33130 Mathematics 1
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 2024 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Anti-requisite(s): 33190 Mathematical Modelling for Science AND 35101 Introduction to Linear Dynamical Systems AND 37131 Introduction to Linear Dynamical Systems AND Spks Between C10154 and C10158
Recommended studies:
Extension 1 Mathematics
Description
This subject develops the knowledge and skills necessary for problem-solving and mathematical modelling at an introductory level. Differential calculus is applied to model situations in science and engineering that involve oscillations. Integral calculus is used to solve selected problems involving first- and second-order differential equations, and to calculate areas, volumes, lengths and other physical quantities. Vectors, matrix multiplication and determinants 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 more functions.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Describe the relevance of mathematics to engineering and science and the role which engineering and science play in the development and evolution of mathematical ideas and methods |
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| 2. | Apply mathematical tools and resources to model real world problems, especially in engineering and science |
| 3. | Demonstrate correct use of mathematical terminology and concepts, and show understanding of those concepts by describing them in both formal and informal language. |
| 4. | Achieve a high level of skill in the mathematical techniques covered in the subject content |
| 5. | Communicate mathematical knowledge clearly, logically and critically. |
| 6. | Use appropriate mathematical software to perform calculations and explore mathematical ideas relevant to the subject content, and demonstrate knowledge of the functions of this software by interpreting output. |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Technically Proficient: FEIT graduates apply abstraction, mathematics and discipline fundamentals, software, tools and techniques to evaluate, implement and operate systems. (D.1)
- Collaborative and Communicative: FEIT graduates work as an effective member or leader of diverse teams, communicating effectively and operating within cross-disciplinary and cross-cultural contexts in the workplace. (E.1)
Contribution to the development of graduate attributes
Engineers Australia Stage 1 Competencies
This subject contributes to the development of the following Engineers Australia Stage 1 Competencies:
- 1.2 Conceptual understanding of the mathematics, numerical analysis, statistics, and computer and information sciences which underpin the engineering discipline.
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3.2. Effective oral and written communication in professional and lay domains.
This subject is fundamental for Mathematics and Science students as it introduces them and contributes to the development of the most important characteristics of the modern scientist. It enables them to understand and apply fundamental mathematical principals to scientific theories and methodologies, to use problem-solving techniques, and to approach scientific challenges systematically. Furthermore, it helps them ensure that their work aligns with professional standards and ethical guidelines, and enables them to efficiently communicate scientific findings.
This subject contributes to the development of the following graduate attributes:
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
Throughout the subject mathematics is presented as a tool, which students are invited to use in the solution to real-world problems
Graduate Attribute 5 - Communication
Students will use formal and informal language to communicate knowledge clearly, logically and critically.
Teaching and learning strategies
Lectures: Students are expected to review the pre-recorded lecture material (of about 2-3 hours per week). Blank slides of the lecture sheets will be made available, and students are encouraged to make their own notes.
Tutorials: Tutorials will be held weekly on campus, with a duration of 2 hours. Skills Development Tests will be held in the tutorial, with feedback given the following week.
In the tutorials, students may be required to work in groups, as discussion of mathematical ideas helps students to learn. Students will be working through problems with the assistance of the tutor, who may also demonstrate mathematical modelling techniques and mathematical programming which the students can then investigate themselves. Students will get more value from the tutorials if they have attempted all tutorial problems before attending the tutorials.
Lectures may be supplemented by a live, on campus workshop to answer student questions.
Content (topics)
Vectors and their application to physical problems. Functions and their relationship to measurement and the interpretation of physical results. Trigonometric functions and inverse trigonometric functions. Inverse functions. Hyperbolic functions. Differentiation. Integrals and methods of integration. Complex numbers. Differential equations arising from physical problems. Oscillatory motion. Matrix multiplication and determinants. Sequences and series, power series including Taylor series.
Assessment
Assessment task 1: Skills Development Tests
| Intent: | These short tests (10 in total, of equal weighting) will provide regular feedback on how students are mastering the necessary skills in each area of the subject. They will be held in the tutorial classes according to the schedule. |
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| 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): D.1 and E.1 |
| Type: | Quiz/test |
| Groupwork: | Individual |
| Weight: | 60% |
| Length: | 30 minutes. |
| Criteria: | Students will be assessed and given feedback on:
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Assessment task 2: Final Examination
| Intent: | The final examination is a test of the core competency in mathematical skills developed throughout this subject. |
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| 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): D.1 and E.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 40% |
| Length: | Allow 2 Hours to complete the exam. Additional time will be allocated to download questions and upload solutions. |
| Criteria: | Students will be assessed on:
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Minimum requirements
To pass the subject, students must achieve at least 50% after all assessments and at least 50% for the final exam. A student who receives less than 50% for the examination, yet manages to achieve 50% or greater overall, will be awarded an X grade.
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. For additional explanations and practice problems we recommend the texbook :Calculus: International metric edition" by Stewart.
Recommended texts
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.
The following is the former textbook in this subject and can also be used:
Stewart, J. Calculus: Concepts & Contexts, Metric International Edition Thomson. (Or Brooks/Cole Cengage).
(The 4th or 5th Edition).
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.
Washington,A.J., BasicTechnical Mathematics with Calculus, any edition
Fitz-Gerald, G.F., Peckham, I.A., Mathematical methods for engineers and scientists, 4th edition