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Unit of study_

MATH1013: Mathematical Modelling

MATH1013 is designed for science students who do not intend to undertake higher year mathematics and statistics. In this unit of study students learn how to construct, interpret and solve simple differential equations and recurrence relations. Specific techniques include separation of variables, partial fractions and first and second order linear equations with constant coefficients. Students are also shown how to iteratively improve approximate numerical solutions to equations.

Code MATH1013
Academic unit Mathematics and Statistics Academic Operations
Credit points 3
MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933
Assumed knowledge:
HSC Mathematics or a credit or higher in MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Please note: this unit does not normally lead to a major in Mathematics or Statistics or Financial Mathematics and Statistics

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

  • LO1. write down general and particular solutions to simple differential equations and recurrence relations describing models of growth and decay
  • LO2. determine the order of a differential equation or recurrence relation
  • LO3. find equilibrium solutions and analyse their stability using both graphical methods and slope conditions
  • LO4. recognise and solve separable first-order differential equations
  • LO5. use partial fractions and separation of variables to solve certain nonlinear differential equations, including the logistic equation
  • LO6. use a variety of graphical and numerical techniques to locate and count solutions to equations
  • LO7. solve equations numerically by fixed-point iteration, including checking if an iteration method is stable
  • LO8. explore sequences numerically, and classify their long-term behaviour
  • LO9. determine the general solution to linear second-order equations or simultaneous pairs of first order equations with constant coefficients.