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Unit of study_

MATH1023: Multivariable Calculus and Modelling

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).

Code MATH1023
Academic unit Mathematics and Statistics Academic Operations
Credit points 3
MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933
Assumed knowledge:
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