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MATH30350

Academic Year 2021/2022

Fourier Analysis (MATH30350)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
3 (Degree)
Credits:
5
Module Coordinator:
Dr Rupert Levene
Trimester:
Autumn
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This course builds on theory covered in earlier modules in Mathematical Analysis to give a self-contained introduction of the theory of Fourier series and Fourier transforms of Riemann integrable functions.

We will cover topics chosen, in the first instance, from:

(1) Pointwise and uniform convergence of sequences and series of functions, including the Weierstrass M-test;

(2) Properties of the Riemann integral;

(3) Fourier series of Riemann integrable functions on the circle;

(4) Fourier transforms of absolutely integrable continuous functions on the real line.

Additional topics and applications may be included, as time allows.

About this Module

Learning Outcomes:

On successful completion of this module, the student is expected to be able to reproduce and demonstrate an understanding of the definitions, theorems, examples and proofs covered in the module, and apply them to problems similar to those encountered in the module.

Student Effort Hours:
Student Effort Type Hours
Lectures

24
Tutorial

12
Specified Learning Activities

36
Autonomous Student Learning

48
Total

120

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.

Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Pre-requisite:
MATH10320 - Mathematical Analysis, MATH10340 - Linear Algebra 1 (MPS), MATH10350 - Calculus (MPS), MATH20060 - Calculus of Several Variables, MATH20300 - Linear Algebra 2 (MathSci)


 

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: In-trimester assignments Unspecified n/a Standard conversion grade scale 40% No
20
 No
Examination: Written examination 2 hour End of Trimester Exam No Standard conversion grade scale 40% No
80
 No

Carry forward of passed components
No
 

Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Elias M. Stein and Rami Shakarchi, "Fourier Analysis, An Introduction", Princeton University Press, 2003.
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