# MATH& 153 Calculus III • 5 Cr.

## Department

## Division

## Description:

Emphasizes the study of infinite sequences and series including power series. Topics include plane analytic geometry, graphing in polar coordinates, and an introduction to vectors. Fulfills the quantitative or symbolic reasoning course requirement at BC. Recommended: MATH& 152.

## Outcomes:

After completing this class, students should be able to:

- To understand the polar coordinate system and plot points and graphs of functions in that system
- To apply the ideas of the derivative and integral in the polar coordinate system
- To calculate rates of change, slopes of tangent lines and areas in polar coordinates
- To understand parametric equations and plot points and graphs of functions in that system
- To apply the ideas of the derivative and integral in parametric equations
- To calculate rates of change, slopes of tangent lines and areas for functions given as parametric equations
- To determine the equations of lines and other simple forms in parametric equations
- To use parametric equations to model rotational and other motion
- To describe the conic sections as loci of points and to give the equations of the conic sections as functions in rectangular coordinates and polar coordinates and as parametric equations
- To describe the meaning of a sequence of numbers
- To graph sequences and determine the convergence or divergence of common sequences
- To describe the meaning of an infinite series of numbers, the meaning the partial sums of a series, and the meaning of convergence for an infinite series
- To recognize a geometric series and determine the value of an infinite geometric series
- To determine whether some classes of series converge or diverge by selecting and applying the appropriate convergence tests:
- Nth term test, ratio test, integral test, P test, alternating series test

- To describe the meaning of power series and to use the appropriate tests to determine their intervals of convergence
- To create Maclaurin and Taylor series for transcendental functions such as sin(x), cos(x), exp(x), ln(x)
- To use Maclaurin and Taylor series to approximate the values of transcendental functions and certain integrals