Calculus III

Course Number:

MTH 253

Transcript Title:

Calculus III

Created:

Aug 15, 2022

Updated:

Jul 12, 2023

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, P/NP, Audit

Default Grading Options

A-F

Repeats available for credit:

0

Alignment with Institutional Learning Outcomes

Major

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

Major

2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving)

Major

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)

Minor

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

To establish an intentional learning environment, Institutional Learning Outcomes (ILOs) 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.

Suggested 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

Outcome #1: Recognize the fundamental role that power series plays in machine calculation and modern computing in general.

• Part One - 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

Outcome #2: Recognize applications in which the concepts of power series, vectors, or vector valued functions can aid in overall understanding.

• Part One: Taylor Series and Applications
• Part Two - 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
• Part Three - Vector Valued Functions
  • Vector Functions and Space Curves
  • Derivatives and Integrals of Vector Functions
  • Arc Length and Curvature
  • Motion in Space: Velocity and Acceleration
  • Parametric Surfaces

Outcome #3: Accurately compute results from models based on infinite series or vector valued functions.

The following topics from above lend themselves to this outcome. In addressing this outcome, we focus on the answer itself, how to get it, and how to check it.

• Part One: Geometric Series, Applications (of Taylor Series)
• Part Two: Dot and Cross Products, Equations of Lines and Planes in Space
• Part Three: Derivatives and Integrals of Vector Values Functions, Arc Length and Curvature, Motion in Space: Velocity and Acceleration.

Outcome #4: Analyze and effectively communicate results within a mathematical context.

This is covered throughout the term and is really an extension of work begun in previous math courses. The following topics from above lend themselves to this outcome. In addressing this outcome, we focus on how to state conclusions and general written communications.

• Part One: Geometric Series, Applications (of Taylor Series)
• Part Two: Dot and Cross Products, Equations of Lines and Planes in Space
• Part Three: Derivatives and Integrals of Vector Values Functions, Arc Length and Curvature, Motion in Space: Velocity and Acceleration.

Suggested Texts and Materials

• Calculus: Concepts and Contexts, 4th ed.  James Stewart (Required)
• Students Solutions Manual is (Optional)
• Graphing utility such as Desmos (Required)
• App or program for 3D graphing including functions and parametric surfaces. Recommended. Our school has a license to use DPGraph, so students and faculty can use it for free.

Department Notes

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