Gwybodaeth Modiwlau

Module Identifier
Module Title
Real Analysis
Academic Year
Semester 1
Exclusive (Any Acad Year)
Reading List
Other Staff

Course Delivery



Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (Written Examination)  100%
Supplementary Exam 2 Hours   (Written Examination)  100%

Learning Outcomes

On completion of this module, a student should be able to:
1. determine the Fourier series of integrable functions of arbitrary period;
2. apply Fourier series techniques to the summation of infinite series;
3. describe the notions of continuity and differentiability for functions of several variables;
4. establish whether functions of two or more variables are continuous and differentiable;
5. determine whether infinite series are convergent by using various convergence tests;
6. describe the notion of uniform convergence of sequences of functions;
7. use the Weierstrass M-test to test the uniform convergence of infinite series of functions;
8. determine the radius of convergence of power series;
9. use standard convergence theorems concerning power series.

Brief description

The study of real analysis is of paramount importance to any student who wishes to go beyond the routine manipulation of formulae to solve standard problems. The ability to think deductively and analyse complicated examples is essential to modify and extend concepts to new contexts. The module is geared to meet these needs.


In this module, the analytical techniques, developed in MA11110, will be extended to a more general setting. This module will provide the foundations of classical analysis in a concrete setting, with a special emphasis on applications.


1. FOURIER SERIES: Convergence theorems (statements only), application of Fourier Series to sum infinite series.
2. CALCULUS OF SEVERAL VARIABLES: Continuity, differentiability, partial derivatives, higher order and mixed partial derivatives.
3. THEORY OF INFINITE SERIES: Tests for convergence, including comparison test, ratio test, integral test. Power series, radius of convergence, absolute convergence.
4. UNIFORM CONVERGENCE OF SEQUENCE OF FUNCTIONS: Uniform convergence of series, the Weierstrass M-test.

Module Skills

Skills Type Skills details
Adaptability and resilience Students are expected to develop their own approach to time-management and to use the feedback from marked work to support their learning.
Co-ordinating with others Students will be encouraged to work in groups to solve problems.
Creative Problem Solving The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Digital capability Use of the internet, Blackboard, and mathematical packages will be encouraged to enhance their understanding of the module content and examples of application
Professional communication Students will be expected to submit clearly written solutions to set exercises.
Subject Specific Skills Broadens exposure of students to topics in mathematics, and an area of application that they have not previously encountered.


This module is at CQFW Level 5