1 x 120-minute lecture-1 weekly
1 x 60-minute lecture-2 weekly
1 x 50-minute tutorial weekly
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:

  1. Understand phase plane analysis
  2. Understand equilibrium points and linearization
  3. Calculate stability of equilibrium points and application of the Lyapunov method
  4. Calculate averaging, regular and singular perturbation methods to solve differential equations
  5. Understand bifurcation of solutions to differential equations
  6. Formulate solutions to ordinary and partial differential equations as problems in calculus of variations
  7. Find approximate solutions to differential equations through the Rayleigh-Ritz and Galerkin methods