# Module Information

Module Identifier
MA13510
Module Title
Introductory Calculus
2013/2014
Co-ordinator
Semester
Intended for use in future years
Mutually Exclusive
May not be taken at the same time as, or after, MA10020.
Pre-Requisite

#### Course Delivery

Delivery Type Delivery length / details
Lecture 22 Hours. (22 x 1 hour lectures)
Seminars / Tutorials 11 Hours. (11 x 1 hour example classes)

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   (written examination)  100%
Supplementary Assessment 2 Hours   (written examination)  100%

### Learning Outcomes

On completion of this module, a student should be able to:
1. integrate polynomials and find areas;
2. integrate selected rational functions;
3. use integration by parts and by substitution in appropriate cases;
4. calculate the partial sums of a sequence and find the sums of arithmetic and geometric progressions;
5. 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.

### Notes

This module is at CQFW Level 4