Math 151 Sections 20 - 22 Fall 2005

Fundamentals

General information about the course is available from the main course page.

We will be following, as closely as possible, the standard syllabus. You should be sure that you can do all of the homework problems mentioned on that page since they will be the basis of the common final exam.

This web page will be a source of all information about this section. In addition, a Sakai site has been created. Use of that site is not required, but I aim to use it for tools to help you assess your progress in learning Calculus. Sakai is a Course Management System that is being tested as a possible replacement for WebCT. No graded work for this course will be put on that site, but features that may be useful for Calculus will be tested. Although those who were planning to maintain Sakai sites were required to attend an intensive orientation session, it should be easy to use. You start by visiting the Sakai portal. This will take you to a Welcome screen (that looks like this screen shot). Enter your eden username and password in the boxes (in the real welcome screen, not the screen shot), and press the login button. You should be automatically enrolled in any site that has been created for one of your courses (this one is 640:151:[20-22] F05). Those sites will be shown in a row of tabs at the top of the window. Your use of Sakai is coordinated through a site called My Workspace. In particular, other sites that can be joined can be found using the Membership menu item in My Workspace. Problems using Sakai should be reported to the student help desk, 732-445-HELP. I can also demonstrate the use of Sakai during my office hours (see my personal home page for a schedule.

Schedule

This material is organized into a table with the lecture numbers serving as links to on-line versions of the lectures. For the first few lectures, those links were in a paragraph at this point of the current page, but those links have been moved. The Sakai site will also contain links in the Resources area of the site.

A selection of homework problems from the official syllabus should be prepared for collection in the recitation/workshop class on Wednesday. These problems will be taken from lectures through the previous Thursday. In particular, for September 14, you should prepare problems 27 and 67 from Appendix D and problems 6, 48, 49 and 52 from section 1.6. Homework assignments are also posted in the Resources section of Sakai site for the course. Since it is easier to add items to Sakai, that site may get updated before this one. The table is an excerpt of the standard syllabus, so you should consult that page for a full list of topics and suggested problems.

Although there is a common final exam for this course, the midterm exams are not common. The midterm exams will be held during the regular lecture period, and in the regular lecture room, on Monday, October 10 and Thursday, November 17. Topics from these exams will also appear on the final exam, along with the material covered in class after the second midterm.

The lecture 11 slides were supplemented with worked textbook problems 3.8#19 and 3.10#25.

The following announcement appears on the Sakai site, and is repeated here: "To honor my promise of no more unannounced quizzes, I am giving notice that part of the workshop period on October 26 and November 30 will be used for a quiz. On October 26, the topic will be differentiation using all rules including the chain rule. The topic of the November 30 quiz will be taken from chapter 5, details will depend on how much is covered in lecture. Note that these are quizzes devoted to a single question (possibly with several parts) to be done in about 15 minutes."

There are no slides for lecture 17; everything was done on the blackboard. Examples were numbers 7, 8, 17, and 23 from section 4.7. Exercises 7 and 8 step through the setup of these problems, encouraging the use of names for all possible variables that appear in a diagram expressing the setting of the problem. Physical restrictions on the variables (usually a requirement that certain measured quantities be positive) are also noted at this stage. The conditions expressing the relations between the variables are solved to reduce the problem to finding a maximum or minimum on a closed interval. In these cases a maximum of a positive quantity that is zero at the endpoint is to be found, so everything reduces to finding the critical value. When you have done the calculus, you need to identify exactly what is requested and that answer must be converted to a measurement. Exercise 17 had variations: (1) it turns out to be equivalent to consider the extreme values of the distance or its square; (2) the ellipse can be parameterized using sine and cosine leading to differentiation with respect to a different independent variable; (3) all ellipses with one axis being the segment [-1,1] on the x axis, and different y axis segments [-b,b] can be considered. In some cases, (-1,0) will be the point on the ellipse most distant from (1,0); in other cases (as in this exercise), some other pair of points with the same x coordinate will give the maximum distance. It was suggested that it would be interesting to identify the case separating these two results, but the blackboard was full and there was too little free space to contain a study of that problem. Exercise 23 is a classical problem, both as a calculus exercise and as an example of an isoperimetric problem which can be studied in great generality.

Grades

All components of the course will contribute to the course grade. Your grade for the course will depend on your rank in class with respect to a total out of 550 points based on the following parts:

• 200 points from final exam;
• 100 points from first midterm;
• 100 points from second midterm;
• 100 points from workshops;
•  50 points from quizzes and homework.

An attempt will be made to have the breaks between letter grades fall in large gaps between scores in this ranking.

You can find your exam scores for this course in the FAS Gradebook. The tables below show average scores for all problems, a distribution of total scores, and a distribution of time spent for the first midterm exam. In order to allow comparison, the scores have been scaled to have a maximum score on each problem of 10 points. Thus, a 15 point problem would have its average multiplied by 2/3.

This table shows results for Exam 1.

Here are some observations on the problems with low average scores. The very low score on problem 1 is troubling since these angles appear in many problems. Without a correct instinctive reaction to the numbers, you won't be able to show what you know about the calculus of the problem. Problem 6 dealt with asymptotes. It concentrated on writing the correct limit statement describing an asymptote because precise use of the language of limits, including the extensions necessary to describe asymptotes, is an important part of describing the problems of calculus. There is no excuse for the low score on problem 3: you were warned several times to expect such a problem, and reminded that you will definitely see it again on the final.

What do these grades mean? On the one hand the grades show something like a classical "curve", so only grades below 40 seem far below the general level of class performance. Other grades are reasonable at this stage of learning the subject. On the other hand, the standards by which the final exam will be graded, and the corresponding distribution of course grades require that, by the end of the course, you know the subject of this exam at the level of a grade of at least 70. In particular, in addition to being able to compute derivatives, you must reach a point where you are able to give correct descriptions using the concept of limit, including a correct use of the definition to obtain a derivative.

Here are the results of Exam 2. The average was 56.397 (with a median of 55). A scatter plot shows the comparison of grades on this exam with the score on exam 1. The line of positive slope in the figure is a regression line (the line that minimizes the sum of the squares of the vertical distances of the points). Individual scores can be found in the FAS Gradebook.

This scatter plot shows a comparison of grades on workshops, homework, and quizzes with the exam scores. In addition to the trend line, there are lines at 80%, 60% and 50%. These fall in the gaps between clusters of grades. The grade on the final exam will be needed to interpret these grades.

The final exam has been graded. Individual scores can be found in the FAS Gradebook. The gradebook entry includes the exam letter grade as determined by the grades in all sections. For the course as whole, the average grade was 112 out of 200 (with a median of 117), and one quarter of the grades were below 83 while one quarter of the grades were above 144. For this section, the average was 101.8 (with a median of 107). For this section, there were four students still on the roster who did not take the exam, 21 in the F region with grades from 38 to 84, 3 in the D region with grades from 94 to 98, 9 in the C region with grades from 100 to 114, 12 in the C+ region with grades from 120 to 137, 6 in the B region with grades from 140 to 149, 3 in the B+ region with grades from 155 to 169, 1 in the A region with grade of 178.

This scatter plot shows a comparison of the total of work during the term (including exams) and the final exam. The graph includes a trend line and grade divisions at totals of 475, 440, 400, 335, and 287. The plot reveals that the cutoff for a grade of C was adjusted to give passing grades to those who showed improvement on the final exam, so failing grades, though numerous, indicated poor performance in all components of the course. The other grade divisions stayed close to department standards for the final exam, while falling in major gaps of the total of all components.