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Course Description: An introduction to differential calculus with an emphasis on applications in the sciences. Derivatives of exponential, logarithmic, trigonometric and algebraic functions will be studied as well as rules for finding these derivatives. Continuity and the meaning of second and third derivatives will be discussed.

- This course also meets PLO #(s)
__3.1, 3.2 and 3.3__of__General Education Program.__ - Prerequisite Courses:
__MS 101__

**A**. __PROGRAM LEARNING OUTCOMES__ (PLOs):

** **The student will be able to:

- Demonstrate understanding and apply mathematical concepts in problem solving and in day to day activities.
- Present and interpret numeric information in graphic forms.
- Communicate thoughts and ideas effectively using proper mathematical terms.

**B**. __STUDENT LEARNING OUTCOMES__ (SLOs): GENERAL

The student will be able to:** **

1. Manipulate algebraic and transcendental functions.

2. Define the derivative.

3. Apply differentiation rules to functions.

4. Use the first and second derivative to analyze functional behavior.

SLO |
PLO 1 |
PLO 2 |
PLO 3 |

1 |
IDM |
ID |
DM |

2 |
IDM |
ID |
ID |

3 |
ID |
ID |
I |

4 |
I |
I |
I |

I = Introduced

D = Demonstrated

M = Mastered

**C**. __STUDENT LEARNING OUTCOMES__ (SLOs): SPECIFIC

The student should be able to:

General SLO 1. Manipulate algebraic and transcendental functions.

Student Learning Outcomes |
Assessment Strategies |

1.1 Solve and evaluate exponential equations and functions. |
Homework and/or quizzes and/or exams |

1.2 Solve and evaluate logarithmic equations and functions. |
Homework and/or quizzes and/or exams |

1.3 Solve and evaluate trigonometric equations and functions. |
Homework and/or quizzes and/or exams |

1.4 Solve and evaluate polynomial and rational equations and functions. |
Homework and/or quizzes and/or exams |

General SLO 2. Define the derivative.

Student Learning Outcomes |
Assessment Strategies |

2.1 Use difference quotient to measure speed. |
Homework and/or quizzes and/or exams |

2.2 Find limits of functions. |
Homework and/or quizzes and/or exams |

2.3 Find the derivative at a point. |
Homework and/or quizzes and/or exams |

2.4 Find the derivative function. |
Homework and/or quizzes and/or exams |

2.5 Find and interpret the second derivative. |
Homework and/or quizzes and/or exams |

General SLO 3. Apply differentiation rules to functions.

Student Learning Outcomes |
Assessment Strategies |

3.1 Apply the power rule. |
Homework and/or quizzes and/or exams |

3.2 Apply the product and quotient rule. |
Homework and/or quizzes and/or exams |

3.3 Apply the chain rule. |
Homework and/or quizzes and/or exams |

3.4 Apply trigonometric rules. |
Homework and/or quizzes and/or exams |

3.5 Apply the exponential and logarithmic rules. |
Homework and/or quizzes and/or exams |

General SLO 4. Use the first and second derivative to analyze functional behavior.

Student Learning Outcomes |
Assessment Strategies |

4.1 Find concavity. |
Homework and/or quizzes and/or exams |

4.2 Find intervals of increasing/decreasing behavior. |
Homework and/or quizzes and/or exams |

4.3 Find linear approximations. |
Homework and/or quizzes and/or exams |

4.4 Optimization. |
Homework and/or quizzes and/or exams |

**D.** __COURSE CONTENT__

- Work with exponential functions.
- Work with logarithmic functions.
- Work with trigonometric functions.
- Work with polynomial functions.
- Continuity.
- Measuring speed.
- Limits
- Derivatives
- Second derivatives.
- Differentiability.
- Derivative rules.
- Linear Approximations.

**E**. __METHODS OF INSTRUCTION__

The course will involve the use of lectures, class discussions, and activities. Small groups of cooperative teaching/learning can be utilized**. **Utilizing graphing tools (graphing calculator or graphing software) will assist students in visualizing equations and graphs. Quizzes and examinations will provide measurement of achievement of course objectives.

**F**. __REQUIRED TEXT(S) AND COURSE MATERIALS__

Hughes-Hallet, D., Gleason, A., McCallum, W. (2002) Calculus. 3rd ed.

New York, N.Y. : John Wiley & Sons, Inc. (or most recent edition).

Scientific calculator

**G.** __REFERENCE MATERIALS__

None

**H.** __INSTRUCTIONAL COSTS__

None

**I**. __EVALUATION__

None

**J**. __CREDIT BY EXAMINATION__

None

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