        This navigation menu requires Javascript to activate.   If you cannot enable Javascript use the breadcrumbs to navigate this website. # 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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