Calculus II

Course Number:

MTH 252

Transcript Title:

Calculus II

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 applications in which the concept of differentiation or integration can aid in overall understanding.

• Integration as Generalized Multiplication
  • Part One -  the question of area, the definite integral
  • Part Two - Area, Volumes, Arc-length, Surface Area, Work, Force Behind a Dam, Centroids and Center of Mass.
• Fundamental Theorem of Calculus and Integration as the inverse of Differentiation
  • Part One - The Fundamental Theorem of Calculus
  • Part Three - Differential Equations and Assumptions about Growth
    • Continuous Growth Model
    • Logistics Model
    • Predator-Prey Models

Outcome #2: Construct appropriate models using definite, indefinite, or improper integrals, or basic differential equations.

• Part Two - Applications using Integration Directly
  • Area under and between functions
  • Volumes:
    • Rotation about the x-axis
    • Rotation about the y-axis
    • Slicing
  • Arc-length and Surface Area
  • Mean Value Theorem for Integrals
  • Work
  • Force of Water Behind a Dam
  • Centroids and Center of Mass
  • Statistics
  • Applications of Integration in Business
  • Other Applications of Integration
• Part Three - Applications of Integration in solving Basic Differential Equations
  • What are differential equations?
  • Differential Equations and Assumptions about Growth
  • Slope Fields
  • Solutions
  • Separable Differential Equations
  • Continuous Growth Model
  • Logistics Model
  • Phase Diagrams
  • Predator-Prey Models

Outcome #3: Accurately compute results from models through the appropriate use of technology, algebra or calculus.

• Part One - Integration
  • Considering the question of area – using limits
  • The definite integral
  • Fundamental Theorem of Calculus
  • Anti-derivatives and indefinite integrals
  • Techniques of integration:
  • substitution
  • integration by parts
  • trigonometric integrals/trig substitution/partial fractions
  • Numerical Integration and approximation
  • Improper Integrals

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

This is also covered throughout the term, and is really a continuation of a process starting in the first math classes we teach. Projects that we assign aid in student achievement of this outcome. Specific topics used for this purpose include:

• Part One - The question of area
  • The definite integral
• Part Two - Area, Volumes, Arc-length, Surface Area, Work, Force Behind a Dam, Centroids and Center of Mass.
• Part Three - Differential Equations and Assumptions about Growth
  • Continuous Growth Model
  • Logistics Model
  • Predator-Prey Models

Suggested Texts and Materials

• Calculus: Concepts and Contexts, 4th ed.  James Stewart (Required)
• Students Solutions Manual is (Optional)
• Graphing utility such as Desmos (Required)

Department Notes

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