# Undergraduate Catalogue of Courses 2012/2013

## MATHEMATICS

MA 2005

INTRODUCTION TO ANALYSIS

CREDIT POINTS 15

*Course Co-ordinator:* Dr C Lopez

*Pre-requisite(s):*
MA 1005 or, with the permission of the Head of Mathematical Sciences, both MA 1007 and MA 1507.

- Fundamental properties of real numbers: field operations, order, completeness.
- Sequences and limits: convergence, basic examples, decimal representation of real numbers.
- Functions of one real variable: limits and continuity, elementary functions, basic results on continuous functions.
- Differentiation of functions of one variable: basic definitions and properties, chain rule, first examples of Taylor polynomials and series
- Integration of functions of one variable: basic definitions and properties, the fundamental theorem of calculus, application to arc lengths of plane curves.

3 one-hour lectures and 1 one-hour tutorial per week (to be arranged).

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour written examination paper. The CAS mark awarded will be the maximum of 100% resit and 80% resit with 20% in-course assessment.