This subject provides the second stage of Mathematics for Engineering (and other interested) students who have completed either MATH141, MATH187 or MATH161.

The aim of this subject is to develop ideas, concepts and skills in Mathematics, especially applied skills, for application in later subjects.

must take MATH283 or any other subject with a prerequisite of MATH142 (or MATH162).

Further Note.

Students who wish to continue with 200 level Mathematics other than MATH283, must take MATH187 and MATH188.

Formal Prerequisites

Students eligible to take MATH142 are those who have completed:

MATH161, or

MATH141, or

MATH187

Assumed knowledge

Students must have a solid knowledge of Fundamentals, Linear Algebra, Functions and Elementary Calculus from MATH141 (or MATH187 or MATH161).

Content

Students in MATH142 are taught the following.

Integration

Revision of the concept of integration; evaluating integrals using analytic techniques; general numerical integration schemes.

Applications of Integration

Finding areas under the curve; finding volumes of solids of revolution; finding arc lengths of functions.

Differential Equations

Introduction to differential equations; techniques for solving first and second order differential equations.

Limits

Revision of limits; L'Hopital's rule; finding limits of various indeterminate forms.

Sequences & Series

Introduction to sequences and their convergence; introduction to series and various tests for proving their convergence or divergence; introduction to Taylor series and Maclaurin series.

After successful completion of this subject the student should be able to:

(i)

demonstrate a basic knowledge of the principles and techniques in Integral Calculus;

(ii)

apply principles and techniques of Integration to find areas, volumes of revolution and to solve Differential Equations;

(iii)

demonstrate a basic knowledge of the principles and techniques in dealing with Series;

(iv)

apply principles and techniques from general Series to the context of Taylor Series;

(v)

demonstrate problem solving skills and the ability to analyse the final results;

(vi)

apply general mathematical principleswithin an engineering context and think logically and analytically through problems.