MATH 263C - Analytic Geometry and Calculus
Four Quarter Hours

I. PREREQUISITES
Successful completion of Mathematics 263B or equivalent.

II. COURSE DESCRIPTION
The main topics covered in 263C are: sequences, infinite series of constant terms, infinite series of functions (and especially power series), conics, polar coordinates, parametric representation of plane curves and curves in three-space, and vectors in three-space. The material presented is well-suited for students in mathematics, engineering, and the sciences, as well as for liberal arts students.

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.

IV. COURSE CONTENT
The course covers Chapters 11, 12, 13 (partially) and sections 14.1-14.4 of Chapter 14, in the text by Varberg and Purcell. The following sections are omitted: 12.3, 12.4, 12.5, and most of Chapter 13, except for Section 13.1. In addition, you can omit the material on the Binomial Series, pages 565-566, and the topic of "tangents in polar coordinates," pages 618-619.

In Chapter 13, read Section 13.1 through Example 4, page 627. Omit Section 3.5, and read sections 13.2, 13.3, 13.4 lightly—only enough to learn the main definitions and results. In this course, your study of vectors is directed primarily to vectors in three-space (Chapter 14) rather than to vectors in the plane (Chapter 13). In fact, for the purposes of this course, it isn't really necessary for you to work problems from Chapter 13 in preparing for the supervised examination.

Make sure you know the rule for differentiating a vector-valued function (given in the "rectangular box," at the top of page 649), and the rule for integrating a vector-valued function as given at the bottom of page 649. Also of considerable importance in Chapter 13 are Theorem A, page 648, Theorem B, page 649, and the definition of the statement at the top of page 648.

In general, throughout your reading of each assigned section, you should learn the definitions of the terms given in bold-face type.

V. EXAMINATION
The course examination for Mathematics 263C in this format is a comprehensive supervised examination consisting of problems covering the material you are responsible for in Chapters 11, 12, 13, 14. The problems are similar to the basic problems in the textbook, and very similar to those in the Sample Examination.

You will have three hours to complete the supervised examination. A hand-held calculator with basic arithmetic and square root functions will not really be needed, but may be used on the examination if you supply your own. Programmable calculators MAY NOT be used.

Note: You will not be required in the examination to prove theorems. However, it is important for you to know what the theorems say and be able to apply them

VI. PREPARING FOR THE EXAMINATION
The most effective way for you to prepare for the examination is to concentrate on solving problems (especially the non-proof type 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. After this, you should work typical problems from each of the assigned sections in the textbook. Some of the higher-numbered problems in the various sections are quite hard, and you will not be held responsible for working these kinds of problems on the supervised examination.

VII. SAMPLE EXAMINATION
A self-check Sample Examination is included with the course credit by examination booklet. There is also an answer key which gives the answers to all problems in the sample examination. The solutions to these problems are given in considerable detail, so that you can follow completely the steps and methods required to solve each problem. The sample examination is provided to 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 books or notes. Finally, evaluate your answers to the sample exam problems using the sample exam answer key.
Sample Examination

If you did not do well on the sample examination, then review more extensively those troublesome areas before applying for the examination. As mentioned earlier, the problems on the supervised examination will be very similar to those on the sample exam. Hence, it should be beneficial to you in preparing for the supervised examination to look carefully at the sample exam answer key for those problems you missed on the sample exam.

VIII. GRADING SCALE
Your course grade will be determined by your percent 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