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.

The content of MATH162 is exactly identical to that of MATH142, but it is offered in Summer Session (starting in December) with fewer contact hours and a lot of emphasis on personal study.

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, may take MATH162, but they must obtain a mark of 65 or higher. It is recommended that these students wait and take MATH188.

Formal Prerequisites

Students eligible to take MATH162 are those who have completed:

MATH161, or

MATH141, or

MATH187

Assumed knowledge

Students must have a solid knowledge of Fundamentals, Linear Algebra, Differentiation, Elementary Integration and Polar Coordinates from MATH141 (or MATH187 or MATH161).

Content

Students in MATH162 are taught the following.

Complex Numbers

Introduction to complex number; arithmetic of complex numbers; DeMoivre's Theorem.

Limits

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

Numerical Integration

General numerical integration schemes; midpoint, Trapezoidal and Simpson's rules; error estimation.

Methods of Integration

Revision of integration; evaluating integrals using more advanced techniques.

Differential Equations

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

Applications of Integration

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

Sequences & Series

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

Taylor Series

Introduction to Taylor polynomials, Taylor series, Maclaurin polynomials 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 Mathematics;

(ii)

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

(iii)

apply general mathematical principles, think logically and analytically.