MAU22S03 Fourier analysis for science
| Module Code | MAU22S03 |
|---|---|
| Module Title | Fourier analysis for science |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Anthony Brown |
| Module Prerequisites | MAU11S02 Mathematics for scientists II |
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.
- Re-assessment, if needed, consists of 100% exam.
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.