Calculus III

Course Number: MTH 253
Transcript Title: Calculus III
Created: September 1, 2012
Updated: August 15, 2019
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

Major 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. Use an understanding of cultural differences to constructively address issues that arise in the workplace and community. (Cultural Awareness)


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

To establish an intentional learning environment, Core Learning Outcomes (CLOs) require a clear definition of instructional strategies, evidence of recurrent instruction, and employment of several assessment modes.

Major Designation

  1. The outcome is addressed recurrently in the curriculum, regularly enough to establish a thorough understanding.
  2. Students can demonstrate and are assessed on a thorough understanding of the outcome.
    • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

Minor Designation

  1. The outcome is addressed adequately in the curriculum, establishing fundamental understanding.
  2. Students can demonstrate and are assessed on a fundamental understanding of the outcome.
    • The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

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

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

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
    • ¬†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.