Calculus III

Course Number: MTH 253
Transcript Title: Calculus III
Created: September 1, 2012
Updated: October 25, 2017
Total Credits: 5
Lecture Hours: 50
Lecture / Lab Hours: 0
Lab Hours: 0
Satisfies Cultural Literacy requirement: No
Satisfies General Education requirement: Yes
Grading options: A-F (default), P-NP, audit
Repeats available for credit: 0


MTH 252 and its prerequisite requirements.

Course Description

Includes infinite sequences and series, Taylor series and applications, equations of lines and planes in three dimensions, vectors in 3D, and differentiation and integration of vector valued functions with applications. Graphing calculator required; TI-89 or access to CAS recommended. Prerequisites: MTH 252 and its prerequisite requirements. Audit available.

Intended Outcomes

Upon successful completion of this course, students will be able to:

  1. Recognize the fundamental role that power series plays in machine calculation and modern computing in general.
  2. Recognize applications in which the concepts of power series, vectors, or vector valued functions can aid in overall understanding.
  3. Accurately compute results from models based on infinite series or vector valued functions.
  4. Analyze and effectively communicate results within a mathematical context.

Alignment with Institutional Core Learning Outcomes

In-depth 1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication)


2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)
3. Extract, interpret, evaluate, communicate, and apply quantitative information and methods to solve problems, evaluate claims, and support decisions in their academic, professional and private lives. (Quantitative Literacy)

Not Addressed

4. Appreciate cultural diversity and constructively address issues that arise out of cultural differences in the workplace and community. (Cultural Awareness)


5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

Outcome Assessment Strategies

At least one project plus some combination of the following:

  • Class participation
  • Group projects
  • Presentations
  • Portfolios
  • Research papers
  • Homework assignments
  • Written paper
  • Quizzes
  • Exams
  • Other assessments of the instructors choosing

Course Activities and Design

This course will be delivered through a combination of lecture and student activities including group and individual problem solving during class. Emphasis is to be given to applications from outside the mathematics classroom. Applications will come from the broadest possible range of disciplines.

Course Content (Themes, Concepts, Issues and Skills)

  1. Infinite Sequences and Series
    • Sequences
    • Series
    • Integral and Comparison Tests
    • Other Tests
    • Power Series
    • Representation of Functions as a Power Series
    • Taylor and Maclaurin Series
    • Ā Applications
  2. Vectors and Geometry of Space
    • Three-Dimensional Coordinate Systems
    • Vectors
    • The Dot and Cross Products
    • Equations of Lines and Planes in Space
    • Functions and Surfaces
    • Cylindrical and Spherical Coordinates
  3. Vector Values Functions
    • Vector Functions and Space Curves
    • Derivatives and Integrals of Vector Functions
    • Arc Length and Curvature
    • Motion in Space: Velocity and Acceleration
    • Parametric Surfaces

Department Notes

Answers to all application problems will be given in complete sentences with correct units. The grade will include at least one project.