ST. LOUIS COMMUNITY COLLEGE AT FLORISSANT VALLEY

COURSE OF STUDY

MTH:186

 

DEPARTMENT:                    Mathematics                        LAST UPDATE:  Summer 2006

 

COURSE TITLE:       Survey Calculus                             CREDIT HOURS:       4

 

LECTURE HOURS PER WEEK:      4                                                     LAB HOURS PER WEEK:  0

 

During the first week of the semester, it is the responsibility of each instructor to furnish, in writing, the course objectives and a course syllabus.  The objectives are stated below.  The syllabus should include instructor information, course information, expected outcomes, course requirements, method of evaluation and an explanation of grading policies, policies on make up work, ground rules for class participation, a tentative class schedule, withdrawal dates, expected classroom behavior, information on the math learning center, consultation (office) hours, and an Americans with Disabilities Act (ADA) accommodations statement.

 

COURSE DESCRIPTION:

 

An introduction to plane analytic geometry and the basic techniques of the differential and integral calculus.  Applications are business oriented.

 

 

COURSE PREREQUISITE:

 

MTH:160 with a grade of “C” or better.

 

TEXT and CALCULATOR REQUIREMENTS:

 

Applied Calculus, Hughes-Hallet, Gleason, Lock, et.al., Third Edition, John Wiley & Sons, Inc., 2006.

 

The use of a TI 83/84 is required of every student in this course.

 

 

COURSE OBJECTIVES:

 

The student will…

  1. graph and analyze polynomial, exponential, and logarithmic functions in order to model real world applications.
  2. investigate the derivative of a function numerically, graphically, symbolically, and in the context of applications involving rates of change.
  3. differentiate polynomial and transcendental functions and use them to solve selected application problems.
  4. study the definite integral as the limit of Riemann sums and learn to compute the definite integral numerically.  The student will learn the connection between differentiation and definite integral.
  5. solve a variety of application problems involving total change by interpreting the definite integral as an area.

 

 SUPPLEMENTARY MATERIALS:

 

  1. For students, a Student Solution Manual with complete solutions to half the odd-numbered problems is available in the Campus Bookstore.
  2. For Faculty, an Instructor’s Manual with Sample Exam Questions with teaching tips and some calculator programs and the Instructor’s Solution Manual with complete solutions to all problems are available from the Mathematics Department.
  3. Students may borrow a Graphing Calculator from the Library.

 

 

ADDITIONAL COMMENTS:

 

  1. The context, focus and pedagogy represented in this text reflect the fact that this text is a product of the “calculus reform” movement.  The content is driven by real-world applications, stressing differentiation as a rate of change and the definite integral as area under a curve and as net change.

 

  1. In this text, the development of topics reflects the Rule of Four: each topic should be developed numerically, graphically, symbolically, and verbally.

 

  1. In chapter 1, Functions and Change, students study the behavior of polynomial and exponential functions though their graphs and as appropriate models of real-world application problems.  The chapter sets the tone for the course. Through ostensibly review, most students will find the approach and emphasis very new.

 

  1. The exercise sets contain a broad variety of numerical, graphical, symbolic, and application problems.  Most exercises are not simply skill work or a minor variation of an example from the text.  Therefore, from each exercise set, the instructor should select a small number of appropriate exercises.  As Gauss said, “Few, but ripe.”

 

  1. The textbook assumes that students can use graphing calculators or graphing software.  We recommend the TI-82 or TI-83. The instructor will need to introduce the basic keys to the class.

COURSE OUTLINE:

                                                                                                             

                                                                         

 

 

Suggested Time Allotment

Chapters

Topics and Sections

(Number of weeks)

 

 

 

Chapter 1

Functions and Change

3.0

 

Omit:        Sections 1.8, 1.9, 1.10

Include:    An introduction to the Graphing Calculator (TI-82 or TI-83)

Include:    Fitting Formulas to Data (pp.75-82)

 

 

 

 

Chapter 2

Rate of Change: The Derivative

3.0

 

 

 

Chapter 3

 Shorts-Cuts to Differentiation

2.0

 

 (As a bridge between Chapters 2 and 3, you may teach: Establishing the Derivative Formulas Page 160.)

 

 

 

 

Chapter 5

Accumulated Change: The Definite Integral

2.5

 

 

 

 

 

 

Chapter 4

Using the Derivative

2.0

 

Select 3-4 sections from this chapter

 

 

 

 

Chapter 6

Using the Definite Integral

1.5

 

 Select 2-3 sections from this chapter and/or from Chapter 8

 

 

 

 

Chapter 7

Antiderivatives

1.5

 

 OPTIONAL – some instructors choose to teach section 7.1 and/or 7.2

 

 

 

 

Tests and Review

 

1.0

 

 

 

 

 

TOTAL:  16 weeks