# MATH& 163 : Calculus III: Analytic Geometry

Sequences, series, Taylor expansions. Vectors, vector functions, space curves. Functions of several variables, partial derivatives, tangent planes. This class will include students from multiple sections. (QS, NS)

## Prerequisites

2.0 or higher in MATH& 152 or equivalent.

## Course Outcomes

A student who successfully completes this class with a grade of 2.0 or better should be able to:

- Apply calculus techniques to parametric equations.
- Find areas and arc lengths in polar coordinates.
- Perform vector arithmetic, including calculating the dot and cross products.
- Find equations of lines and planes in three-space.
- Find derivatives, integrals, velocity, acceleration, arc length, and curvature of vector functions.
- Calculate partial derivatives of functions of several variables.
- Find tangent planes and linear approximations of functions of several variables.
- Find extrema and saddle points of functions of several variables.
- Calculate double integrals over rectangular and general regions, both in rectangular and polar coordinates.
- Calculate centers of mass of laminas.
- State the difference between a sequence and a series.
- Use various tests to determine if a series converges.
- Determine if a power series converges.
- Be able to represent a function as a power series.
- Find Maclaurin and Taylor series of functions.