68107 Calculus 2
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 2025 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 68106 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): 33230 Mathematics 2 AND 33290 Statistics and Mathematics for Science
Description
This subject introduces calculus for functions of several variables and covers the underpinning concepts of calculus and real analysis, as well as the solution of coupled ordinary differential equations. Topics to be covered include the formal definitions of limits, continuity and derivatives, Riemann integration, partial derivatives, the gradient, optimisation and Lagrange multipliers, integration in higher dimensions, systems of linear differential equations, solution of such systems using diagonalisation. 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)
- Synthesise: Investigate real-world problems by analysing and critically evaluating different solutions to complex challenges. (2.2)
- Evaluate: Collaborate to create and implement professional solutions to educational problems. (3.3)
- Analyse: Derive innovative solutions to complex mathematical and educational problems. (4.1)
- Synthesise: Through reflection, own and understand their learning journey. (4.2)
- Synthesise: Develop and Communicate complex ideas. (5.2)
Contribution to the development of graduate attributes
This subject provides the student with knowledge and skills to prepare them for professional practice.
This subject contributes to the development of the following Science graduate attributes:
Graduate Attribute 1 – Disciplinary knowledge
Activities in this subject develop practical skills in single and multivariable calculus and introduce the formal language of mathematical proofs required in more advanced mathematical discourse. This attribute is assessed in Assessment tasks 1 (Weekly Homework).
Graduate Attribute 2 – Research, inquiry and Critical Thinking
The collaborative approach to problem formulation used in Weekly Homework (Assessment Task 1) helps students develop skills in identifying and evaluating alternative approaches to modelling and solving problems.
Graduate Attribute 4 – Reflection, Innovation and Creativity
Micro-teaching (Assessment Task 2) will enable the students to go beyond the course material and demonstrate the creative use of mathematics to solve interesting problems.
Graduate Attribute 5 – Communication
Micro-teaching (Assessment Task 2) develops the skills of communicating the results of a complex mathematical problem to a diverse audience.
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 foundational problem solving and modelling skills which will be extended in the later subjects (Calculus 3). Students will also develop a high standard of written communication to explain their solutions and the steps taken to arrive that those solutions. Feedback from the homework will be given by the tutors in the problem-solving component of the tutorials in the subsequent week.
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. Students will prepare and present to their colleagues solutions of relevant mathematical problems, as though presenting to a class of Year 11 or Year 12 students. 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.
To derive maximum benefit from the online learning opportunities, students should preview the topics/problems to be discussed in class using resources available through Canvas to obtain further insight and come prepared to contribute to the discussion. Preparation might include reading notes, viewing a Kaltura video and/or attempting specific questions. A collaborative approach is used in the problem-solving component of the tutorials. Students will be presented with open-ended scenarios and problems which can be modelled using the mathematical skills which have been developed and through online resources. The problems will be broken down into smaller subsections and discussed collaboratively.
Content (topics)
Topics include: Introduction to concepts from analysis, 3D geometry and functions of several variables; partial derivatives; optimisation; multiple integrals and their applications in various contexts; linear algebra including eigenvalues, eigenvectors and applications; 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, 2.2 and 4.1 |
| 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. 2. Research, inquiry and critical thinking. 4. Reflection, Innovation, Creativity. 5. Communication. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 2, 4 and 5 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 3.3, 4.2 and 5.2 |
| 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. |