Module Identifier MA20110  
Module Title REAL ANALYSIS  
Academic Year 2001/2002  
Co-ordinator Dr T McDonough  
Semester Semester 1  
Other staff Dr K Rowlands  
Pre-Requisite MA11110  
Mutually Exclusive MX30110  
Course delivery Lecture   19 x 1 hour lectures  
  Seminars / Tutorials   3 x 1 hour example classes  
Assessment Exam   2 Hours (written examination)   100%  
  Resit assessment   2 Hours (written examination)   100%  

General 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.

Learning outcomes

On completion of this module, a student should be able to:


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. Cauchy's principle of convergence for series.
4. UNIFORM CONVERGENCE OF SEQUENCE OF FUNCTIONS: Uniform convergence of series, Weierstrass' M-test. Cauchy's principle for uniform convergence.

Reading Lists

** Recommended Text
Haggarty, R. (1993) Fundamentals of Mathematical Analysis. 2nd. Addison Wesley 0201631970
Marsden, J & Hoffman, M. (1993) Elementary Classical Analysis. 2nd. Freeman 0716721058
** Supplementary Text
Bartle, R & Sherbert, D. (1992) Introduction to Real Analysis. 2nd. Wiley 0471510009
Parzynski, W & Zipse, P. Introduction to Mathematical Analysis. McGraw-Hill 0070488452