CALCULUS II

                                                                  MA 191

 

 

Catalogue Description

 

         This course offers a study of integral calculus, antiderivatives, definite and indefinite integrals. Logarithmic and exponential functions, hyperbolic functions and techniques of integration are also studied.

 

Prerequisites: Math 190 Calculus I or equivalent

 

Goals

 

         A.  To introduce the student to the basic theories of the 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 the variety of those applications.

 

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

 

Procedures

 

         A.  Lecture/Discussion

         B.   Use of available software (Derive)

         C.  Use of graphing calculators

         D.  Computer software supplements in Math Resource Center

 

Course Content

 

         A.  Integration

 

               1.   Antiderivatives and the indefinite integral

               2.   Substitution

               3.   Summation notation and accompanying theorems

               4.   Estimation of area as numerical computation of sums of areas of inscribed and circumscribed rectangles; Areas as limits

               5.   Definite integration

               6.   Fundamental Theorem

                           a)   Proof

                           b)   Common Notations

                           c)   Properties and Corollaries

               7.   Mean-Value theorem for integrals

        

         B.  Applications of Integration

 

               1.   Area between curves

               2.   Volumes (slices, discs, washers, shells)

               3.   Length of a plane curve

               4.   Surfaces of revolution

               5.   Rectilinear Motion

               6.   Fluid pressure and force

 

         C.  Special Functions

 

               1.   Inverses in general (includes review of domain, range, one-to-one

               2.   Derivative of an inverse function

               3.   Logarithmic functions

               4.   Natural logarithm as an integral

               5.   Irrational exponents

               6.   Exponential functions (definition, differentiation, and integration)

               7.   Limits and graphs of logarithmic and exponential functions

               8.   Hyperbolic functions

               9.   First-order differential equation

 

         D.  Inverse Trigonometric and Hyperbolic Functions

 

               1.   The inverse trigonometric functions

               2.   Derivatives and integrals

               3.   Inverse hyperbolic functions

 

         E.   Techniques of Integration

 

               1.   Review of basics

               2.   By parts

               3.   Powers of sine and cosine

               4.   Powers of secant and tangent

               5.   Trigonometric substitutions

               6.   Involving ax2+bx+c

               7.   Rational functions and partial fractions

 

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., Philadelphia, Pa., 1990

 

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

 

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

 

Software

 

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

 

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

 

Derive A Mathematical Assistant, Version 1.62, Soft Warehouse Inc., Honolulu, Hawaii, 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 Pub., Co., Inc., Reading, Mass., 1988.