CALCULUS  III

                                                                  MA 290

 

Catalogue Description

 

            This is a continuation of Calculus II.  Topics studied include improper integrals, L’Hopital’s Rule, infinite series, conic sections, polar coordinates, parametric equations, and introduction to vectors.

 

Goals

 

            A.  To introduce the traditional material covered in the 2nd year Calculus sequence.

            B.   To sharpen the calculus background of students.

            C.  To prepare students for more advanced math courses such as Advanced Calculus, Differential Equations, etc.

 

Procedures

 

            A.  Lecture/Discussion

            B.   Use of available software (Derive)

            C.  Possible use of graphing calculators

            D.  Computer software supplements in Math Resource Center

 

Course Content

 

            A.  Improper Integrals; L'Hopital's Rule

                        1.   Improper Integrals

                        2.   L'Hopital's Rule (Indeterminate Forms of Type 0/0)

                        3.   Other Indeterminate Forms

 

            B.  Infinite Series

                        1.   Sequences

                        2.   Monotone Sequences

                        3.   Infinite Series

                        4.   Convergence: The Integral Test

                        5.   Additional Convergence Tests

                        6.   Applying the Comparison Test

                        7.   Alternating Series: Conditional Convergence

                        8.   Power Series

                        9.   Taylor & MacLaurin Series

                     10.    Taylor Formula with Remainder, Convergence of Taylor Series

                     11.    Computation Using Taylor Series

12.     Differentiation and Integration of Power Series

 

            C.  Topics In Analytic Geometry

                        1.   Introduction to the Conic Sections

                        2.   Parabola; Translation of Coordinate Axes

                        3.   The Ellipse

                        4.   The Hyperbola

 

            D.  Polar Coordinates and Parametric Equations

                        1.   Polar Coordinates

                        2.   Graphs in Polar Coordinates

                        3.   Area in Polar Coordinates

                        4.   Parametric Equations

 

            E.   Vectors (An Introduction)

 

Evaluation methods at the discretion of the instructor.

 

Bibliography

 

Required Text:       

 

Anton, Howard, Calculus with Analytic Geometry, 5th ed., John Wiley & Sons, New York, N.Y.  1995.

 

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

 

Lial, Margaret L. & Miller, Charles D., Finite Math & Calculus with Applications, 3rd Ed., Scott, Foreman & Co.  1989.

        

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

 

Software

 

Andrews, Richard, Student Edition of Mathcad , Addison Wesley Pub., Reading, Mass.,  1988

 

Burgmeier, Kost, Explorations Programs in Calculus, Prentice Hall, Englewood Cliffs., N.J.  1985.

 

Derive A Mathematical Assistant, Version 1.62, Soft Warehouse Inc., Honolulu, Hawaii, USA.,  1988

 

Finney, Hoffman, Schwartz, Wilde, The Calculus Toolkit, Addison Wesley Pub., Reading, Mass.,  1986

 

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

 

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

 

Meyers, Roy, Surface Plotter, Elm Software, Leechburg, Pa.,  1987

 

Rowell, James, Mathematical Modeling with Mathcad Explorations in the Calculus and Beyond, Addison Wesley Pub., Co., Inc., 1990

 

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

 

 

 

 

 

                             


SAMPLE WEEKLY PROGRESS

 

 

 

TEXT:  Anton, Calculus with Analytic Geometry, John Wiley & Sons, New York, N.Y.  1988

 

                                             Calculus III

 

 

WEEK

 

1          Sec. 10.1, (2 Classes), Sec. 10.2

2          Sec. 10.3, 11.1, 11.2

3          Sec. 11.3, (2 Classes), 11.4

4          Sec. 11.5, 11.6 (2 Classes)

5          Review, Exam #1, Sec. 11.7

6          Sec. 11.8, 11.9 (2 Classes)

7          Sec. 11.10, 11.11, 11.12

8          Sec. 11.12, 12.1, 12.2

9          Review, Exam #2, Sec. 12.3

10        Sec. 12.4, 13.1, 13.2

11        Sec. 13.2, 13.3, (2 Classes)

12        Sec. 13.4, (2 Classes), 14.1

13        Review, Exam #3, Sec. 14.2

14        Sec. 14.3, 14.4, Review

15        Review