# School of Mathematics and Statistics

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2011/2012 Sem. 1

## MT1001 INTRODUCTORY MATHEMATICS

Students who have a B at Advanced Higher (including units 1 and 2) or B at A-level may miss out this module and take MT1002 in the first semester instead.

## Aims

This module is designed to give students a secure basis in elementary calculus, allowing them to tackle the mathematics needed in other sciences.

Students wishing to do more mathematics will be given a good foundation from which they can proceed to the module MT1002 Mathematics.

Some of the work covered is a revision and reinforcement of material in the Scottish Highers and many A-Level syllabuses.

## Objectives

By the end of the course students should be able to:

- solve algebraic equations and inequalities;

- manipulate algebraic and trigonometric expressions;

- recognise arithmetic, geometric and binomial expansions;

- define the exponential and logarithm functions;

- understand the idea of the limit of a function and apply it to the concept of continuity;

- understand the concept of a derivative;

- differentiate polynomial, exponential, logarithmic, trigonometric and inverse trigonometric functions and use the rules for differentiating products, quotients and functions of a function;

- calculate higher derivatives;

- use differentiation to assist in the sketching of curves and in the determination of maxima and minima;

- calculate both indefinite and definite integrals using standard integrals, integration by substitution, by parts or by partial fractions;

- use inverse trigonometric functions;

- apply the methods of integration to evaluate areas.

## Textbooks

Calculus, International Metric Edition 7e, James Stewart. Available from www.cengage.co.uk.

## 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 2 hour exam at the end of the semester.

Re-assessment is entirely by a 2 hour exam in August.

## Prerequisites

SCE Higher Mathematics or GCSE A-level Mathematics.

## Availability

This module is taught every year in Semester 1 at 9.00.

## Lecturers

Dr J N Reinaud (Module coordinator), Dr A Haynes, Dr V Archontis