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 computer algebra system 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.
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
- Analyze limits of elementary functions numerically, graphically, and analytically.
- Calculate derivatives of functions given either implicitly or explicitly.
- Calculate integrals of functions, using the method of substitution where applicable.
- Apply the theory of derivatives to the representation 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.
- Interpret and communicate calculus concepts in a neat and organized manner using appropriate symbols, notation, and vocabulary.
Course Objectives
- Analyze limits of elementary functions numerically, graphically, and analytically.
Learning Activity Artifact
- Other (please fill out box below)
- Quizzes
Procedure for Assessing Student Learning
- Quantitative Reasoning Rubric
- Calculate derivatives of functions given either implicitly or explicitly.
Learning Activity Artifact
- Other (please fill out box below)
- Quizzes
Procedure for Assessing Student Learning
- Quantitative Reasoning Rubric
- Calculate integrals of functions, using the method of substitution where applicable.
Learning Activity Artifact
- Other (please fill out box below)
- Quizzes
Procedure for Assessing Student Learning
- Quantitative Reasoning Rubric
- Apply the theory of derivatives to the representation 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)
- Quizzes
Procedure for Assessing Student Learning
- Quantitative Reasoning Rubric
- Use differential calculus to model and solve various application problems, interpret results, and evaluate the reasonableness of the results in context.
This objective is a course Goal Only
Learning Activity Artifact
- Other (please fill out box below)
- Quizzes/exams
Procedure for Assessing Student Learning
- Quantitative Reasoning Rubric
- 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
- Interpret and communicate calculus concepts in a neat and organized manner using appropriate symbols, notation, and vocabulary.
Learning Activity Artifact
- Other (please fill out box below)
- Quizzes
Procedure for Assessing Student Learning
- Quantitative Reasoning Rubric