Pure & Applied Analysis (Ord) (U01647)

? Credit Points : 20 ? SCQF Level : 9 ? Acronym : MAT-3-PAAO

Syllabus Summary: Sequences and series, uniform convergence, the Riemann integral, convergence of Fourier series, applications, functions and distributions, transform techniques, existence and uniqueness for Partial Differential Equations, fundamental solutions and Green's functions.

Entry Requirements

? Pre-requisites : MAT-2-FoC, MAT-2-SVC, MAT-2-LiA, MAT-2-MAM or MAT-2-am3, MAT-2-mm3, MAT-2-am4, MAT-2-mm4 or MAT-2-mi3, MAT-2-mi4

? Prohibited combinations : MAT-3-PAAS2, MAT-3-PAA, MAT-3-PAAS2O

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Ordinary), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 3rd year

? Delivery Period : Full Year (Blocks 1-4)

? Contact Teaching Time : 3 hour(s) per week for 22 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
08/01/2008	12:10	13:00	Lecture Theatre B, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	12:10	13:00	KB
Lecture	Friday	12:10	13:00	KB

? Additional Class Information : Supervision: one hour per week (shared with other 'core' courses), at a time to be arranged with Supervisor.

Summary of Intended Learning Outcomes

The following are the learning objectives for the Honours version, MAT-3-PAA; for this (Ordinary) version there is more emphasis on the technical, rather than conceptual elements, which will be reflected by a different examination.

1. Understanding the definitions and concepts of convergence, Cauchy sequences, and completeness in R and C.
2. Understanding the notions of open and closed subsets of Rn and their relationship to convergence.
3. Ability to test sequences and series of functions for uniform convergence.
4. Familiarity with the idea that problems of analysis such as convergence of Fourier series can be couched in and resolved using the language of metric spaces.
5. Understanding basic Harmonic Analysis techniques and their use in PDEs