MA13510 - INTRODUCTORY CALCULUS

Module Identifier

MA13510

Module Title

INTRODUCTORY CALCULUS

Academic Year

2004/2005

Co-ordinator

Dr T McDonough

Semester

Intended for use in future years

Next year offered

N/A

Next semester offered

N/A

Pre-Requisite

MA12510

Mutually Exclusive

May not be taken at the same time as, or after, any of MA10010 to MA11410, MA12010, MA12110, MA12210, MA12610, MA13010, MA13110, MA13610.

Course delivery

Lecture

22 x 1 hour lectures

Seminars / Tutorials

11 x 1hour example classes

Assessment

Assessment Type	Assessment Length/Details	Proportion
Semester Exam	2 Hours	100%
Supplementary Assessment	2 Hours	100%

Learning outcomes

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

integrate polynomials and find areas;
integrate selected rational functions;
use integration by parts and by substitution in appropriate cases;
calculate the partial sums of a sequence and find the sums of arithmetic and geometric progressions;
add and multiply matrices, compute the inverse of a 2 ? 2 matrix and use it to solve linear simultaneous equations in two unknowns.

Brief description

The purpose of this module is to introduce the basic concepts of calculus to students without A-level qualifications in Mathematics at a level suitable for application in other areas. The syllabus includes the methods of the calculus applied to simple functions leading to tangents and gradients; trigonometric functions; the logarithmic and exponential functions. Elementary integration (of polynomials) is also introduced.

Aims

To make the most fundamental notions of calculus used in other fields comprehensible to students.

Content

1. INTEGRATION: The problem of areas, the fundamental theorem of calculus. Integration of simple functions, integration by parts and by substitution. Application to finding areas and volumes of solids of revolution.
2. SEQUENCES AND SERIES: Recurrence relations, partial sums, arithmetic and geometric progressions, the binomial theorem.
3. INTRODUCTION TO MATRICES AND DETERMINANTS: Solution of linear equations
4. COORDINATE GEOMETRY IN THE PLANE: The straight line, conics. Plane polar coordinates.

Reading Lists

Books
** Recommended Text
D J Booth (1998) Foundation Mathematics 3rd. Addison-Wesley 0201342944

Notes

This module is at CQFW Level 4