60 hours

Hawthorn

Credit Points: 12.5 Credit Points

Related Course/s:

Aims & Objectives:

• Introduce mathematical concepts underlying the field of differential equations.
• Demonstrate how differential equations naturally arise in the mathematical description of physical and engineering problems.
• Introduce methods for solving differential equations which model realistic physical applications.

• See differential equations as a rigorous way of modelling physical phenomena.
• Derive major differential equations from physical principles.
• Understand the role of initial and boundary conditions in determining the solutions of equations.
• Choose and apply appropriate methods for solving differential equations.

Teaching Methods:

Assessment:

Generic Skills Outcomes:

• Ability to apply knowledge of basic science and engineering fundamentals.
• Ability to communicate effectively, not only with engineers but also with the community at large.
• Ability to undertake problem identification, formulation and solution.

Content:

• Special non-linear first order ODEs: Bernoulli's and Riccati's equations.
• Second order ODEs with non-constant coefficients and methods of their solution: power series,
  radius and interval of convergence; power series method and Legendre polynomials; Frobenius
  methods for Bessel functions; orthogonal solutions to second order differential equations;
  orthogonal eigenfunction expansions.
• Derivation of basic second order PDEs with constant coefficients from physical principles applied
  to problems in heat transfer, electrical fields and fluid motion: Laplace's, Poisson's, heat and wave
  equations. Classification of linear second order PDEs and boundary conditions.
• Methods for PDEs: reduction to ODEs by separation of variables and series solutions for PDEs.
  Physical examples: solutions of second order linear PDEs in simple rectangular and circular
  geometries; membranes and Bessel functions; Laplacian in polar and spherical coordinates.

Textbooks:

References: