CALCULUS & ANALYTIC GEOMETRY I

MA 192

Catalogue Description

This course presents a study of differential calculus of polynomial and trigonometric functions, applications of differentiation including maximum-minimum problems and Newton’s Method and Prolle’s Theorem. Anti-differentiation, definite, and indefinite integrals are also involved. This course is part of a 12 semester hour sequence in Calculus for Pre-Engineering students. (4 credits)

Prerequisite: Ma 165 or equivalent

Goals

A. To provide fundamental concepts in Differential and Integral Calculus.

B. To prepare students for scientific and technological majors.

Procedures

A. Lecture/Discussion

B. Readings and problems assigned

C. Computer Software Supplements in Math Resource Center

Course Content

A. The Cartesian Plane and Functions

1. The Real Line

2. The Cartesian Plane, the Distance Formula and Circles

3. Graphs of Equations

4. Lines in the Plane

5. Functions

6. Review of Trigonometric Functions

B. Limits and Continuity

C. Differentiation

1. The Derivative and the Tangent Line Problem

2. Velocity, acceleration, and other Rates of Change

3. Differentiation Rules for Sums, Constant Multiples, Powers, Sines and Cosines

4. Differentiation Rules for Products, Quotients, Secants & Tangents

5. The Chain Rule

6. Implicit Differentiation

7. Related Rates

D. Applications of Differentiation

1. Extrema on an Interval

2. The Mean Value Theorem

3. Increasing and Decreasing Functions and the First Derivative Test

4. Concavity and the Second Derivative Test

5. A Summary of Curve Sketching

6. Optimization Problems

7. Other Applications

E. Integration

1. Antiderivatives and Indefinite Integration

2. Integration by Substitution

3. Area, the Fundamental Theorem of Calculus

F. Further Applications of the Integral

1. Improper Integrals

2. Volumes of Solids of Revolutions by Disc and Shell Method

3. Volumes of Other Solids

4. Surfaces of Revolution

5. Center of Mass and Moments

6. Centroids

7. Moments of Inertia

8. Fluid Force

Evaluation Methods

1. Preparation of homework assignments.

2. Class Participation

3. Periodic Tests and Comprehensive Final Examination.

Bibliography

Required Text: Finney, Ross L. and Thomas, George B. Jr., Calculus, 2nd Ed., Addison-Wesley Publ. Co., Reading, Mass., 1994.

Larson & Hostetler, Calculus with Analytic Geometry, 5th Ed., D.C. Heath Co., 1994.

Thomas, George B. Jr. and Finney, Ross L., Calculus and Analytic Geometry, 8th Ed., Addison-Wesley Publ. Co., Reading, Mass., 1992.

Required Calculator: TI-81 or TI-82 Graphing Calculator

Relevant Software

Anderson, Richard, Student Edition of MATHCAD, Addison-Wesley Publ. Co., Reading, Mass., 1988.

Finney, Hoffman, Schwartz, Wilde, The Calculus Toolkit, Addison-Wesley Publ. Co., Reading, Mass., 1986.

Pence, Dennis, Calculus Activities for the TI-81 Graphic Calculator, PWS-Kent, Boston, Mass., 1992.

DERIVE - A Mathematical Assistant, Soft Warehouse, Inc., Honolulu, Hawaii