ELEMENTARY FUNCTIONS

                                                                     MA 166

 

 

Catalogue Description

 

            An introductory treatment of properties of elementary functions with emphasis on graphical analysis is presented in this course.  The course also investigates the graphical meaning of the derivative and integral.  3 Credits.  Prerequisite: Ma 165 or Equivalent.

 

Goals

 

            A.   To increase the student's understanding of elementary functions.

            B.   To interpret information given by a graph.

            C.   To relate graphs to elementary functions.

D.   To increase the student's ability to express information in graphical, formula and verbal forms.

            E.   To show the correlation between theoretical and practical problems.

            F.   To develop an ability to use quantitative reasoning.

 

Procedures

 

            A.   Lecture/Discussion

            B.   Classroom work with graphing calculators

            C.   Small group problem solving sessions.

D.   At least one project where a student can find that he is able to model with graphs and with elementary functions.

            E.   Daily homework problems from the text.

 

Course Content

 

            A.   Relations, Functions and Graphs

                        1.   Using Graphs to represent problems.

                        2.   Applications and Mathematical Models

                        3.   Graphs of Functions

 

            B.   Solving Equations Algebraically and Graphically

                        1.   Solving Equations Algebraically

                        2.   Solving Equations Geometrically

                        3.   Solving Systems of Equations Algebraically

                        4.   Solving Systems of Equations Geometrically

                        5.   Solving Higher Order Equations

 

            C.   Polynomial Functions and Roots of Polynomial Equations

                        1.   Analytic Geometry of Lines

                        2.   Quadratic Functions and Geometric Transformations

                        3.   Higher Degree Polynomial Functions

                        4.   Maximum and Minimum Values

                        5.   The Complex Number System

                        6.   Division of Polynomials

                        7.   Conjugate Roots and Descartes' Rule of Signs

                        8.   DeMoivres' Theorem

 

            D.   Continuity and Theory of Equations

                        1.   Real Zeros of Polynomials

                        2.   More on Zeros

                        3.   Upper and Lower Bounds for Real Zeros

                        4.   Number of Local Maximum or Minimum Values

 

            E.   Exponential and Logarithmic Functions

                        1.   Piecewise Functions

                        2.   Exponential Functions

                        3.   Logarithmic Functions

                        4.   Properties of Logarithms

                        5.   Solving Maximum - Minimum Problems

                        6.   Mathematical Models, Recursion, and Difference Equations

 

 

            F.   Trigonometric Functions

                        1.   Circular Functions

                        2.   Trigonometric Graphs

                        3.   Inverse Trigonometric Functions

                        4.   Trigonometric Equations and Maximuim - Minimum Problems

 

            G.   An Introduction to Polar Coordinates

                        1.   Polar Form

                        2.   Graphing Polar Equations

 

            H.   An Introduction to Graphing in Three Dimensions

                        1.   Representing Points

                        2.   Graphing in Three Dimensions

 

            I.    Additional Topics

                        1.   Arithmetic Sequences and Series

                        2.   Geometric Sequences and Series

                    

            Evaluation methods

                        1.   Four to Six Hourly Tests.  Lowest or one missed exam will be drooped from the evaluation.

                        2.   Project relating a live situation to Modeling by Graphical and Formula Methods.

                        3.   Final Exam

 

                              TESTS                                60%

                              PROJECT                           20%

                              FINAL EXAM                       20%

                       

Required Text:       Cohen, David, Pre-Calculus, 5th Ed., West Publishing Co., New York, 1996.

 

Required Calculator                TI-82 or TI-83

 

Bibliography

Connally, Eric, et al., Precalculus:  Functions Modeling Change (Preliminary Edition), John Willey & Sons, Inc., New York, 1998.

Contemporary Precalculus through Applications:  Functions, Data Analysis and Matrices, North Carolina School of Science and Mathematics, Janson Publications, Inc., 1996.

 

Demana et al., Precalculus:  Functions and Graphs, 2d ed., Addison-Wesley Publishing, Reading, Mass., 1992.

Gordan, Sheldon, et al., Functioning in the Real World:  A Precalculus Experience Addison-Wesley, New York, 1997.

Hornsby and Lial, A Graphical Approach to Precalculus, Addison-Wesley Publishing, Reading, Mass., 1998.

 

            Leithold, Louis, College Algebra, Addison-Wesley Publishing, Reading, Mass., 1989.

           

            Leithold, Louis, Before Calculus:  Functions, Graphs, and Analytic Geometry, Addison-Wesley Publishing, Reading, Mass., 1994.

 

            Lial and Miller, Pre-Calculus, Scott, Foresman Co., Glenview, Ill., 1988.

 

Runyan and Runyan, Precalculus:  Making Connections, Preliminary ed., Prentice Hall, 1999.

 

Stewart, Redlin, and Watson, Precalculus:  Mathematics for Calculus, 3d ed., Brooks Cole, 1998.

 

Swokowski and Cole, Precalculus:  Functions and Graphs, 8th ed., Brooks Cole, 1998.

 

Software   

 

            Derive for Windows, Version 4.

 

            West Math Tutor, Cohen College Algebra, 1995.