Math& 153 ~ Calculus III  
 
 
 

Course Description
This course covers polar coordinates, parametric equations, and vectors in space, vector-valued functions, and infinite series.

Pre-requisite
Math 152 with a grade of C or higher.

Mode of Delivery (Modes)
Lecture

Offered
Fall, Winter, Spring

Required for:
MATH 254, MATH 238


Course Content

Text: Calculus: Early Transcendentals, 5th Ed., Stewart, Cengage

9. Differential Equations
9.1 Modeling with Differential Equations
9.2 Direction Fields and Euler's Method
9.3 Separable Equations
9.4 Exponential Growth and Decay
9.5 The Logistic Equation
9.6 Linear Equations
9.7 Predator-Prey Systems

10. Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations
10.2 Laboratory Project: Families of Hypocycloids
10.3 Tangents and Areas
10.4 Arc Length and Surface Area
10.5 Polar Coordinates
10.6 Areas and Lengths in Polar Coordinates
10.7 Conic Sections
10.8 Conic Sections in Polar Coordinates

11. Infinite Sequences and Series
11.1 Sequences
11.2 Series
11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series
11.6 Absolute Convergence and the Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
11.9 Representation of Functions as Power Series
11.10 Taylor and Maclaurin Series
11.11 The Binomial Series

12. Vectors and the Geometry of Space
12.1 Three-Dimensional Coordinate Systems
12.2 Vectors
12.3 The Dot Product
12.4 The Cross Product
12.5 Equations of Lines and Planes
12.6 Quadric Surfaces
12.7 Cylindrical and Spherical Coordinates