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MATH162 - Mathematics 1E, Part 2

Intention

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.

Clientele

MATH162 caters for students who
have completed MATH187, MATH141 or MATH161, and
have not yet completed MATH142 nor MATH188, and
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.

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