MATH3205
10 units
3000 level
Course handbook
Description
The course introduces Fourier analysis from an applied perspective. Fourier series and the Fourier transform are developed as links between the domains of time and frequency. Connections between the analogue and digital worlds are made through the sampling theorem and the Fast Fourier Transform. Applications to quantum physics are explored through Heisenberg uncertainty. Further applications to partial differential equations, tomography and probability/statistics are also explored.
Availability2024 Course Timetables
Callaghan
- Semester 1 - 2024
Learning outcomes
On successful completion of the course students will be able to:
1. read, follow and critique arguments of a mathematical nature.
2. formulate and communicate reasoned arguments of a mathematical nature.
3. apply the techniques of Fourier analysis to problems in physics and engineering.
Content
- Separation of variables
- Fourier series, Fourier transforms and applications
- Sturm-Liouville problems and expansions
- Shannon sampling and Heisenberg uncertainty
- Discrete and Fast Fourier Transforms
- Applications: tomography, partial differential equations, probability.
Assumed knowledge
MATH2310
Assessment items
In Term Test: Class Test
Written Assignment: Homework assignments (x5)
Formal Examination: Examination ' Formal
Contact hours
Semester 1 - 2024 - Callaghan
Lecture-1
- Face to Face On Campus 3 hour(s) per week(s) for 13 week(s) starting in week 1
Course outline
- MATH3205 - Semester 1, 2024 (Callaghan) (PDF, 224.8 KB)
The University of Newcastle acknowledges the traditional custodians of the lands within our footprint areas: Awabakal, Darkinjung, Biripai, Worimi, Wonnarua, and Eora Nations. We also pay respect to the wisdom of our Elders past and present.