68106 Calculus 1
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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): 68102 Mathematics for Secondary Education Foundations
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 33130 Mathematics 1 AND 33190 Mathematical Modelling for Science AND 35511 Linear Dynamical Systems AND 37131 Introduction to Linear Dynamical Systems
Recommended studies:
68102 Maths for Secondary Education - Foundations
Description
This subject develops the knowledge and skills necessary for problem-solving and mathematical modelling at an introductory level. Concepts in calculus are explored. Differential calculus is applied to model situations in science, engineering, and other disciplines that involve growth, change and movements. Integral calculus is used to solve selected problems involving first order differential equations, and to calculate areas, volumes, lengths and other physical quantities. Vectors are introduced and applied to problem-solving and modelling. Sequences and series are reviewed and power series introduced where power series are used to approximate functions.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | apply fundamental concepts of mathematics to solve problems involving spatial position and movement |
|---|---|
| 2. | apply knowledge of the conceptual development of calculus to explain procedures in differentiation and integration |
| 3. | use mathematical, engineering and scientific terminology and symbols to define concepts |
| 4. | apply mathematical knowledge and skills in a variety of situations, in both familiar and new contexts |
| 5. | communicate the mathematical knowledge clearly, logically and critically |
| 6. | reflect on the roles of mathematics and mathematics education in societies and cultures |
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: Develop a professional identity as a leader in mathematics and mathematics education. (1.2)
- 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 development of the following graduate attributes in Science:
Graduate Attribute 1 - Disciplinary knowledge
A broad introduction to the most important and widely used concepts in mathematics is given.
Graduate Attribute 2 - Research, inquiry and critical thinking
Throughout the subject mathematics is presented as a tool, which students are invited to use in the solution to real-world problems.
Graduate Attribute 3 - Professional, ethical and social responsibility
Students are required to reflect on the way that mathematics is communicated about in school settings.
Graduate Attribute 4 - Reflection, innovation, creativity
Students are required to reflect on ways to be creative in their presentation of mathematical knowledge.
Graduate Attribute 5 - Communication
Students will use formal and informal language to communicate knowledge clearly, logically and critically.
Teaching and learning strategies
This subject requires about 2-3 hours on Canvas per week to work through Canvas pages and associated activities. There is also about 2-3 hours of online homework each week and an optional drop-in tutorial. 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 two later subjects (Calculus 2 and 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.
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 once.
Feedback on microteaching will be provided via discussions in the tutorials with peers and the tutor.
Content (topics)
Vectors and their application to physical and geometric problems. Functions and their relationship to measurement and the interpretation of physical results. Trigonometric functions and inverse trigonometric functions. Inverse functions. Conceptual and historical development of ideas in calculus. Differentiation. Integrals and methods of integration. Differential equations arising from physical problems. Sequences and series, power series including Taylor series.
Assessment
Assessment task 1: Weekly Homework
| Intent: | This task develops the following graduate attributes: 1. Disciplinary Knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 3, 4 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: | 70% |
| Length: | About two hours of work outside class time. |
| Criteria: | Students will be assessed and given feedback on:
|
Assessment task 2: Micro-teaching
| Intent: | This task develops the following graduate attributes: 1. Disciplinary Knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3, 4, 5 and 6 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 4.1 and 5.1 |
| Type: | Demonstration |
| Groupwork: | Individual |
| Weight: | 20% |
| Length: | The micro-teaching will take about 20 minutes at the start of each tutorial. Students will know in advance which questions they are to present. |
| Criteria: | Students will be assessed on:
|
Assessment task 3: Engagement in online tasks
| Intent: | This task develops the following graduate attributes: 1. Disciplinary Knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3, 5 and 6 This assessment task contributes to the development of course intended learning outcome(s): 1.2, 3.1 and 4.1 |
| Type: | Reflection |
| Groupwork: | Individual |
| Weight: | 10% |
| Criteria: | Students will be assessed on the quantity and quality of their interactions via various online interactive elements. This may include responding to the posts of others on discussion boards and short formative quizzes. |
Minimum requirements
Students must achieve 50% overall in order to pass this subject.
Required texts
There is no required text for this subject - all information can be found in the lecture notes, recordings, and online notes as well as the solutions to the Tutorial problems. However it is recommended that students have access to a standard First Year Calculus text such as Stewart Calculus: International metric edition, or Thomas: Calculus, 15th Edition, for additional explanations and practice problems.
Recommended texts
Thomas' Calculus, Pearson. E-edition: ISBN-13: 9780137616077.
Stewart, J. Calculus, International Metric Version, 8th Edition (Cole Cengage).
Working questions from this textbook (or similar texts) will build your skills and your confidence in this subject.
References
Other good books on 1st year mathematics for scientists and engineers are:
Kreyszig, Advanced Engineering Mathematics. Any Edition
James, G. (2008). Modern Engineering Mathematics. 4th Edition. Pearson.
Trim, D. (2008) Calculus for Engineers 4th Edition. Pearson.
Recommended readings on the history of calculus include:
Strogatz, S. (2019). Infinite powers: How calculus reveals the secrets of the universe. Houghton Mifflin Harcourt.
Boyer, C. B. (1959). The history of the calculus and its conceptual development:(The concepts of the calculus). Courier Corporation.