Calculus I

Course Number: MTH 251
Transcript Title: Calculus I
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

Course Description

Includes limits, continuity, derivatives and applications. Graphing calculator required, TI-89 or other CAS calculator recommended. Prerequisites: MTH 112. Audit available.

Intended Outcomes

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

  1. Recognize applications in which the concept of limits and derivatives can aid in overall understanding.
  2. Construct appropriate models using limits and derivatives.
  3. Accurately compute results from models through the appropriate use of technology, limits, derivatives and algebra.
  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. Limits
    1. Introduction – instantaneous rate of change and the need for limits
    2. One and two-sided limits; Squeeze Theorem
    3. Continuity and The Intermediate Value Theorem
    4. Limit Theorems and Evaluating Limits
    5. Limits at infinity and infinity as a limit
    6. Limit definition of derivative
    7. Derivatives as functions; Higher order derivatives
    8. Derivatives and the shape of graphs
  2. Derivatives
    1. Derivatives of polynomials and the binomial expansion theorem
    2. Derivative of the exponential function
    3. Derivative Theorems; Product Rule – Quotient Rule
    4. Derivatives of Trig functions
    5. Chain Rule
    6. Implicit Differentiation
    7. Derivatives of inverse functions; Derivative of Cosh and Sinh
    8. Tangent line approximations and differentials
  3. Applications
    1. Related Rates
    2. Extreme Value Theorem and closed interval problems.
    3. First and Second Derivative Tests
    4. Calculus and Graphing
    5. Mean Value Theorem for Derivatives
    6. L'Hospital's Rule
    7. Newton's Method
    8. Optimization

Department Notes

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