# Real Analysis 2 - MA5513

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## Module delivery information

Location Term Level1 Credits (ECTS)2 Current Convenor3 2020 to 2021
Canterbury
Autumn 5 15 (7.5) DR I Wood

## Overview

This module builds on the Stage 1 Real Analysis 1 module. We will extend our knowledge of functions of one real variable, look at series, and study functions of several real variables and their derivatives.

The outline syllabus includes: Continuity and uniform continuity of functions of one variable, series and power series, the Riemann integral, limits and continuity for functions of several variables, differentiation of functions of several variables, extrema, the Inverse and Implicit Function Theorems.

42 hours

## Method of assessment

80% exam, 20% coursework

B. S. Thomson, A. M. Bruckner, and J. B. Bruckner, Elementary Real Analysis (2nd Edition), 2008.
W. Rudin, Principles of mathematical analysis (3rd Edition), International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York-Auckland-DÃ¼sseldorf, 1976.
T.M Apostol, Mathematical analysis (2nd edition).. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1974.
K.G. Binmore, Mathematical analysis. A straightforward approach (2nd edition). Cambridge University Press, Cambridge-New York, 1982.

See the library reading list for this module (Canterbury)

## Learning outcomes

The intended subject specific learning outcomes. On successfully completing the module students will be able to:

1 demonstrate knowledge and critical understanding of the well-established principles within mathematical analysis;
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the following areas: uniform continuity of functions, sequences of functions, uniform convergences, series, power series, Riemann integration, functions of several variables, differentiation of functions of several variables;
3 apply the concepts and principles in mathematical analysis in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically the appropriateness of different tools and techniques.

The intended generic learning outcomes. On successfully completing the module students will be able to:

Demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation.

## Notes

1. Credit level 5. Intermediate level module usually taken in Stage 2 of an undergraduate degree.
2. ECTS credits are recognised throughout the EU and allow you to transfer credit easily from one university to another.
3. The named convenor is the convenor for the current academic session.