The University of Newcastle, Australia
Not currently offered
Course code

MATH3205

Units

10 units

Level

3000 level

Course handbook

Description

Introduces the basics of Fourier analysis as a prelude to applications. The course develops Fourier analysis from a general pure mathematical perspective starting with Lebesgue integration and elements of the theory of Hilbert spaces, leading to Fourier series, Fourier integrals and the fast Fourier transform, and then to applications such as partial differential equations and sampling. These subjects are of great importance to the electrical engineering and physics communities. The course concludes with more modern topics such as Gabor and wavelet transforms.


Availability

Not currently offered.

This Course was last offered in Semester 1 - 2018.


Learning outcomes

On successful completion of the course students will be able to:

1. In-depth knowledge of Fourier analysis and its applications to problems in physics and electrical engineering.

2. An ability to communicate reasoned arguments of a mathematical nature in both written and oral form.

3. An ability to read and construct rigorous mathematical arguments.


Content

  • Basics of Lebesgue integration
  • Elements of Hilbert spaces and orthogonal expansions
  • Fourier series and Fourier transforms of continuous data; applications to partial differential equations, sampling and uncertainty
  • Fast Fourier transform of discrete data
  • Time-frequency and time-scale analysis

Assumed knowledge

MATH3205Fourier AnalysisIntroduces the basics of Fourier analysis as a prelude to applications. The course develops Fourier analysis from a general pure mathematical perspective starting with Lebesgue integration and elements of the theory of Hilbert spaces, leading to Fourier series, Fourier integrals and the fast Fourier transform, and then to applications such as partial differential equations and sampling. These subjects are of great importance to the electrical engineering and physics communities. The course concludes with more modern topics such as Gabor and wavelet transforms.FSCITFaculty of Science724School of Mathematical and Physical Sciences103000This Course was last offered in Semester 1 - 2018.MATH2320 and MATH2330

Basics of Lebesgue integration

Elements of Hilbert spaces and orthogonal expansions

Fourier series and Fourier transforms of continuous data; applications to partial differential equations, sampling and uncertainty

Fast Fourier transform of discrete data

Time-frequency and time-scale analysis YOn successful completion of this course, students will be able to:1In-depth knowledge of Fourier analysis and its applications to problems in physics and electrical engineering.2An ability to communicate reasoned arguments of a mathematical nature in both written and oral form.3An ability to read and construct rigorous mathematical arguments. In Term Test: Class TestWritten Assignment: Homework assignments (x5)Presentation: Presentation (x5)Formal Examination: Examination ¿ Formal


Assessment items

In Term Test: Class Test

Written Assignment: Homework assignments (x5)

Presentation: Presentation (x5)

Formal Examination: Examination ¿ Formal