MTH2032

Differential equations with modelling ( 6 points, SCA Band 2, 0.125 EFTSL)

Leader: Dr Leo Brewin

Offered:
Clayton Second semester 2006 (Day)
Gippsland Second semester 2006 (OCL)

Synopsis: The study of Models of physical problems particularly heat conduction and oscillations, using computer simulation, laboratory experiments and mathematical analysis. Computer algorithms and mathematical techniques for ordinary differential equations using Euler and Predictor-Corrector methods with exact solutions found using separation of variables, integrating factors and substitution methods. The partial differential equations for material transport, heat conduction and wave motion are derived using physical models and solved using separation of variables and computational algorithms. Applications are to wave motion and heat conduction in a variety of practical situations.

Objectives: On completion of this unit students will have an understanding of: the importance of differential equations in a variety of applications; the analytic, computational and graphical approaches to the study of differential equations; the importance of initial and boundary conditions and the differences between ordinary and partial differential equations; the basic principles of numerical computation; the significance of differential equations in modelling real-world problems. Students will also have developed skills in: applying problem-solving techniques for the solution of ordinary and partial differential equations; using a computer algebra package; using a spreadsheet package for numerical computations; constructing a simple mathematical model in terms of a differential equation and interpreting and communicating the results.

Assessment: Examination (3 hours): 50% + Continuous assessments: 50%

Contact Hours: Three 1-hour lectures and one 1.5 hour workshop per week

Prerequisites: MAT1085 or MTH1030

Corequisites: MTH2010

Prohibitions: MAT2902, MAT2911