MATH104 - Differential and Integral Calculus

Year

Credit points

Campus offering

Prerequisites

Nil

Teaching organisation

Unit rationale, description and aim

This unit builds upon the prerequisite knowledge of basic calculus to provide a solid base for further study by providing a brief review and extension of functions including transcendental functions, and introduction to complex numbers and an introduction to differential and integral calculus. A study of calculus is fundamental in all Mathematics and is a requirement of all Initial Teacher Education (ITE) Mathematics courses. The aim of this unit is to ensure that all students have a similar and solid understanding of the basic calculus required in later units in the Mathematics sequence. 

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.

On successful completion of this unit, students should be able to:

LO1 - Apply the properties of limit and convergence in infinite series to simple problems (GA4, GA5, GA8) 

LO2 - Apply knowledge of circular and hyperbolic functions including their identities (GA4, GA5, GA8, GA10) 

LO3 - Demonstrate knowledge of the derivative, including the use of first principles to derive rules of differentiation (GA4, GA5, GA8, GA9) 

LO4 - Apply the derivative to problem solving, including curve sketching, related rates and optimization and other related problems. (GA4, GA5, GA8) 

LO5 - Anti-differentiate functions and use these to solve problems (GA4, GA5, GA8, GA10) 

LO6 - Apply anti-differentiation and definite integrals to problems in areas, volumes, arclength (GA4, GA5, GA8) 

Graduate attributes

GA4 - think critically and reflectively 

GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession 

GA8 - locate, organise, analyse, synthesise and evaluate information 

GA9 - demonstrate effective communication in oral and written English language and visual media 

GA10 - utilise information and communication and other relevant technologies effectively.

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 theorem of calculus. 
• Applications of integration. 
• Infinite and improper integrals. 

Learning and teaching strategy and rationale

This unit includes 4 contact hours per week for 12 weeks, comprising 2 hours of lectures and 2 of tutorials. 

As is common in Mathematics a variety of Active Learning strategies promote the best acquisition of skills and understanding. This allows students to learn the skills via Interactive Lectures, or suitable online strategies, and then build understanding, competence and confidence via (face-to-face) tutorials involving cooperative groups, peer review and other relevant strategies. In all cases this should be supported using available online technology. 

This unit will normally include the equivalent of 24 hours of lectures together with 24 hours attendance mode tutorials. 150 hours in total with a normal expectation of 48 hours of directed study and the total contact hours should not exceed 48 hours. The balance of the hours becomes private study. 

Assessment strategy and rationale

A range of assessment procedures will be used to meet the unit learning outcomes and develop graduate attributes consistent with University assessment requirements.  Such procedures may include, but are not limited to: essays, reports, examinations, student presentations or case studies 

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 a variety of skills at their fingertips from which to choose and an ability to recall those skills under some pressure. The assessment strategy chosen, while traditional, tests and supports student learning. The continuous assessment component helps reinforce learning and builds collaborative skills. The examination components ensures that students have fully integrated the learning and can bring a variety of strategies to bear under pressure. 

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, assignments, tests and examinations are expected to be handwritten and so submitted as hardcopy, rather than through Turnitin. The expected tasks for this unit will all fit into this category. 

Overview of assessments

Mathematics units at ACU are included in the 3A Mathematics, Statistics discipline cluster. This is a cluster for which universities are assumed to provide additional support, either via dedicated computer lab time and resources and/or additional teaching time. In the absence of the additional computer support, an addition hour of face to face contact is provided — in keeping with past practice at ACU.

Representative texts and references

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

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

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