MATH
263B - Analytic Geometry and Calculus
Four Quarter Hours
10/97
I.
PREREQUISITES
Successful completion of Ohio University Mathematics 263A or equivalent.
II.
COURSE DESCRIPTION
The main topics to be studied in this Math 263B course, using the text
by Varberg and Purcell, are:
| (1) | applications of the definite integral to find areas of plane regions, volumes of solids of revolution, and volumes of solids of known cross-sections; |
| (2) | techniques of integrating and differentiating the so-called elementary function, especially those elementary functions called transcendental functions; |
| (3) | indeterminate forms and improper integrals. |
Considerable emphasis is given to manipulative skills.
To learn to differentiate and integrate various combinations of elementary functions, including especially the transcendental functions, introduced in Chapter 7, you will need to learn, memorize, and practice using standard integration and differentiation formulas cited in your text. This is important in being able to apply calculus in a number of diverse situations.
The material presented in the text is well-suited for students in mathematics, engineering, liberal arts, and the sciences.
III.
TEXTBOOK AND SUPPLIES
ISBN 013518911X
Varberg, Dale, and Purcell, Edwin J., Calculus, 7th ed., Upper
Saddle River, New Jersey: Prentice Hall, Inc., 1997
...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.
COURSE CONTENT
Math 263B covers Chapters 5, 7, 8, 9, and the first two sections of Chapter
6. The following sections are omitted: 5.2, 5.10, 6.3, 6.4, 6.5. 6.6,
6.8, 7.10, 8.7, 9.6. In addition, you can omit the Mean Value Theorem
for Integrals, page 281 of the text, and the material on Inverse Hyperbolic
Functions, beginning on page 393 of the text.
| Notes: | (1) | Some problems in the problem sets are marked with the symbol PC or C to indicate that a computer or calculator is needed in solving these problems. These type problems will not be on your examination. | |
| (2) | You will not be required in the examination problems to prove theorems. However, it is important you know what the theorems say, and be able to apply them | ||
V.
EXAMINATION
The Independent and Distance Learning Programs course examination for
Mathematics 263B is a comprehensive supervised examination consisting
of problems covering the material you are responsible for in Chapters
5 through 9. The problems are similar to those in the textbook, and very
similar to those in the Sample Examination. The course examination
includes word or stated problems, and manipulative exercises.
You will have three hours to complete the supervised examination. A hand-held calculator will not really be needed, but may be used on the examination if you supply your own.
A calculator with
basic functions including percent and square root will be sufficient for
the examination; programmable calculators may not be used.
VI.
PREPARING FOR THE EXAMINATION
The most effective way to prepare for the examination is to concentrate
on solving problems (especially the non-proof problems) from the problem
sets of each assigned section. However, for the necessary background to
solve problems, you will need to understand the concepts and important
results in each section. Thus, before you turn to problem solving, it
is highly recommended that you first read carefully the material in each
section and work through the details of each example.
As noted in the textbook, the short list of standard integration formulas given on page 404 of your text is so useful in evaluating integrals that the list should be memorized. Actually, it is not necessary for you to memorize Formula 15 in the list. Furthermore, formulas 11 and 12 do not need to be memorized because they can so easily be derived. Thus,
Also, memorize most of the list of derivative formulas given on the back cover of the text. However, it is not necessary for you to memorize the formulas for Dx coth x, Dx sech x, Dx csch x and Dx sec-1x.
The problems in the supervised exam emphasize evaluating derivatives and integrals. To gain facility in differentiation and techniques of integration, you should work a considerable number of these kinds of problems from each problem set.
VII. SAMPLE EXAMINATION
A self-check sample examination is included with this syllabus. There is also an answer key which gives the answer to all problems in the sample examination. The solutions to these problems are given in sufficient detail that you should be able to follow completely the steps and methods required to solve each problem. The sample examination should also help you make a final determination as to whether or not you are prepared to take the supervised examination.
It is recommended that you do not take the sample examination until you feel you have adequately mastered the course material. When you do feel prepared to take the sample examination, take it without using your book or notes. Finally, evaluate your answers using the answer key. Sample Examination
If you did not do well on the sample exam, then review more extensively those troublesome areas before applying for the examinations. As mentioned earlier, the problems on the supervised examination will be quite similar to those on the sample exam. Hence, it should also be helpful to you in preparing for the supervised exam to look carefully at the solutions in the sample exam answer key for those problems you answered incorrectly on the sample exam.
VIII.
GRADING SCALE
Your course grade will be determined by your percentage score on the examination
using the following scale:
88-100% = A to A+
75-87% = B to B+
60-74% = C to C+
50-59% = D to D+
Below 50% = F
Tel: 1-800-444-2910