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MATH188 - Mathematics 2: Series and Integral Calculus

Intention

This subject provides the second stage of Mathematics for all Mathematics--and other interested--students who have completed MATH187.

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

Clientele

MATH188 caters for students who
have completed MATH187 and
wish to continue with any 200 level Mathematics subject other than MATH283.

Formal Prerequisites

Students eligible to take MATH188 are those who have completed MATH187.

Assumed knowledge

Students must have a solid knowledge of Fundamentals, Linear Algebra, Differentiation and Polar Coordinates from MATH187.

Content

Students in MATH188 are taught the following.
Integration Introduction to integration, including definite and indefinite integrals; evaluating integrals using a number of elementary and more advanced techniques.
Applications of Integration Finding areas under the curve; finding volumes of solids of revolution; finding arc lengths of functions.
Numerical Integration General numerical integration schemes; midpoint, Trapezoidal and Simpson's rules.
Differential Equations Introduction to differential equations; techniques for solving first and second order differential equations.
Sequences & Series Introduction to sequences and their convergence; introduction to series and various tests for proving their convergence or divergence; power series.
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 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 principles and think logically and analytically through problems.

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