# School of Mathematics and Statistics

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2011/2012 Sem. 1

## MT2001 MATHEMATICS

This is a core second level mathematics module which must be taken by anyone planning to pursue Honours level material in Mathematics, Statistics or Physics.

## Aims

To extend the knowledge and skills gained by students in the module MT1002 in preparation for Honours study.

In particular

- to enhance their skills and understanding of calculus to include functions of several variables;

- to develop an appreciation of basic ideas in Linear Algebra.

## Objectives

By the end of the course a student should be able to demonstrate:

- how to determine the Taylor series of a function and estimate the error associated with a Taylor polynomial;

- an understanding of the concepts of continuity and differentiability of functions of several variables; partial differentiation and an appreciation of the difference between partial and ordinary differentiation;

- how to determine the local behaviour of surfaces at stationary points;

- how to determine integrals over areas and volumes (and when necessary use different co-ordinate systems including cylindrical and spherical polars);

- an ability to work with the fundamental concepts of vector space theory;

- an ability to manipulate matrices in order to find inverses and determinants;

- how to determine the eigenvalues and eigenvectors of a square matrix (and diagonalisation when appropriate);

- how to obtain a Fourier series representation of simple function and interpret its properties.

## Textbooks

Advanced Engineering Mathematics E Kreyszig; Wiley

Calculus (6th Edition) E W Swokowski, M Olinick, D Pence; PWS; 1994.
[This book is out of print, but may be available second-hand.]

H Anton; Elementary Linear Algebra, Wiley; 1991

## Lectures, practicals and tutorials

The average load, in hours per week, is as follows:
Lectures: 5
Practicals: 1
Tutorials: 1
These figures do not include the revision and exam period at the end of each semester.

## Assessment

30% of the assessment mark is from continuous assessment during the semester. The remainder is from a 3 hour exam at the end of the semester.

Re-assessment is entirely by a 3 hour exam in August.

MT1002

## Availability

This module is taught every year in both Semester 1 and Semester 2 at 12.00.

## Lecturers

First Semester: Dr A P Naughton (Module coordinator), Dr C V Tran, Dr Y Peresse

Second Semester: Dr S Huczynska (Module coordinator), Prof D G Dritschel, Dr A P Naughton