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# MATH 163 – Calculus III

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

·         5.1 Sequences

·         5.2 Infinite Series

·         5.3 The Divergence and Integral Tests

·         5.4 Comparison Tests

·         5.5 Alternating Series

·         5.6 Ratio and Root 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

·         7.5 Conic Sections

·         7.1 Parametric Equations

·         7.2 Calculus of Parametric Curves

·         7.3 Polar Coordinates

·         7.4 Area and Arc Length in Polar Coordinates

Unit 3: Vectors

·         2.1 Vectors in the Plane

·         2.2 Vectors in Three Dimensions

·         2.3 The Dot Product

·         2.4 The Cross Product

·         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

·         3.4 Motion in Space