Calculus II

Course Number: MTH 252
Transcript Title: Calculus II
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

Prerequisites

MTH 251 and its prerequisite requirements.

Course Description

Includes anti-derivatives and integrals, definite and improper integrals, and applications including direct application of integration and solving basic differential equations. Graphing calculator required, TI-89 or other CAS calculator recommended.Prerequisites: MTH 251 and its prerequisite requirements. Audit available.

Intended Outcomes

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

  1. Recognize applications in which the concept of differentiation or integration can aid in overall understanding.
  2. Construct appropriate models using definite, indefinite, or improper integrals, or basic differential equations.
  3. Accurately compute results from models through the appropriate use of technology, algebra or calculus.
  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)

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, 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. 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
  2. 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
  3. 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 Model

Department Notes

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