**Course Description: **This
course will expand on the applications and techniques of differentiation learned
in the first and second quarters. It will introduce the student to the calculus
of sequences and series and the use of the MacLaurin
and Taylor series to approximate functions. It will introduce the student to
the calculus of curvilinear functions and the concept of the vector and vector
functions. It will also introduce the
concept of a partial derivative and the maximization of functions given in more
than one independent variable.

**Textbook: **Herman,
E. J. & Strang, G. (2018). *BBCC
Calculus III*, published by OpenStax, remixed by Lulu.

**Unit 1: Sequences and
Series**

· 5.3 The Divergence and Integral Tests

· 6.1 Power Series and Functions

· 6.2 Properties of Power Series

· 6.3 Taylor and Maclaurin Series

**Unit 2: Parametric
and Polar Coordinates**

· 7.2 Calculus of Parametric Curves

· 7.4 Area and Arc Length in Polar Coordinates

**Unit 3: Vectors**

· 2.2 Vectors in Three Dimensions

· 2.5 Equations of Lines and Planes in Space

· 2.7 Cylindrical and Spherical Coordinates

**Unit 4: Vector-Valued
Functions**

· 3.1 Vector-Valued Functions and Space Curves

· 3.2 Calculus of Vector-Valued Functions

· 3.3 Arc Length and Curvature