Calculus II

Course Number: MTH 252
Transcript Title: Calculus II
Created: September 1, 2012
Updated: June 9, 2016
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

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

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

In-depth

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

In-depth

3. Apply the knowledge, skills and abilities to enter and succeed in a defined profession or advanced academic program. (Professional Competence)

Not Addressed

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

Minimally

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. 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.