CALCULUS FOR BUSINESS

                                                           AND SCIENCE I & II

                                                                 MA 200/201

 

 

Catalogue Description

           

            This course is designed to provide a foundation in those topics in Calculus that are relevant to students in the managerial, life and social sciences.  Topics begin with functions and progress through single variable and multivariable calculus.  3 credits. 

Prerequisite: Ma 165 or equivalent.

 

Goals

 

            A.   To increase the student's ability to express problems using written and verbal skills.

            B.   To develop the mathematical skills of differential and integral calculus.

            C.   To integrate the mathematical knowledge from algebra and pre-calculus into the                                    calculus.

            D.   To develop the ability to use a variety of problem solving techniques.

            E.   To construct mathematical models for business problems.

 

Procedures

 

            A.   Lecture/Discussion

            B.   Media presentations (videos, computers).

            C.   Small group problem solving sessions.

            D.   Directed discovery sessions.

            E.   Homework problems from the text.

            F.   One project to model a practical problem to be solved by calculus methods.

 

Course Content

 

            A.   The Derivative

                        1.   Limits & Continuity

                        2.   Rates of Change

                        3.   The Derivative

 

            B.   Differentiation

                        1.   Basic Rules of Differentiation

                        2.   The Product and Quotient Rules

                        3.   The Chain Rule

                        4.   Marginal Problems

                        5.   Higher Order Derivatives

                        6.   Implicit Differentiation

 

            C.   Applications of the Derivative

                        1.   Increasing and Decreasing Functions

                        2.   Relative Maxima and Relative Minima

                        3.   Concavity & Points of Inflection

                        4.   The Second Derivative Test

                        5.   Curve Sketching

                        6.   Absolute Maxima and Absolute Minima

                        7.   Optimization Problems

 

            D.   Exponential and Logarithmic Functions

                        1.   Laws of Exponents and the Exponential Function

                        2.   Laws of Logarithms and Logarithmic Function

                        3.   Differentiation of the Exponential Function

                        4.   Differentiation of the Logarithmic Function

 

            E.   The Integral

                        1.   Antiderivatives

                        2.   Rules of Integration

                        3.   Integration by Substitution

                        4.   Integration of Parts

                        5.   The Definite Integral

                        6.   Area Under a Curve

                        7.   Areas of Planner Regions

                        8.   Applications

 

            F.   Additional Topics in Integration

                        1.   Applications to Economics

                        2.   Improper Integrals

                        3.   Applications to Probability

 

            G.   Calculus of Several Variables

                        1.   Functions of Several Variables

                        2.   Partial Derivatives

                        3.   Maxima and Minima of Functions of Several Variables

 

            Evaluation methods

                        1.   Six hourly tests.  Lowest or one missed exam will be dropped from the                                                                  evaluation.

                        2.   Project relating a real world problem to be modeled to a calculus model and                                                           solved.

                        3.   Final Exam:

 

                              Five hourly tests.....................................60%

                              Project....................................................20%

                              Final Exam..............................................20%

 

 

Bibliography

 

Required Text:       Lial, Margaret L., Hungerford, Thomas W. & Miller, Charles D.,                                                                                 Mathematics with Applications, 6th Ed., Harper Collins, 1995.

 

                                 Barnett, Raymond A. and Ziegler, Michael R., Essentials of College                                                                       Mathematics, Dellin Publ. Co., San Francisco, Ca., 1989.

 

                                 Cannon, Raymond & Williams, Gareth, Calculus Management, Social and Life                                                       Sciences, W.C. Brown Pub., Dubuque, Ia,  1988.

 

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

 

                                 Eaves, Edgar D. and Carruth, J. Harvey, Introductory Mathematical                                                                        Analysis, W.C. Brown Publ., Dubuque, Ia., 1985.

 

                                 Lial, Margaret L. & Miller, Charles D., Finite Mathematics & Calculus with                                                           Applications, 3rd Ed., Scott, Foresman & Co., Glenview, Ill., 1989.

 

                                 Zitarelli/Coughlin, Finite Mathematics with Calculus: An Applied Approach,                                                          Saunders College Publ., New York, N.Y., 1989.

           

Software

 

                                 Andrews, Richard, Student Edition of MATHCAD , Addison-Wesley,                                                                         Reading, Mass.,  1988.

 

                                 Finney, Hoffmann, Schwartz, Wilde, The Calculus Toolkit, Addison-Wesley,

                                 Reading, Mass., 1986

 

                                 Flanders, Harley, Microcalc 4.01, Software for Teaching/Learning                                                                           Calculus, Ann Arbor, Mi.,  1987.

 

                                 Fraleigh, Pakula, Exploring Calculus with the IBM PC, Addison-Wesley,                                                                Reading, Mass., 1986.

 

                                 Kemeny, Kurtz, Calculus, Tru Basic Inc., New Hampshire,  1988.

                                

                                 Tront, Joseph, Eureka, John Wiley & Sons, New York, N.Y., 1987.

 

                                 Waits, Demana, Master Grapher and 3D Grapher, Addison-Wesley, Reading,                                                         Mass., 1988.

 

                                 Wells, David, Practice Problems for Calculus, Compress, Bridgeport, Ct.,                                                               06610.