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.

Credits

4

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

1. Analyze limits of elementary functions numerically, graphically, and analytically.
2. Calculate derivatives of functions given either implicitly or explicitly.
3. Calculate integrals of functions, using the method of substitution where applicable.
4. 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.
5. Use differential calculus to model and solve various application problems, interpret results, and evaluate the reasonableness of the results in context.
   
6. Apply the Mean Value Theorem for derivatives and integrals to given functions.
7. Use a computer algebra system, as a means of discovery, to reinforce concepts, and as an efficient problem-solving tool.
8. Interpret and communicate calculus concepts in a neat and organized manner using appropriate symbols, notation, and vocabulary.

Course Objectives

1. 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
2. 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
3. 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
4. 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
5. 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

   Scientific Reasoning

   • SR3
6. Apply the Mean Value Theorem for derivatives and integrals to given functions.

   This objective is a course Goal Only

7. 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

8. 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