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 later units in the Mathematics sequence 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 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. This unit accepts 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 in the Mathematics sequence, especially for those units. 

2025 10

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Prerequisites

Nil

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, infinit...

Learning Outcome 01

Solve mathematical problems using limits, infinite series, and circular and hyperbolic functions, including the use of relevant identities.
Relevant Graduate Capabilities: GC1, GC2, GC7, GC8

Apply knowledge of the derivative, including the u...

Learning Outcome 02

Apply knowledge of the derivative, including the use of first principles, to derive rules of differentiation.
Relevant Graduate Capabilities: GC1, GC2, GC7, GC8

Interpret and apply derivatives to solve problems ...

Learning Outcome 03

Interpret and apply derivatives to solve problems in curve sketching, related rates, optimization and other related problems.
Relevant Graduate Capabilities: GC1, GC2, GC7, GC8

Perform anti-differentiation of functions and solv...

Learning Outcome 04

Perform anti-differentiation of functions and solve related mathematical problems.
Relevant Graduate Capabilities: GC1, GC2, GC7, GC8

Apply anti-differentiation and definite integrals ...

Learning Outcome 05

Apply anti-differentiation and definite integrals to compute areas, volumes, and solve applied problems.
Relevant Graduate Capabilities: GC1, GC2, GC7, GC8

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

To successfully complete an undergraduate Mathematics sequence, 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 supervised test components 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 take home 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.

Overview of assessments

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.

Weighting

35%

Learning Outcomes LO1, LO2, LO3
Graduate Capabilities GC1, GC2, GC7, GC8

Assessment Task 2: Take Home Assignment/s Contin...

Assessment Task 2: Take Home Assignment/s

Continuous assessment – A single task which is submitted in 1, 2 or 3 parts across the semester as stipulated by the lecturer.

Weighting

30%

Learning Outcomes LO1, LO2, LO3, LO4, LO5
Graduate Capabilities GC1, GC2, GC7, GC8

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.

Weighting

35%

Learning Outcomes LO1, LO2, LO3, LO4, LO5
Graduate Capabilities GC1, GC2, GC7, GC8

Learning and teaching strategy and rationale

As is common in Mathematics a variety of Active Learning approaches promote the best acquisition of skills and understanding. Lectures will typically be structured to provide explanations of the material to be covered, along with examples of the applications of that material, as well as formal and informal tasks for students that will reinforce that learning. Splitting the taught content of the lectures into short topics will ensure increased student engagement with the material, as well as providing opportunities for students to consolidate their learning before new material is covered. 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.

Representative texts and references

Representative texts and references

Anton H, Bivens I, Davis S (2016) Calculus: Early Transcendentals, 11th Edition New York: John Wiley & Sons. 

Ayres, F. & Mendelson, E. (2013) Schaum’s Outline of Calculus, 6th Edition, McGraw-Hill

Betounes, D & Betounes, M.R. (2019) Calculus: Concepts and Computation, 3rd Edition Kendall/Hurt Publications. 

Courant, R., Robbins, H. & Stewart, I. (1996) What is Mathematics? Oxford: Oxford University Press. 

Edwards, C.H. & Penney D.E. (2007) Calculus and early trancendentals. Prentice-Hall Inc. 

Hughes-Hallett, D. et al (2005) Calculus Single and Multivariable, New York: John Wiley & Sons 

Spivak, M. (2008) Calculus, 4th Edition, Publish or Perish 

Stein, S.K. & Barcellos, A. (1992) A Calculus and Analytic Geometry, New York: McGraw Hill 

Stewart, J. (2015) Single Variable Calculus: Volume 1 8th Edition, CENGAGE Learning Custom Publishing 

Strang, G. (2017) Calculus 3rd Edition, Wellesley-Cambridge 

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