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.