MAU22S03 Fourier analysis for science

Assessment Details

• This module is examined in a 2-hour examination at the end of Semester 1.
• Continuous assessment contributes 20% towards the overall mark.
• The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows: 
  1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session; 
  2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam; 
  3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

Contact Hours

11 weeks of teaching with 3 lectures and 1 tutorial per week.

Learning Outcomes

On successful completion of this module, students will be able to

• Calculate and interpret the real and complex Fourier series of a given periodic function.
• Obtain and interpret the Fourier transform of non-periodic functions.
• Evaluate integrals involving the Dirac delta function.
• Solve ordinary differential equations with constant coefficients of first or second order, both homogeneous and inhomogeneous.
• Obtain series solutions (including Frobenius method) to ordinary differential equations of first or second order.

Module Content

• Vector spaces and inner products of functions.
• Fourier series, Fourier transform, Dirac delta function.
• Applications of Fourier analysis.
• Ordinary differential equations (ODE).
• Exact solutions of first and second order ODE.
• Series solutions of ODE, Frobenius method.

Recommended Reading

• Advanced engineering mathematics by Erwin Kreyszig.