Catalog Course Search Details

 Department:    MATH&

 Course #:    151

 Credits:    5

 Variable:     No

 IUs:    5

 CIP:    270101

 EPC:    n/a

 REV:    2024

 Course Description  

This is the first in a sequence of four calculus courses for students who are planning to major in engineering, mathematics, or the sciences, and introduces the concepts of limits and differentiation. Topics include limits of algebraic, trigonometric, and exponential functions, the derivative of a function and derivative techniques, curve sketching, and an introduction to antiderivatives. Graphing technology required.

 Prerequisite  

Prerequisite: Math& 142 with a grade of C or higher, appropriate placement score, or instructor permission.

Contact Hours (based on 11 week quarter)

Lecture: 55

Lab: 0

Other: 0

Systems: 0

Clinical: 0

Intent: Distribution Requirement(s) Status:  

Academic Natural Sciences, Quantitative  

Equivalencies At Other Institutions

Learning Outcomes

After completing this course, the student will be able to:

1. Calculate limits of functions using graphs, numerical data and analytically with limit rules.
2. Evaluate limits using L�Hospital�s Rule.
3. Determine the continuity of a function using limits.
4. Define the derivative as a rate of change and use it in graphical and applied contexts.
5. Calculate the derivative of polynomial, rational, trigonometric, and other common transcendental functions using the rules of differentiation (power, chain, product, quotient, etc.)
6. Linearize a function using the derivative.
7. Construct graphs of functions using calculus, by finding local extremes, inflection points, and asymptotes.
8. Set up and solve applications, including optimization and related rates.
9. Compute numerical approximations using appropriate methods.
10. Compute elementary antiderivatives.

General Education Learning Values & Outcomes

Revised August 2008 and affects outlines for 2008 year 1 and later.

Course Contents

1. Limits
   • Evaluate limits
   • Determine continuity
   • L'Hospital's Rule
   • Indeterminant forms
   • The precise definition of a limit (optional)
2. Derivatives
   • Derivatives as a rate of change
   • Limit definition of a derivative
   • Derivatives of polynomials, rational functions, exponential, and logarithm functions.
   • Product Rule, quotient rule, chain rule
   • Higher order derivatives
   • Implicit differentiation
   • Derivatives of hyperbolic functions (optional)
3. Applications
   • Growth and decay
   • Related rates
   • Optimization
   • The Mean Value Theorem
   • The Intermediate Value Theorem (optional)
   • Newton�s Method (optional)
4. Graphical Analysis
   • Intercepts
   • Asymptotes
   • Symmetry
   • Intervals of increasing and decreasing
   • Maximum and minumum values
   • Concavity and inflection points
5. Other Topics
   • Compute basic anti-derivatives