Unit of study_

# MATH1923: Multivariable Calculus and Modelling (Adv)

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).

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 outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.