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Calculus I

Course Number: MTH 251
Transcript Title: Calculus I
Created: September 1, 2012
Updated: December 19, 2014
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

Prerequisites

MTH 112

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.

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. 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.