Unit of study_

# MATH1023: Multivariable Calculus and Modelling

### 2024 unit information

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling. 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 mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable. 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

#### Science

 Prerequisites: ? None None MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933 Knowledge of complex numbers and methods of differential and integral calculus including integration by partial fractions and integration by parts as for example in MATH1021 or MATH1921 or MATH1931 or HSC Mathematics Extension 2

At the completion of this unit, you should be able to:

• LO1. apply mathematical logic and rigor to solving problems
• LO2. express mathematical ideas and arguments coherently in written form
• LO3. set up differential equations which arise from mathematical models of interest to scientists and engineers
• LO4. understand the relationship between a first-order differential equation, its direction field, and its solution curves
• LO5. solve separable and first-order linear differential equations
• LO6. solve second-order homogeneous linear differential equations with constant coefficients
• LO7. calculate partial derivatives and understand their geometric significance
• LO8. find equations of tangent planes to surfaces
• LO9. calculate the directional derivative and gradient vector, and understand their physical significance.
• LO10. optimise functions of two or more variables

## 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
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
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

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### Modes of attendance (MoA)

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## Important enrolment information

### Departmental permission requirements

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