# Difference between revisions of "Math 116: Essentials of Calculus"

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# Review of Algebra (4 lectures) | # Review of Algebra (4 lectures) | ||

− | # * Determine the graph of a line given two points, a point and a slope, the general form of a line, the slope-intercept form of a line | + | #* Determine the graph of a line given two points, a point and a slope, the general form of a line, the slope-intercept form of a line |

− | # * Determine the slope of a line given two coordinate points, the equation of a line given the slope and a point, equation of a line given two points, and the x- & y-intercept of a line | + | #* Determine the slope of a line given two coordinate points, the equation of a line given the slope and a point, equation of a line given two points, and the x- & y-intercept of a line |

− | # * Find the secant line of a function on an interval, and use that to understand the average rate of change of a function | + | #* Find the secant line of a function on an interval, and use that to understand the average rate of change of a function |

− | # * Approximate the tangent line at a point, and use that to understand the instantaneous rate of change of a function | + | #* Approximate the tangent line at a point, and use that to understand the instantaneous rate of change of a function |

# Limits and Derivatives (4 lectures) | # Limits and Derivatives (4 lectures) | ||

− | # * Determine the limit of standard functions, e.g., polynomials, rational functions, exponentials, logarithms | + | #* Determine the limit of standard functions, e.g., polynomials, rational functions, exponentials, logarithms |

− | # * Determine the limits of more complicated functions composed of simpler functions. | + | #* Determine the limits of more complicated functions composed of simpler functions. |

− | # * Define the derivative, take derivatives of polynomials using definition | + | #* Define the derivative, take derivatives of polynomials using definition |

− | # * Derive the differentiation rules for polynomials, exponentials, logarithms | + | #* Derive the differentiation rules for polynomials, exponentials, logarithms |

# Product, Quotient, and Chain Rules (2 lectures) | # Product, Quotient, and Chain Rules (2 lectures) | ||

− | # * Derive the product, quotient, and chain rules | + | #* Derive the product, quotient, and chain rules |

− | # * Use the product, quotient, and chain rules to compute complicated derivatives composed of simpler functions | + | #* Use the product, quotient, and chain rules to compute complicated derivatives composed of simpler functions |

# Optimization and Applications (4 lectures) | # Optimization and Applications (4 lectures) | ||

− | # * State the derivative rules for local extreme | + | #* State the derivative rules for local extreme |

− | # * Use the derivative rules to find the local extrema of a function on an interval. Then find the global maximum (or minimum) of a function on an interval | + | #* Use the derivative rules to find the local extrema of a function on an interval. Then find the global maximum (or minimum) of a function on an interval |

− | # * Use the derivative to solve problems in business, e.g., maximize profits, minimize costs, etc. | + | #* Use the derivative to solve problems in business, e.g., maximize profits, minimize costs, etc. |

− | # * Use Newton's method for root finding to locate local extrema. | + | #* Use Newton's method for root finding to locate local extrema. |

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## Revision as of 17:52, 28 January 2011

## Contents

## Catalog Information

### Title

Essentials of Calculus

### (Credit Hours:Lecture Hours:Lab Hours)

(1:1:0)

### Offered

Fall, Winter

### Prerequisite

Math 110

### Description

This course gives a brief overview of differential calculus. Topics covered include limits, derivatives, and applications of differentiation to optimization of functions.

## Desired Learning Outcomes

- Review of Algebra (4 lectures)
- Determine the graph of a line given two points, a point and a slope, the general form of a line, the slope-intercept form of a line
- Determine the slope of a line given two coordinate points, the equation of a line given the slope and a point, equation of a line given two points, and the x- & y-intercept of a line
- Find the secant line of a function on an interval, and use that to understand the average rate of change of a function
- Approximate the tangent line at a point, and use that to understand the instantaneous rate of change of a function

- Limits and Derivatives (4 lectures)
- Determine the limit of standard functions, e.g., polynomials, rational functions, exponentials, logarithms
- Determine the limits of more complicated functions composed of simpler functions.
- Define the derivative, take derivatives of polynomials using definition
- Derive the differentiation rules for polynomials, exponentials, logarithms

- Product, Quotient, and Chain Rules (2 lectures)
- Derive the product, quotient, and chain rules
- Use the product, quotient, and chain rules to compute complicated derivatives composed of simpler functions

- Optimization and Applications (4 lectures)
- State the derivative rules for local extreme
- Use the derivative rules to find the local extrema of a function on an interval. Then find the global maximum (or minimum) of a function on an interval
- Use the derivative to solve problems in business, e.g., maximize profits, minimize costs, etc.
- Use Newton's method for root finding to locate local extrema.

### Prerequisites

Math 110

### Minimal learning outcomes

### Textbooks

Possible textbooks for this course include (but are not limited to):