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. 1. Calculate limits of elementary functions numerically, graphically, and analytically.
   
2. 2. Calculate derivatives of functions given either implicitly or explicitly.
3. 3. Apply the method of substitution to calculate integrals of functions where applicable.
4. 4. 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.
5. 5. Use differential calculus to model and solve various application problems, interpret results,
   and evaluate the reasonableness of the results in context.
   
6. 6. Apply the Mean Value Theorem for derivatives and integrals to given functions.
7. 7. Use a computer algebra system, as a means of discovery, to reinforce concepts, and as an
   efficient problem-solving tool.
8. 8. Communicate calculus concepts in a neat and organized manner using appropriate
   symbols, notation, and vocabulary.
9. 9. 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

1. 1. Calculate limits of elementary functions numerically, graphically, and analytically.
   
2. 2. Calculate derivatives of functions given either implicitly or explicitly.
3. 3. Apply the method of substitution to calculate integrals of functions where applicable.
4. 4. 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.
5. 5. Use differential calculus to model and solve various application problems, interpret results,
   and evaluate the reasonableness of the results in context.
   
6. 6. Apply the Mean Value Theorem for derivatives and integrals to given functions.
7. 7. Use a computer algebra system, as a means of discovery, to reinforce concepts, and as an
   efficient problem-solving tool.
8. 8. Communicate calculus concepts in a neat and organized manner using appropriate
   symbols, notation, and vocabulary.
9. 9. 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.