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:

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

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