syllabus

 

I.               MATH 131-132,  Calculus and Analytic Geometry I, II                                                             4, 4 cr. hrs.

 

II.             Fall, 2001;  Spring, 2002 

                                                                                  INSTRUCTOR:  Herman Matthews

                                                                                  Office:  F-207, Ext. 6226

 

            Office Hours: These are posted on the door of my office, together with my complete schedule.

                                                                       

III.       COURSE PREREQUISITES:  MATH 120 or high school algebra and trigonometry equivalent

 

IV.       COURSE DESCRIPTION/COURSE GOALS: Single variable differential and integral calculus, with supporting material from analytic geometry.  Goals: 1) To help students gain an appreciation of the problem-solving power of calculus.  2) To place calculus and its development in a correct historical perspective.  3) To teach students the standard techniques and tools of calculus that are so widely applied in the sciences.  4) To develop particularly an appreciation of the notion of limit as applied to continuous functions, the derivative, and definite integral.  5) To see how calculus serves through its problem-solving power to provide models of many natural phenomena.

 

V.             RELATIONSHIP OF THIS COURSE TO CONTENT AREA KNOWLEDGE AND SKILLS:  This course occupies a central position in the student's mathematical development.  It develops, to some degree, a large number of basic skills needed by mathematicians continuing to graduate work, going into industry, or preparing for teaching.  Basic problem-solving skills are enhanced as the student moves into the realm of "higher math" and applies the limit concept through problems involving rates of change and the integral.  The course makes constant use of most topics studied in high school mathematics, such as algebra, geometry, trigonometry, and functions.

 

VI.       TEXT:  Stewart, James, Calculus – 3rd edition (early transcendentals version),

                          Brooks/Cole Publishing Company, Pacific Grove, CA   1995

 

VII.      COURSE OBJECTIVES: 1) To improve basic problem-solving skills.  2) To improve algebraic and geometric skills.  3) To apply the methods of calculus to problems in a variety of science and social science areas (particularly to physics, chemistry, biology, and economics).  4) To increase ability to solve "real life" problems in various areas.  5) To increase ability to graph and interpret graphs.  6) To understand the limit concept as it appears in a variety of situations: continuity, the derivative, the definite integral, and the fundamental theorem of calculus.  7) To learn how to evaluate integrals by correctly applying appropriate standard techniques.  8) To increase ability to use calculators (or computers) efficiently as tools for solving certain types of problems.  9) To increase ability to identify, illustrate, analyze, and use a wide variety of applications in mathematics.  10) To increase awareness of the mathematical needs of other disciplines.

 

VIII.    OUTLINE OF COURSE CONTENT/UNITS OF INSTRUCTION:

 

1.        Foundations:  basic logic, the real number system, the Cartesian coordinate system, functions and their 

                  graphs, use of calculators, principles of problem solving

 

2.        Limits and Rates of Change: 

                    (a) the problems of tangent lines and velocity, simple limits of functions, calculations of limits

                    (b) precise definition of limit, application to continuity, tangents, velocity and other rates of change

                    (c) analysis and proofs of selected theorems

 

3.    Derivatives and Applications:

                    (a) definition of derivatives, formulas, properties, and applications to the natural and social sciences,

                    derivatives of the trigonometric functions

                    (b) chain rule, implicit differentiation, higher derivatives, related rates, and linear approximations

                   

4.    Inverse Functions:

                    (a) logarithmic functions as inverses of exponential functions, the derivatives of both types of functions

                    (b) application to exponential growth and decay

                    (c) inverse trigonometric functions and hyperbolic functions

                    (d) indeterminate forms and l'Hospital's rule

 

5.    The Mean Value Theorem (MVT) and Curve Sketching:

                    (a) definition of maxima and minima, the MVT, intervals of increase or decrease

                    (b) first and second derivative tests, inflection points and concavity, and applications to graphing

                    (c) graphing with calculus and calculators

                    (d) applied extrema problems, applications to economics

                    (e) antiderivatives

 

6.    Integrals and Properties:

                    (a) sigma notation and applications to area

                    (b) the definite integral and fundamental theorem of calculus

                    (c) rules for integration by substitution

                    (d) the logarithm defined as an integral and exponential function as inverse of logarithmic function

 

7.    Applications of Integrals:

                    (a) areas, volumes, and work

                    (b) average value of a function over an interval

 

8.    Techniques of Integration:

                    (a) integration by parts, trigonometric integrals, trigonometric substitutions

                    (b) integration of rational functions by partial fractions, the use of rationalizing substitutions

                    (c) strategies for integration, use of tables, and approximate integrations

                    (d) improper integrals

 

9.    Further Applications of Integration (as time permits)

                    (a) differential equations, arc length, and area of a surface of revolution

                    (b) applications to physics, biology, and economics

 

IX.    REQUIRED READINGS: Textbook

 

X.    SUGGESTED READING/BIBLIOGRAPHY: Occasion references to other texts or jounal articles 

 

XI.    METHODS OF INSTRUCTION AND LEARNING: Lecture and problem-solving activities constitute the principal methods of instruction.  Attention will be given to the nature of proof, analysis of theorems, and writing of theorems and problems.  All students are expected to do homework, which will be assigned daily. Students are encouraged to use calculators for certain portions of the work, but not as a crutch for common and simple calculations.  Some concepts may be computerized for illustrations, but the emphasis will be on understanding rather than on "pushing buttons."

 

XII.     COURSE REQUIREMENTS/METHODS OF ASSESSMENT/EVALUATION/DOCUMENTATION:  All students are expected to attend classes regularly and to keep up their homework.  Three or four major tests and a final exam will be the main evaluation tools, with periodic homework or quizzes given at the option of the instructor.  Weighting of tests, quizzes, homework, and final exam will be at the discretion of the instructor.  Absence on test days will be viewed as a serious matter and make-up tests will be more difficult, if allowed. Grading will be scaled to the following scheme so that students can determine average grades more easily:

 

                    A    90.0 and above

                    B    80.0 - 89.9

                    C    70.0 - 79.9

                    D    60.0 - 69.9

                    F    below 60.0.

 

The final exam will be given only on the official date designated by the University, excepting the requirements of early grades for seniors or emergency cases.  Students who for some valid reason must take an incomplete must contract for this grade and complete the work within a designated time frame.  See the Catalog for more information regarding the incomplete grade. 

 

XIII.    CLINICAL/LABORATORY/FIELD EXPERIENCES: None required

 

XIV.    DATE OF REVISION: January 11, 1999