Useful links
Unit of study_
MATH1021: Calculus Of One Variable
2025 unit information
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. Students are strongly recommended to complete MATH1021 or MATH1921 Calculus Of One Variable (Advanced) before commencing MATH1023 Multivariable Calculus and Modelling or MATH1923 Multivariable Calculus and Modelling (Adv).
Unit details and rules
Managing faculty or University school:
Science
| Study level | Undergraduate |
|---|---|
| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 3 |
|
Prerequisites:
?
|
None |
|---|---|
|
Corequisites:
?
|
None |
| Prohibitions:
?
|
MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931 |
| Assumed knowledge:
?
|
HSC Mathematics Extension 1 or equivalent |
At the completion of this unit, you should be able to:
- LO1. apply mathematical logic and rigour to solve problems
- LO2. read and write basic set notation
- LO3. demonstrate competency in arithmetic operations with complex numbers in Cartesian, polar, and exponential form
- LO4. use de Moivre’s theorem to find powers and roots of complex numbers
- LO5. solve simple polynomial equations involving complex numbers
- LO6. apply an intuitive understanding of a limit and knowledge of basic limit laws to calculate the limits of functions
- LO7. use the differential of a function to calculate critical points and apply them to optimise functions of one variable
- LO8. find inverse functions
- LO9. use L’Hopital’s rule to find limits of indeterminate forms
- LO10. find Taylor polynomials and the Taylor series expansion of a function
- LO11. approximate definite integrals by finite sums and vice versa
- LO12. express areas, and volumes of revolution, as definite integrals
- LO13. apply standard integration techniques to find anti-derivatives and definite integrals
- LO14. determine properties of a function defined by an integral using the graph of its integrand
- LO15. express mathematical ideas and arguments coherently in written form.
Unit availability
This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.
The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.
Find your current year census dates
Modes of attendance (MoA)
This refers to the Mode of attendance (MoA) for the unit as it appears when you’re selecting your units in Sydney Student. Find more information about modes of attendance on our website.
Important enrolment information
Departmental permission requirements
If you see the ‘Departmental Permission’ tag below a session, it means you need faculty or school approval to enrol. This may be because it’s an advanced unit, clinical placement, offshore unit, internship or there are limited places available.
You will be prompted to apply for departmental permission when you select this unit in Sydney Student.
Read our information on departmental permission.
