Unit rationale, description and aim
Calculus was developed to study quantities and processes that are continuously changing and so is crucial for modelling and understanding most physical processes. To support further development of more advanced mathematical skills, it is important that all students have a known and relatively advanced understanding of basic calculus. The study of calculus is fundamental in all Mathematics and is a requirement of a variety of career-oriented degrees including Computer Sciences and all Initial Teacher Education (ITE) Mathematics courses.
This unit builds upon a basic knowledge of basic calculus obtained in high school to provide a solid base for further study by providing a brief review and extension of those concepts: functions, limits, continuity, differentiation and integration. It is accepted that students who have studied calculus at high school may have differing levels of knowledge.
The aim of this unit is to consolidate and extend students’ knowledge and understanding and to ensure that students have, at minimum, a known level of competence with the basic ideas of calculus that may then be applied in later units.
Learning outcomes
To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.
Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.
Explore the graduate capabilities.
Solve mathematical problems using limits, infinite...
Learning Outcome 01
Apply knowledge of the derivative, including the u...
Learning Outcome 02
Interpret and apply derivatives to solve problems ...
Learning Outcome 03
Perform anti-differentiation of functions and solv...
Learning Outcome 04
Apply anti-differentiation and definite integrals ...
Learning Outcome 05
Content
Topics will include:
- Review of functions. Circular Functions and their inverses, and Hyperbolic functions, their inverses.
- Sequences and series.
- Gradients, limits, tangents and normals.
- Differentiation by rules.
- Applications, including curve sketching, concavity, related rates, optimization, and other relevant topics.
- Antidifferentiation and applications of antiderivatives.
- First order linear differential equations.
- The definite integral and Fundamental theorems of calculus.
- Applications of integration.
- Improper integrals.
Assessment strategy and rationale
Multi-mode Delivery:
To successfully complete this unit, students need an understanding of a variety of basic Mathematical topics and an ability to apply that understanding to a variety of problems. To succeed at problem solving in Mathematics, students must have these skills at their fingertips and be able to recall them and choose an appropriate approach under some pressure. The assessment strategy chosen, while traditional, tests and supports student learning by providing opportunities to develop and test their problem-solving skills through the unit.
At specified times, through the semester, students will sit two invigilated test components on-campus to ensure that students have fully integrated the learning and can independently bring a variety of strategies to bear to solve a variety of problems.
The assignment will allow students to develop other skills including traditional and technological problem-solving methods.
Typing of Mathematical notation either requires a significant investment of time, or knowledge of advanced Mathematical typesetting software. Neither of those skills are suitable for an undergraduate course in Mathematics. Consequently, the lecturer may request that assignments and tests are handwritten. Use of AI to solve problems is not allowed in these tests.
Online Unscheduled Delivery:
To successfully complete this unit, students need an understanding of a variety of basic Mathematical topics and an ability to apply that understanding to a variety of problems. To succeed at problem solving in Mathematics, students must have these skills at their fingertips and be able to recall them and choose an appropriate approach under some pressure. The assessment strategy chosen, while traditional, tests and supports student learning by providing opportunities to develop and test their problem-solving skills through the unit.
At specified times, through the term, students will sit two invigilated test components to ensure that students have fully integrated the learning and can independently bring a variety range of strategies to bear to solve a variety of problems. Use of AI to solve problems is not allowed in these tests.
The assignment will allow requires students to develop other skills including traditional and technological problem-solving methods.
Typing of Mathematical notation either requires a significant investment of time, or knowledge of advanced Mathematical typesetting software. Neither of those skills are suitable for an undergraduate course in Mathematics. Consequently, the lecturer may request that assignments and tests are handwritten.
To pass the unit, students must demonstrate achievement of every unit learning outcome and obtain a minimum mark of 50% for the unit.
Overview of assessments
Multi-mode
Assessment Task 1: Test 1 Content and applicatio...
Assessment Task 1: Test 1
Content and application test. This test will be conducted under supervision and on campus.
35%
Assessment Task 2: Assignment/s Continuous asses...
Assessment Task 2: Assignment/s
Continuous assessment – A single task which is submitted in 1, 2 or 3 parts across the semester as stipulated by the lecturer.
30%
Assessment Task 3: Test 2 Content and applicatio...
Assessment Task 3: Test 2
Content and application test. This test will be conducted under supervision and on campus.
35%
Online Unscheduled
Assessment Task 1: Test Content and application ...
Assessment Task 1: Test
Content and application test. This test will be conducted online under appropriate arrangements, as determined by the teaching team.
35%
Assessment Task 2: Assignment(s) Continuous asse...
Assessment Task 2: Assignment(s)
Continuous assessment. - A single task which is submitted in one, two or three parts across the the study period as stipulated by the lecturer.
30%
Assessment Task 3: Test 2 Content and Applicatio...
Assessment Task 3: Test 2
Content and Application Test. This test will be conducted under appropriate arrangements, as determined by the teaching team.
35%
Learning and teaching strategy and rationale
Multi-mode:
The teaching approach within this unit puts the student at the centre of their learning. This is achieved by using an approach that integrates asynchronous interactive online elements with learning experiences and practical exercises that facilitate problem solving and peer collaboration. This allows students to learn the skills and then build understanding, competence and confidence through tutorials that ideally occur face to face. Face-to-face learning supports immediate feedback, peer interaction, and collaborative problem-solving, essential elements in developing mathematical thinking, while also enabling tutors to identify and address misconceptions early. Continuous formative learning opportunities allow for the early detection of problems a student might be having and ensures that appropriate guidance can be given early enough to support later learning in the unit. Students will be required to submit responses to questions dealing with simple problems in calculus. In all cases this should be supported using available online technology.
Online Unscheduled Delivery:
The teaching approach within this unit puts the student at the centre of their learning. This is achieved by using an approach that integrates asynchronous interactive online elements with learning experiences and practical exercises that facilitate problem solving and peer collaboration. Access to fundamental knowledge is provided through online resources that enable students to build their understandings in a flexible manner. Students are given the opportunity to build upon this knowledge through social learning experiences conducted through practical activities online. These opportunities enable students to build more complex understandings through peer interactions and structured learning experiences. This approach allows students to develop problem solving skills which align to vocational requirements and underpin further study.