Year
2016
Units
4.5
Contact
1 x 120-minute lecture-1 weekly
1 x 60-minute lecture-2 weekly
1 x 50-minute tutorial weekly
1 x 60-minute lecture-2 weekly
1 x 50-minute tutorial weekly
Prerequisites
1 of MATH2702, MATH2711, MATH2121, MATH2023, ENGR2711
Enrolment not permitted
1 of MATH8702, MATH9702 has been successfully completed
Topic description
First and second order differential equations in the phase plane. Linear approximations at equilibrium points. Index of a point; limit cycles; averaging, regular and singular perturbation methods. Stability and Liapunov's method. Bifurcation. Basic ideasof calculus of variations. The Euler-Lagrange equations; eigenvalue problems. Applications to second and higher order differential and partial differential equations. Rayleigh-Ritz and Galerkin methods.
Educational aims
The course Bachelor of Mathematics aims to develop the skills and knowledge required by a graduate in Mathematics.
Expected learning outcomes
At the completion of the topic, students are expected to be able to:
- Understand phase plane analysis
- Understand equilibrium points and linearization
- Calculate stability of equilibrium points and application of the Lyapunov method
- Calculate averaging, regular and singular perturbation methods to solve differential equations
- Understand bifurcation of solutions to differential equations
- Formulate solutions to ordinary and partial differential equations as problems in calculus of variations
- Find approximate solutions to differential equations through the Rayleigh-Ritz and Galerkin methods
Key dates and timetable
Timetable details for 2016 are no longer published.
Sturt Rd, Bedford Park
South Australia 5042
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