
	Department of Mathematics and Computer Science

Notes for Calculus Classes

UNDER ON-GOING REVISION

by D. C. Smolarski, S.J.

DISCLAIMER: The contents of this page, with the exception of text quoted verbatim from official university publications, represent the opinions and preferences of the author, and should not be interpreted as official policies of Santa Clara University or its Department of Mathematics.

Grades and Subsequent Courses

The undergraduate bulletin of Santa Clara University contains the following statements, which is the published policy of the Department of Mathematics and Computer Science regarding grades in prerequisite courses:

(For Math 12:) A grade of C- or higher in MATH 12 is strongly recommended before taking MATH 12.

Although this admonition is not as strong as the published requirement for Chemistry 12 (where the student must have completed the prerequisite course with a grade of C- or better or cannot register for the subsequent course) or the requirements published at other schools (e.g., at UC Santa Barbara, a student cannot register for the 2nd Calculus course (Math 3B) without a minimum grade of C), the intent is similar.

Therefore, students who receive a grade less than a C- in a calculus course should normally retake the course before enrolling in the next course of the sequence.

Homework

Homework is precisely that: Work to be done at Home.

Thus, homework is not work that is done at the beginning of class when difficult problems are reviewed by the professor. Homework is meant to help a student understand the concepts presented in the previous class and is meant to be performed when a student reviews the class lecture and prepares for the next class period. Students who encounter difficulties in completing a homework assignment should discuss such difficulties during the professor's office hours before the class at which the assignment is due.

There is a significant amount of material scheduled to be covered during the quarter, and there is very little time available for any professor to do all homework problems at each class period. In addition, in most mathematics courses, many concepts build on other ones. Homework is a means to help reinforce the foundational concepts to provide a basis for subsequent concepts. For this reason, in many elementary level courses, it is highly desirable that students complete mathematical assignments as soon as possible after they have been assigned, to provide them with the knowledge and skills needed for other material.

Lectures in university-level courses are meant to be a forum in which new material is presented and old material which may be confusing is reviewed. It is not intrinsically a forum in which assignments are reviewed although, occasionally, if a great number of students have questions about the same topic or homework problem, and could not see the professor during office hours, then such review might be appropriate.

My policy is that Calculus homework is to be turned in at the beginning of a class period. Only after all the homework is submitted, do I answer questions about the homework.

Some students may disagree with this policy, arguing that they did not have a chance to complete all the problems. In response, I argue that (1) overall, the homework counts only 10% of the total grade so a few problems not completed would not affect a person's grade that much; (2) problems which caused significant problems should, as a general rule, be discussed with the instructor outside of class, during office hours.

How to Best Make Use of Study Sheets (Previous Exams)
or How to Avoid Flunking a Midterm

Some instructors make previous exams available to students to be used as "study sheets" or "practice exams." There is a right way and a wrong way to make use of such resources.

The wrong way is to "do" the sample test with textbook and classnotes open, with unlimited time, and withOUT ever checking to see whether your answers are, in fact, correct. Students who take this approach usually do very poor on the "real" exam. An equally wrong way is to obtain the correct answers for the sample exam and merely examine the answers, thinking, "Oh yeah, I know how to do that!" Students who take this approach also usually do not do well on a "real" exam.

The problem with these approaches is that a student may not realize that he or she actually did not obtain the correct answer unless the answers are checked or will not know whether he or she will remember the correct approach to solving a problem during a real exam.

The right way to make use of practice exams is to work on the problems in a "test" environment. In other words, without notes or book, a student "takes" the test in a limited amount of time and then checks the answers against the posted correct answers. Those problems in which incorrect answers were received should be examined specially, and if a student is confused about techniques or theory, the instructor should be consulted.

The right way to study for the final includes reviewing all the midterms as well. In particular, problems that were missed on the midterms should be reworked until they can be done correctly.

Fr. Smolarski has been known to put problems on the final which previously appeared during the quarter on midterm exams. (He has also been known occasionally to put one or other problem from a sample example on the current quarter's exams.) Instead of the class doing better on such problems than on those they have not seen, statistics show that the class, as a whole, in fact does not do significantly better on those problems the second time than they did the first time. This indicates that many people did not review the earlier exams nor did they attempt to "learn from their mistakes."

Web Resources

There are many resources on the Web in the form of interactive tutorials, practice quizzes, graphical demonstrations, etc., related to Calculus concepts. One can find some of these by searching the Web using keywords such as calculus, tutorial and graphics.