Template:MATHS 789:Further Details

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Water Waves
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Water Waves
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Nonlinear Partial Differential Equations

This course is an introduction to nonlinear partial differential equations, focusing on nonlinear wave phenomena. The course will closely follow the book Wave Motion by Billingham and King. We will consider applications from physics, ocean engineering, chemical engineering, civil engineering and biology. The underlying partial differential equations will be derived and the properties of the solutions will be investigated. Simulations of the PDEs will be obtained using MATLAB.

Shock Waves
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Shock Waves

The main topics of the course are:

  • Traffic Waves (incl. Burgers' Equation)
  • Shock Formation
  • Compressible Gas Dynamics
  • Nonlinear Shallow-Water Waves (incl. Korteweg-deVries Equation)
  • Reaction–Diffusion Systems (incl. FitzHugh-Nagumo Equations)

Assignments: There will be three assignments and one project.

Assessment: The final grade will be calculated: 30% assignments, 10% project, and 60% final exam.

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Notes

Notes for the course.


Please consult the Course Coordinator or the Postgraduate Advisor for further details:

Steve Taylor Rm 303.523, Ext 86622, homepage
Office hours: Monday, Wednesday, Friday 11-12 or by appointment.
or pgadvice@math.auckland.ac.nz

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