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I.
PREREQUISITES
Although the minimum prerequisite for this course is two years of high-school
algebra or MATH 113, a better background would be three years of high-school
mathematics or MATH 115, Precalculus (available as an Ohio University
Independent Study course).
II.
COURSE DESCRIPTION
This course is designed expressly for students majoring in business, management
sciences, social sciences such as economics and psychology, and life sciences
and should prove to be very useful and interesting. The course stresses
the application of the concepts of calculus to subjects such as
business administration, economics, finance, marketing, psychology, physics,
biology, medicine, ecology, etc. In essence, calculus is studied as a
tool for solving problems encountered in other disciplines, rather than
as a branch of mathematics. Therefore, this course avoids excessive mathematical
rigor as well as involved mathematical proofs. The emphasis is on applying
calculus.
The course focuses
the basic concepts of calculus: functions, limits, continuity, derivatives,
rules of differentiation, curve sketching, optimization problems, and
multivariate calculus and its applications. Your primary goal should be
to master the tools of calculus and their application to word problems
related to the subjects mentioned above. The recommended textbook presents
the material in an intuitive way and illustrates the uses of calculus
through examples and discussion. Try to develop your skills in interpreting
word problems and applying calculus to achieve their solutions.
You will begin the course with a review of high-school algebra and solving
equations used in various applications. Then you will study such topics
as: solving inequalities, finding equations of straight lines, limits
of functions, derivatives of functions, rules of differentiation, curve
sketching, and optimization (maxima-minima) problems. From there, you
will go on to study the calculus of functions of two variables, involving
partial derivatives, extreme values (maxima-minima problems) of these
functions, and the method of Lagrange Multipliers to maximize or minimize
the function f(x, y), subject to the given constraint.
Notice that many functions in applied problems depend on more than one
variable; for example, the cost of manufacturing and marketing a unit
of a certain product depends on the costs of material, labor, transportation,
insurance, advertising, research, and other such factors.
III.
TEXTBOOK AND SUPPLIES
There are several
good textbooks available that cover the material of this course (see the
section on “Reference Textbooks” below). However, the examination
is based upon the following:
ISBN 0534339719
Taylor, Claudia D. and Lawrence Gilligan, Applied Calculus,
4th ed., Pacific Grove, CA: Brooks/Cole Publishing Co., 1996
You may use a calculator
for your study and on the examination, although it may not be of great
help. The calculator must have only basic functions (a TI 30 or similar);
you may not use a TI-82, TI-85, TI-92 or similar models from Hewlett-Packard
or other manufacturers.
...available from
EdMap's distance-learning online
bookstore.
| STUDENTS
ARE STRONGLY ADVISED NOT TO BUY TEXTBOOKS UNTIL REGISTERED
IN COURSES AS REQUIRED EDITIONS CAN CHANGE WITHOUT NOTICE. |
IV.
SYLLABUS OF THE COURSE
The examination
will cover the following topics:
Chapter 1 - Algebra
Review
Emphasis on Sections 1.1, 1.2, and 1.3
Also study Sections 1.4, 1.5, and 1.6
Chapter 2 - Functions, Limits, and the Derivative
Study all sections and the Chapter Review, with emphasis on Sections 2.1,
2.2, 2.4, 2.5, 2.6, and 2.7. Notice that you need the information from
Section 2.3 to study 2.4 and 2.7.
Chapter 3 - Differentiation
and Applications
Study Sections 3.1 through 3.5; this is the core chapter of the course
Chapter 4 - Curve
Sketching and Optimization
Study all sections thoroughly; pay special attention to 4.4, 4.5, and
4.6
Chapter 9 - Multivariable
Calculus
Study all sections except 9.6; pay special attention to 9.4 and 9.5. This
is the other core chapter for the course.
You may omit the
study of “Alternative Sections” from all assigned chapters.
Be sure that you learn the techniques of solving problems as illustrated
by “Examples” in the chapters and review the key ideas presented
in the “Chapter Review” for each assigned chapter. It will be
to your benefit to work the “Review Exercises” and “Chapter
Tests” for practice. I may select problems for the examination from
these sources.
V.
NATURE OF THE EXAMINATION
You must know all of the material from the syllabus above, but a sample
examination for your practice is provided at the end of this Information
Sheet. The examination has a total of 125 possible points, divided as
follows:
| 1. |
A “true/false” problem and a “fill-in-the-blanks”
problem based on overall factual knowledge of the course. (Total credit,
15 points) |
| 2. |
Six problems based on rules of differentiation, partial derivatives,
equations of straight lines and tangent lines of the curve of a function,
curving sketching, and solving optimization problems using concepts
of calculus. These problems will be drawn from Chapters 3, 4, and
9 (see sections 4.6, 9.4 and 9.5). (Total credit, 60 points) |
| 3.
|
Five additional
problems drawn from all assigned sections of the chapters, plus
an additional Bonus problem for extra credit. (Total credit, 50
points, 10 points for bonus)
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You will be allowed
three hours to complete the examination. All materials will be provided;
you are not permitted to use books, notes, or supplementary aids, except
your calculator. Remember, your calculator must conform to the requirements
listed under III. of this Information Sheet
VI.
A WORD OF ADVICE
Be sure that you are well-prepared and relaxed when you take the examination.
Browse and read the entire examination. Do not get nervous and panic if
it seems you cannot answer certain problems; if you stay calm and cool,
I am certain that you will be able to work all the problems. The problems
on the examination have various levels of difficulty; some will be trivial
or easy, others will be routine to challenging. To gain confidence, take
the Sample Examination that is included–but try to duplicate the
actual test situation by giving yourself a three-hour time limit and not
using any books or notes. Then check your answers against the key, and
re-study any sections for problems that you missed. In view of my long
experience of teaching, I would suggest that you take the sample examination,
check your answers, review what you missed, and then just relax! Sample Examination
VII.
GRADING CRITERIA
Assigned point credits for each problem will be indicated. You will earn
some “goodwill points” for neat and organized answers written
legibly and fully. Your final grade will be based on the percentage of
total credit points earned, using the following scale:
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90 -100 %
80 - 89 %
70 - 79 %
60 - 69 %
Below 60 % |
=
A
= B
= C
= D
= D- or F at instructor’s discretion
(be aware that D- is
not a passing grade at many schools) |
Plus and minus grades
may be given at the discretion of the instructor. Your instructor has
two weeks to grade and return your examination after receiving it from
the IDL office.
VIII.
REFERENCE TEXTS
There are several texts which cover the material of this course syllabus.
The following are my recommendations (if you already have one of these
texts, you may use it in place of the required text, although you will
have to determine from the index where to find the topics covered on the
examination).
Berresford, Geoffrey
C., Brief Applied Calculus, Houghton-Mifflin, 1996
Barnett, R. A. and
Michael R. Ziegler, Calculus for Business, Economics, Life Sciences,
and Social Sciences, 7th ed., Prentice-Hall, 1996
Ramaley, Applied
Calculus, Wm. C. Brown Company, 1996
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