - Professional, Ethical and Social Reaponsibility
The ability to acquire, develop, employ and integrate a range of technical, practical and professional skills, in appropriate and ethical ways within a professional context, autonomously and collaboratively and across a range of disciplinary and professional areas. Time management skills, personal organisation skills, teamwork skills, computing skills, laboratory skills, data handling, quantitative and graphical literacy skills.
Graduate Attribute 5 - Communication
An understanding of the different forms of communication - writing, reading, speaking, listening - including visual and graphical, within science and beyond and the ability to apply these appropriately and effectively for different audiences.
Teaching and learning strategies
This subject requires about 1-2 hours on Canvas per week and a 2 hour tutorial once a week. There is also about 2-3 hours of written homework each week. Students are required to read the Canvas pages online and engage with asynchronous discussions via discussion boards. As students complete the interactive elements on Canvas they are provided with formative feedback on the comprehension of concepts, and on skill development.
Through the weekly homework tasks, students will build their advanced problem solving and modelling skills. Students will also develop a high standard of written communication to explain their solutions and the steps taken to arrive that those solutions.
In the interactive and collaborative weekly tutorials students will learn the professional skills of presenting short mathematical explanations to their peers, as though to a high school class. These skills will be assessed in the Micro-teaching task, where students will demonstrate their discipline knowledge in the context of professional practice. Oral and written communication to a target audience is key. Each student will do this at least twice, with one occasion to include the socio-cultural angle of the maths (i.e. who invented this, Why? When?).
Feedback on microteaching will be provided via discussions in the tutorials with peers and the tutor.
Content (topics)
Topics include: Introduction to concepts from analysis, 3D geometry and functions of several variables; multiple integrals and their applications in various contexts; linear algebra including eigenvalues, eigenvectors and applications; Systems of linear ordinary differential equations; Mathematica via Wolfram Alpha is used as appropriate.
Assessment
Assessment task 1: Weekly Homework
| Intent: | This task develops the following graduate attributes: 1. Disciplinary Knowledge. 2. Research, inquiry and critical thinking. 4. Reflection, Innovation, Creativity. 5. Communication. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 3 and 5 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 4.1 and 5.1 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 50% |
| Length: | About two hours of work outside class time. |
| Criteria: | Students will be assessed and given feedback on: 1. The ability to use key mathematical concepts in their appropriate context 2. The ability to obtain the correct solution to problems 3. Clear communication of how they arrived at the solution, including all steps 10 weekly homework activities provide opportunity to address each criteria. |
Assessment task 2: Micro-teaching
| Intent: | This task develops the following graduate attributes: 1. Disciplinary Knowledge. 3. Professional, ethical and social responsibility 4. Reflection, Innovation, Creativity. 5. Communication. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 2, 4, 5 and 6 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 3.1, 4.1 and 5.1 |
| Type: | Demonstration |
| Groupwork: | Individual |
| Weight: | 50% |
| Length: | About two hours of work outside class time. |
| Criteria: | Students will be assessed on: 1. Correct choice and use of problem solving strategies 2. Ability to generate correct quantitative solutions 3. Clear communication of how they arrived at the solution 4. Responses to questions Micro-teaching sessions will take about 30 minutes at the start of each two hour tutorial. Students will know in advance which questions they are to present. |
Minimum requirements
Students must achieve 50% overall in order to pass this subject.