Real Analysis

Cod y Modiwl: MA20110
Teitl y Modiwl: Real Analysis
Blwyddyn Academaidd: 2027/2028
Semester: Semester 1
Cyd-gysylltydd y Modiwl: Dr Robert Douglas
Rhestr Ddarllen: Gweld ar Aspire
Rhagofynion: MA11110 neu MT11110
Anghymharus (Unrhyw Flwyddyn Acad): MT20110
Staff Eraill sy'n Cyfrannu: Dr Gwion Evans; Dr Robert Douglas

Dulliau Asesu

Math o Asesiad	Manylion Asesiad	Cyfran
Arholiad Semester	2 Awr (Written Examination)	100%
Arholiad Ailsefyll	2 Awr (Written Examination)	100%

Canlyniadau Dysgu

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

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.

Disgrifiad cryno

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.

Nod

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.

Cynnwys

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.

Sgiliau Modiwl

Math o Sgiliau	Manylion Sgiliau
Addasrwydd a gwydnwch	Students are expected to develop their own approach to time-management and to use the feedback from marked work to support their learning.
Cydlynu ag erail	Students will be encouraged to work in groups to solve problems.
Cyfathrebu proffesiynol	Students will be expected to submit clearly written solutions to set exercises.
Datrys Problemau Creadigol	The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Gallu digidol	Use of the internet, Blackboard, and mathematical packages will be encouraged to enhance their understanding of the module content and examples of application
Sgiliau Pwnc-benodol	Broadens exposure of students to topics in mathematics, and an area of application that they have not previously encountered.

Nodau

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 5