Unit of study_

# MATH1923: Multivariable Calculus and Modelling (Adv)

### 2023 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. Additional topics covered in this advanced unit of study include the use of diagonalisation of matrices to study systems of linear equation and optimisation problems, limits of functions of two or more variables, and the derivative of a function of two or more variables. 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

#### Mathematics and Statistics Academic Operations

Code MATH1923 Mathematics and Statistics Academic Operations 3
 Prerequisites: ? None None MATH1003 or MATH1013 or MATH1907 or MATH1903 or MATH1023 or MATH1933 (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent

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

• LO1. apply mathematical logic and rigour 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. understand the concepts of limit and derivative for functions of more than one variable.
• LO8. calculate partial derivatives and understand their geometric significance
• LO9. find equations of tangent planes to surfaces
• LO10. calculate the direction derivative and gradient vector, and understand their physical significance
• LO11. optimise functions of two or more variables
• LO12. understand the connections between multivariable calculus and linear algebra

## 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 2 2023
Normal day Camperdown/Darlington, Sydney
Session MoA   Location Outline
Semester 2 2020
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Remote
Semester 2 2022
Normal day Camperdown/Darlington, Sydney
Semester 2 2022
Normal day Remote

### 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.