MATH 143 Calculus III
1. Catalog Description
MATH 143 Calculus III (4)
(Also listed as HNRS 143)
GE B1
Infinite sequences and series, vector algebra, curves. 4 lectures. Prerequisite: MATH 142 with a grade of C- or
better or consent of instructor.
2.
Required Background or Experience
Math 142.
3. Learning Objectives
The student should:
a. Understand parametric equations and polar coordinates, and their applications.
b. Understand vector algebra and elementary differential vector calculus.
c. Be able to test infinite series for convergence.
d. Be able to calculate power series and Taylor series.
4. Text and References
Weir, Maurice, et al., Thomas’ Calculus, 12th edition, Addison-Wesley, 2010.
5. Minimum Student Materials
Paper, pencils and notebook.
6. Minimum University Facilities
Classroom with ample chalkboard space for class use.
7. Content and Method
The sections listed below are considered to be the core of the course. It is estimated that about 30 lectures will be needed
to cover them. Quarters vary from 38 to 41 lectures. Possible uses for any remaining lectures include:
1. Covering more sections
2. Covering some sections in more depth
3. Computer labs
4. Group projects/class presentations
It is also possible to free up more class time by assigning some sections as reading assignments.
Comments accompanying some of the sections are intended to give some guidance to new
instructors as well as to suggest possible ways in which class time might be saved without losing
important content.
Modified 3/21/2014
Math 143, page 2.
Chapter
No. of Lectures
CHAPTER 10- Infinite Sequences and Series
13
The goal of the chapter is to develop Taylor Series.
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
Sequences
Infinite Series
The Integral Test (error estimates may be skipped)
Comparison Tests (may only cover the limit comparison tests)
The Ratio and Root Tests
Alternating Series, Absolute and Conditional Convergence
Power Series
Taylor and Maclaurin Series
Convergence of Taylor Series
The Binomial Series and Applications of Taylor Series (may only cover the binomial series)
Note: it is recommended that some time be spent teaching strategies for testing series. Students
should be able to decide which test is the most appropriate to apply to any given series.
CHAPTER 11 - Parametric Equations and Polar Coordinates
11.1
11.2
11.3
11.4
11.5
6
Parametrizations of Plane Curves
Calculus with Parametric Curves
Polar Coordinates
Graphing in Polar Coordinates
Areas and Lengths in Polar Coordinates
CHAPTER 12 - Vectors and the Geometry of Space
12.1
12.2
12.3
12.4
12.5
6
Three-Dimensional Coordinate Systems
Vectors
The Dot Product
The Cross Product
Lines and Planes in Space
CHAPTER 13 – Vector-Valued Functions and Motion in Space
13.1
13.2
13.3
13.4
13.5
13.6
5
Curves in Space and Their Tangents
Integrals of Vector Functions; Projectile Motion
Arc Length in Space
Curvature and Normal Vectors of a Curve
Tangential and Normal Components of Acceleration
Velocity and Acceleration in Polar Coordinates (may be covered lightly)
Total
30
Math 143, page 2.
Method
Largely lecture with chalkboard illustration of the discussion along with supervised work and individual
conferences.
8.
Methods of Assessment
The primary methods of assessment are examinations, quizzes and homework. A comprehensive final examination is
required. Students are expected to show their work, and are graded on the correctness of their answers as well as
their understanding of the concepts and techniques.