Note: This unit version is currently being edited and is subject to change!
MATH1021: Calculus of One Variable (2019 - Semester 1)
| Unit: | MATH1021: Calculus of One Variable (3 CP) |
| Mode: | Normal-Day |
| On Offer: | Yes |
| Level: | Junior |
| Faculty/School: | School of Mathematics and Statistics |
| Unit Coordinator/s: | |
| Session options: | Semester 1 |
| Versions for this Unit: |
| Campus: | Camperdown/Darlington |
| Pre-Requisites: | None. |
| Prohibitions: | MATH1011 OR MATH1901 OR MATH1906 OR MATH1111 OR ENVX1001 OR MATH1001 OR MATH1921 OR MATH1931. |
| Brief Handbook Description: | Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include complex numbers, functions of a single variable, limits and continuity, differentiation, optimisation, Taylor polynomials, Taylor's Theorem, Taylor series, Riemann sums, and Riemann integrals. |
| Assumed Knowledge: | HSC Mathematics Extension 1. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). |
| Timetable: | MATH1021 Timetable | |||||||||||||||
| Time Commitment: |
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Learning outcomes are the key abilities and knowledge that will be assessed in this unit. They are listed according to the course goal supported by each. See Assessment Tab for details how each outcome is assessed.
(1) Maths/ Science Methods and Tools (Level 1)| Assessment Methods: |
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| Grading: |
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Note that the "Weeks" referred to in this Schedule are those of the official university semester calendar https://web.timetable.usyd.edu.au/calendar.jsp
| Week | Description |
| Week 1 | Sets, numbers, and complex numbers |
| Week 2 | The complex plane, polar form |
| Week 3 | Roots of complex numbers, review of functions |
| Week 4 | Heuristic and intuition of limits, definition of limits |
| Week 5 | Limit laws and continuity |
| Week 6 | Differentiation, extreme values, L'Hopital's rule |
| Week 7 | Taylor polynomials and approximation |
| Week 8 | The remainder term, basic Taylor series |
| Week 9 | Riemann sums and the Riemann integral |
| Week 10 | The Fundamental Theorem of Calculus |
| Week 11 | Approximating integrals with Taylor polynomials, volumes |
| Week 12 | Further integration techniques |
| Week 13 | Revision/further applications |
| Exam Period | Assessment Due: Exam |
Course Relations
The following is a list of courses which have added this Unit to their structure.
Course Goals
This unit contributes to the achievement of the following course goals:
| Attribute | Practiced | Assessed |
| (1) Maths/ Science Methods and Tools (Level 1) | No | 100% |
These goals are selected from Engineering & IT Graduate Outcomes Table 2018 which defines overall goals for courses where this unit is primarily offered. See Engineering & IT Graduate Outcomes Table 2018 for details of the attributes and levels to be developed in the course as a whole. Percentage figures alongside each course goal provide a rough indication of their relative weighting in assessment for this unit. Note that not all goals are necessarily part of assessment. Some may be more about practice activity. See Learning outcomes for details of what is assessed in relation to each goal and Assessment for details of how the outcome is assessed. See Attributes for details of practice provided for each goal.
