CALCULUS I

MATH 190

1. Catalog Description

Differential calculus of polynomial and trigonometric functions is the focus of this course. The course includes topics such as limits, derivatives and applications of differentiation.

2. Goals

A. To introduce the student to the basic theories of calculus as well as the accompanying mathematical techniques and procedures required.

B. To show the student several practical applications of the calculus among the vast number and variety of those applications.

C. To develop the students’ ability to reason logically and transfer mathematical concepts from one situation to another rather than simply memorize mechanical procedures.

D. Students will be able to read and comprehend mathematical materials and texts.

E. Students will be able to express mathematical concepts and solutions in writing by producing reports based on computer labs.

3. Procedures

A. Lecture/Discussion

B. Daily reading of the textbook and homework assignments with in-class discussion of solutions.

C. Computer labs using Matlab or other relevant software.

D. Students presentations and discussions of solutions to specific math problems at the blackboard.

E. Students will be able to express mathematical concepts and solutions in writing by producing reports based on computer labs.

F. Possible use of graphing calculators.

4. Course Content

A. Review of inequalities and absolute value.

B. Limits

1. Intuitive approach

2. Computational techniques

C. Continuity

D. Limits and continuity of trigonometric functions including special limits

E. Differentiation

1. Rates of change

2. Tangent lines

3. Derivative defined via differences quotient and numerical computation as estimates of the derivative

4. Computational techniques

F. Applications of the derivative

1. Related Rates

2. Concavity

3. Extrema, derivative tests

4. Graph sketching

5. Maxima and Minima problems and applications

6. Rolle’s theorem and mean-value theorem

7. Rectilinear motion

5. Evaluation Methods

A. Quizzes. Quizzes will be given as necessary.

B. In-class examinations and a comprehensive final exam.

C. Computer labs. Students will write reports based on computer explorations of the applications of calculus.

6. Bibliography

Required Text: Larson, Roland E., Hostetler, Robert P., Calculus with Analytic Geometry, 6^th Ed., Houghton Mifflin Company, Boston, Mass 1998.

Anton, Howard, Calculus, a new horizon, 6^th Ed., John Wiley & Sons, New York, N.Y., 1999.

Bittinger, Marvin, Calculus and its applications, 7^th Ed., Addison-Wesley, Reading Mass., 2000.

Coughlin/Zitarelli, Brief Calculus with Applications, Saunders Pub., Philadelphia, Pa., 1990.

Stewart, James, Calculus with early transcendental functions, 4^th Ed., Brooks/Cole, Pacific Grove Ca., 1999.

7. Software

A. Matlab, Version 5.2, The Math Works Inc., Natic, Mass. 1998.