Unit of study_

# MATH1933: Multivariable Calculus and Modelling (SSP)

The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1923 Multivariable Calculus and Modelling (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.

Code MATH1933 Mathematics and Statistics Academic Operations 3
 Prerequisites: ? None None MATH1003 or MATH1903 or MATH1013 or MATH1907 or MATH1023 or MATH1923 (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
• LO13. gain an appreciation of a diverse range of mathematical problems and applications through participating in class discussions and the completion of assignments
• LO14. grasp new mathematical concepts beyond routine methods and calculations.

## Unit outlines

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