Math 251:07--09 Spring 2001

Announcements

1. The first exam, covering the portions of chapters 12 and 13 indicated on the first handout, was held on Tuesday, February 6. Graded exams were returned in lecture on Friday, February 9. All exams should receive the same treatment: the assigned homework is the best guide to the type of problem that will appear, both in the scope of topics and as a guide to the weight given to individual topics; and graded exams will be returned in the next lecture.
2. Maple Lab 0 was collected in lecture on Friday, February 9. Graded labs were returned in lecture on Tuesday, February 13. Although the grade on this lab will not be used in computing course grades, it indicates how all labs will be graded. In particular, the instructions that call for you to insert comments into the worksheet to interpret Maple's computations are given special attention in grading, since this part of the lab requires more than passive observation of a computation of a given expression. Also the appearance of your report will become more important on later labs, since you will have learned more ways to control it.
3. Maple Lab 1 was distributed with the exam on February 6. Approximately two weeks will be allowed for its completion. More precisely, the completed labs were collected in lecture on Tuesday, February 27 -- two weeks after the return of the graded Lab 0.
4. Exam 2, covering Chapter 14, was given on Friday, March 2.
5. Maple Lab 2 was distributed on February 27, coinciding with the collection of Lab 1. Approximately two weeks were allowed for its completion. More precisely, the completed labs were collected in lecture on Tuesday, March 20.
6. Exam 3, covering Chapters 15 (section 1 thru 6) and 16 (sections 1 thru 7, except 5), was given on Tuesday, April 3. Several comments have were received shortly before that date saying that this time is inconvenient, but there was insufficient notice to allow the exam to be rescheduled. I responded individually to those who sent me mail on this, but it is also important to note here that many of the requests for a make-up exam were not valid. The only general policy concerning concentrations of exams is one dealing with final exams and is stricter than the "no more than two exams in 24 hours" phrasing that one often hears. The precise statement should be found on the Registrar's exam rule page and printed schedules of courses. Had there been more notice, this segment of the course could have been planned to use an alternate exam date, but the only way to assure that the whole class has the same information about the exam is to stick to the original schedule.
7. Maple Lab 3 was distributed on Tuesday, March 20, coinciding with the collection of Lab 2. Completed labs were due Friday, April 6.
8. Maple Lab 4 was distributed at the time of Exam 3 on Tuesday, April 3. Completed labs were collected on Friday, April 20.
9. Exam 4, covering topics on triple integrals from Chapters 15 and 16, was given on Tuesday, April 24.
10. Reading Period this semester is Tuesday, May 1 and Wedensday, May 2. On those days, there will be extended office hours from 1 to 7 PM in Hill 438.
11. The final exam will be held on Friday, May 4 from 8 to 11 AM in the regular lecture room PH-111 (the earlier announcement about a room change was incorrect and should be forgotten). While the questions on the exam should look familiar if you use your class exams to prepare, blue books will be used so you will be totally responsible for organizing the solution and identifying the answer.

Important links

• Main course page with links to the history of the course and general recommendations. Although this lecture section departs from the suggestions in many ways, there are fundamental similarities.
• Semester course Page with common features of the course this semester.
• Lecture Schedule for these sections with homework problems through the next exam.
• Lecturer's Home Page

Directory

• Lecturer R. T. Bumby (Office hours: MTW6 in Hill 438)
• Recitation Instructor (all sections), Rich Mikula (Office hours: TTh4 in Hill 618)

Course handouts

• First handout outlining course through first exam and giving some general information. This was distributed at first lecture.
• Maple Lab 0. This was distributed at the meeting in the computer lab on January 17. It is a slight rewording and reformatting of the file available on the general course page, but the problems are the same.
• Maple Lab 1. This was distributed at the first exam on February 06. It is a significant revision of the file available on the general course page, so only the version customized for these section should be used here. By the same token, students from other sections lurking here should not expect work on this version to be considered equivalent to the traditional lab.
• Maple Lab 2. This was distributed in lecture on February 27.
• Comments on Solving Systems of Equations that address some difficulties exposed by many solutions to the exam problems. This was not distributed in class, but was posted here on March 07. Illustrations were taken from the second exam.
• Maple Lab 3. This was distributed in lecture on March 20.
• Maple Lab 4. This was distributed in lecture on April 3.

Copies of slides shown in lecture.

They are in two formats: the viewing format has two slides per page, and the printing format has four slides per page. Some typographical errors may remain in these files. Since the material is typeset, it would be necessary to recreate them from the source to make these corrections, but the tools for doing this or on my home computer, so there may be some delay in making corrections.

• Lecture 1, Sections 12.1 and 12.2, January 16. viewing and printing
• Lecture 2, Sections 12.3 and 12.4, January 19. viewing and printing
• Lecture 3, Section 12.5, January 23. viewing and printing
• Lecture 4, Sections 13.1 and 13.2, January 26. viewing and printing
• Lecture 5, Section 13.3, January 30. viewing and printing. You can also download (using shift-click) the Maple worksheet shown in lecture and view it by running Maple on it from your own terminal.
• Lecture 6, Section 13.4, February 02. viewing and printing.
• Lecture 7, Sections 14.1 and 14.2, February 09. viewing and printing.
• Lecture 8, Sections 14.3 and 14.4, February 13. viewing and printing. There are also individual graphics from this lecture: A paraboloid with planes through a point parallel to the coordinate planes view 1 and view 2; and, at that point of the surface, the tangent plane and a non-tangent plane. The touching aspect of tangents are a feature of convex surfaces; an example of a tangent plane that crosses the surface was also shown (and will be added to this page when a suitable image becomes available).
• Lecture 9, Section 14.5, February 16. viewing and printing.
• Lecture 10, Section 14.6, February 20. viewing and printing.
• Lecture 11, Section 14.7 and 14.8, February 23. viewing and printing. You can also download (with shift-click) a Maple worksheet of examples shown in lecture. Executing the sheet line by line in Maple will show the calculations. Comments have been added after some of the instructions to indicate the significance of the result. Feel free to experiment with these demonstrations. For example, you can change the options on the graphs to get a clearer view of the nature of the critical points.
• Lecture 12, Sections 16.1 thru 16.3, February 27. viewing and printing.
• Lecture 13, Sections 15.1 thru 15.3, March 06. viewing and printing.
• Lecture 14, Section 15.4, March 09. viewing and printing.
• Lecture 15, Section 16.4, March 20. viewing and printing.
• Lecture 16, Sections 15.6 16.6, March 23. viewing and printing. The "Fiddling with the roof" slide is not included here since an electronic version of that page is not available.
• Lecture 17, Section 16.7, March 27. viewing and printing.
• Lecture 18, Section 15.5, March 30. viewing and printing.
• Lecture 19, Section 16.8, April 06. viewing and printing.
• Lecture 20, Section 15.7, April 10. viewing and printing.
• Lecture 21, Section 16.5 and 16.9, April 13. viewing and printing.
• Lecture 22, Section 12.7 and 15.8, April 17. viewing and printing.
• Lecture 23, Section 15.9, April 20. viewing and printing.

Homework and Workshops

The list of homework problems in the initial handout has been copied to a web page and extended through the exam on March 02. At any given time, it should show the schedule through the next exam. This list represents the problems that are closest to those planned for exams. By concentrating on even numbered problems, it was intended that these would form the basis for class discussion or graded homework. The problems are arranged in clusters, so nearby problems should illustrate similar methods. You should work as many exercises as you need in order to become comfortable with the topics in each section. Any difficulties in these problems should be explored during the recitation class. Reconciling different answers to a question can lead to an interesting class discussion.

The Main course page contains a link to list of suggested homework problems that claims to have been prepared for the Spring 2001 semester by R. T. Bumby on June 23, 2000. It is likely that the only change since that date was to assert that the list is relevant to the current semester. That list emphasized problems whose answers could be easily checked.

A few of the recitation meetings will have some time devoted to workshops. There will also be some homework problems collected for grading. Details will be announced as available, both in lecture and in this space. In particular, for Jan. 24 you should hand in your solutions to 12.1 #8, 12.3 #44, and 12.4 #26; for Jan. 31 you should hand in your solutions to 12.5 #28 and 12.5 #36; for Feb. 28 you should hand in your solutions to 14.2 #8 and #10, 14.3 #56, and 14.4 #4; for Mar. 21 you should hand in your solutions to 16.2 #20 and 16.3 #18; for Mar. 28 you should hand in your solutions to 15.3 #14 and 15.4 #18; for Apr. 18 you should hand in your solutions to 15.7 #4 and #10.

Exam schedule:

Information on grades.

There will be no attempt to identify letter grades for individual exams since the course grade depends only on properties of the list of totals of all grades. However, a report on the distribution of scores on the exams will be posted here. In the table of problem averages, scaling means that the raw score has been multiplied by 10 over the maximum score allowed for the problem to allow easy comparison between problems. (These numbers were changed on March 27 when it was noticed that the formula on the spreadsheet containing course records based averages on only a small portion of the class. Changes were slight, but the current numbers should give a more accurate description of the work of the whole class.

The grades below 60 on the first exam should be considered unsatisfactory. Students with grades in this range may have gaps in the prerequisites for this course and should consider dropping. Including these scores lowers the average to 79.28 with a median of 81, while the largest concentration of grades is around 85. The large number of perfect scores also shows that even minor slips were easily avoided. Generally, there was little on the exam to distinguish between grades in the A/B range (and possibly even including some grades of C+).

Exam 2
Prob. # Scaled Avg. 1 9.58 2 7.63 3 7.35 4 8.60 5 8.37 6 7.97 7 6.50 8 7.71 9 8.65		Range Count 100 2 97-99 5 93-96 12 88-92 12 83-87 10 77-81 4 71-73 5 65-69 6 below 60 7

The average for the second examwas 80.96. Since there was the opportunity to get much lower grades, and a limited range of higher grades, the median was much higher (the table shows it to be around 85). Nine more did not take the exam, although they are still listed on the roster.

To determine mid-term (warning) grades, a sum of exam scores below 120 was considered unsatisfactory. A scatter plot showing the relation between grades on the first two exams has been added this part of the current page.

Exam 3
Prob. # Scaled Avg. 1 8.17 2 7.26 3 4.48 4 7.01 5 2.65 6 5.99		Range Count 88-100 6 78-83 8 69-76 11 59-67 13 49-57 12 45-47 4 25-41 11

For the third exam, we have a two scatter plots: one comparing scores to the sum of the scores on the first two exams, and one showing scores separated by the number of lecture attendance sheets that were signed between the second and third exam. The average was 61.7; the median for this exam was 61.

Exam 4
Prob. # Scaled Avg. 1 5.32 2 9.00 3 3.58 4 9.42 5 8.23 6 6.58		Range Count 98-100 3 87-93 4 80-85 6 75-78 9 67-73 9 62-65 8 56-60 6 49-51 3 40-45 7 28-32 4

The scatter plot shows the result on this exam compared to the sum of the first three exams. The average score on this exam was 65.8 with a median of 67.

Final Exam
Prob. # Scaled Avg. 1 8.03 2 8.21 3 6.60 4 6.75 5 5.60 6 7.71 7 6.24 8 7.56 9 5.93 10 6.68 11 8.15 12 7.41 13 5.21		Range Count 200 3 186-196 6 174-180 4 168-171 2 155-164 8 142-150 7 130-139 7 115-125 12 89-106 10 25-67 4

The scatter plot compares the 400 point classwork total (exams, homework, and Maple labs) to the 200 point final exam. The average score on the final was 137.4. The trend line is pulled down by a few scores that were very low. These should be re-examined before grades are finalized. Use of familiar problems on the final exam allowed very high grades, but also magnified any gap in preparation for those problems.

Grades for the course have been submitted. When I get past the clutter in my mailbox, I will respond to e-mail messages for information on the exam and course grades. There were 10 grades of A, one TB+ that would be an A except for a missing fourth Maple lab, 13 other grades of B+, 8 grades of B, 13 grades of C+, 9 grades of C. There were 6 grades that were recorded as TD to indicate that they were below the standard for a C, but this could be attributed to a lack of Maple labs. The remaining 13 grades contain a mix of W, TZ, and F: those who remembered to drop the course have W; one who left after one week and submitted no work that could be graded has a TZ; one student with a weak record was not on the final roster, so no grade was reported; all other grades were required to be recorded as F even if the course was not completed. Only two grades of F included a grade on the final exam.

Maple Lab seed files.

To transfer file to current directory by ftp, use shift-click (there should be a less awkward way, but I couldn't make it work). This gives you your very own copy of the file which you can open in Maple. The Save command in Maple will replace the file opened by Maple with the current contents of your worksheet. If you want to save several generations of your work, use the SaveAs command to save the current worksheet under a new name. The seed file contains the Maple instructions that are in the printed description of the lab. Simple instructions that you learned about in previous labs are left for you to construct in the form that you need them.

The seed file for Lab 0 leaves you little more than the task of executing the worksheet line by line and editing the result.

The seed file for Lab 1 contains the definitions of the vector operations in a form suitable for this course, and ends with a definition of the vector (actually using the Maple datatype of a "list") r (although one talks about a function r(t), the calculation should be done with this expression r). You are responsible for creating the plots and translating the formulas described in the printed description into Maple instructions. As the first step in question 3, you should give the instruction "v:=diff(r,t);" since many of the formulas are based on having something called v available.

The seed file for Lab 4 specifies a different region for the plot in (1a) than given in the printed instructions. You may use either definition of the region in your report. Since the interval will be refined in (1c), it is more appropriate that the plot in (1a) use the simplest region containing the whole intersection, which is the one given in the seed file. Warning: The situation is more serious. Equation (1) of the description introduced a coefficient of 2 before the x² term that should not be there, and is not present in the definition of z1 in the seed file. The description of how the graphs should behave was based on the definition in the seed file and not on the equation (1). Everything should behave better if you use the formula from the seed file.

• lab 0
• lab 1
• lab 2
• lab 3
• lab 4