# MATH 181 Calculus I

Students will develop skills in the initial content of both differential and integral calculus including finding limits of functions; exposure to the epsilon-delta process and continuity; finding derivatives of polynomial, rational, radical, trigonometric, inverse trigonometric, exponential, and logarithmic functions, and inverse functions; the chain rule; and integration by substitution. Applications dealing with optimization, related rates, Newton's method, L'Hopital's rule, motion problems and the properties of the graphs of functions are covered. Theorems include the mean-value theorem for derivatives and integrals, the squeeze theorem, and the fundamental theorems of calculus. Implicit differentiation, differentials and summations of area will be used when appropriate. The use of a graphing calculator will be an integral part of the course. Credit will only be granted for one of the following: MATH 140, MATH 145, or MATH 181.

### Credits

### Prerequisite

MATH 153 or MATH 155 with a grade of C or higher, or appropriate score on the mathematics placement test### Hours Weekly

4 hours weekly### Course Objectives

- Calculate limits of elementary functions numerically, graphically, and analytically.
- Calculate derivatives of functions given either implicitly or explicitly.
- Apply the method of substitution to calculate integrals of functions where applicable.
- Apply the theory of derivatives to the graphing of curves and to solve related rate and

optimization problems, and estimation of zeroes of a function with Newton’s method. - Use differential calculus to model and solve various application problems, interpret results,

and evaluate the reasonableness of the results in context. - Apply the Mean Value Theorem for derivatives and integrals to given functions.
- Use a computer algebra system, as a means of discovery, to reinforce concepts, and as an

efficient problem-solving tool. - Communicate calculus concepts in a neat and organized manner using appropriate

symbols, notation, and vocabulary. - Identify and implement appropriate technologies to efficiently complete tasks that involve the

solving of cross-discipline, mathematically appropriate problems and creating new works to

communicate the processes used and solution.

### Course Objectives

- Calculate limits of elementary functions numerically, graphically, and analytically.
This objective is a course Goal Only

- Calculate derivatives of functions given either implicitly or explicitly.
This objective is a course Goal Only

- Apply the method of substitution to calculate integrals of functions where applicable.
This objective is a course Goal Only

- Apply the theory of derivatives to the graphing of curves and to solve related rate and

optimization problems, and estimation of zeroes of a function with Newton’s method.#### Learning Activity Artifact

- Other (please fill out box below)
- Exam 2 (graphing and Newton's Method), Final exams (Related Rates and Optimization)

#### Procedure for Assessing Student Learning

- Scientific Reasoning Rubric

#### Scientific Reasoning

- SR2

- Use differential calculus to model and solve various application problems, interpret results,

and evaluate the reasonableness of the results in context.#### Learning Activity Artifact

- Other (please fill out box below)
- Final exam (related rates and optimization)

#### Procedure for Assessing Student Learning

- Scientific Reasoning Rubric

#### Scientific Reasoning

- SR3

- Apply the Mean Value Theorem for derivatives and integrals to given functions.
This objective is a course Goal Only

- Use a computer algebra system, as a means of discovery, to reinforce concepts, and as an

efficient problem-solving tool.This objective is a course Goal Only

- Communicate calculus concepts in a neat and organized manner using appropriate

symbols, notation, and vocabulary.#### Learning Activity Artifact

- Other (please fill out box below)
- Final exam, project

#### Procedure for Assessing Student Learning

- Scientific Reasoning Rubric

#### Scientific Reasoning

- SR1

- Identify and implement appropriate technologies to efficiently complete tasks that involve the

solving of cross-discipline, mathematically appropriate problems and creating new works to

communicate the processes used and solution.#### Learning Activity Artifact

- Other (please fill out box below)
- Projects

#### Procedure for Assessing Student Learning

- Technological Literacy Rubric

#### Technological Literacy

- TL1
- TL2