Unit of study_

MATH1021: Calculus Of One Variable

2024 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:

Code MATH1021 Mathematics and Statistics Academic Operations 3
 Prerequisites: ? None None MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931 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.

Session MoA   Location Outline
Semester 1 2024
Normal day Camperdown/Darlington, Sydney
Intensive January 2024
Block mode Camperdown/Darlington, Sydney
Semester 2 2024
Normal day Camperdown/Darlington, Sydney
Outline unavailable
Session MoA   Location Outline
Semester 1 2020
Normal day Camperdown/Darlington, Sydney
Intensive January 2020
Block mode Camperdown/Darlington, Sydney
Outline unavailable
Semester 2 2020
Normal day Camperdown/Darlington, Sydney
Intensive August 2020
Block mode Camperdown/Darlington, Sydney
Outline unavailable
Semester 1 2021
Normal day Camperdown/Darlington, Sydney
Semester 1 2021
Normal day Remote
Intensive February 2021
Block mode Camperdown/Darlington, Sydney
Intensive February 2021
Block mode Remote
Semester 2 2021
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Remote
Semester 1 2022
Normal day Camperdown/Darlington, Sydney
Semester 1 2022
Normal day Remote
Intensive January 2022
Block mode Camperdown/Darlington, Sydney
Intensive January 2022
Block mode Remote
Semester 2 2022
Normal day Camperdown/Darlington, Sydney
Semester 2 2022
Normal day Remote
Semester 1 2023
Normal day Camperdown/Darlington, Sydney
Semester 1 2023
Normal day Remote
Intensive January 2023
Block mode Camperdown/Darlington, Sydney
Intensive January 2023
Block mode Remote
Semester 2 2023
Normal day Camperdown/Darlington, Sydney

Modes of attendance (MoA)

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Important enrolment information

Departmental permission requirements

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