Math 251:19--20 Fall 2001

Announcements

1. In this section, the course will be divided into four parts, each leading to a form of the Fundamental Theorem of Calculus. There will be an exam at the end of each part. The exam should take about 60 minutes, so there will be time for a brief survey of the next part of the course while waiting for the Campus Bus to bring members of the class from remote corners of the New Brunswick area campus. The first exam was on Friday, September 21. It aimed for the topics in Sections 16.1 - 16.3, building on the first few sections of chapters 12, 13, and 14. See the Important Link below to the Lecture Schedule for details, including homework assignments.
2. You have approximately two weeks to complete each Maple lab assignment. Several revisions will be needed to produce an attractive report, so you should work on parts of the project whenever you have time. Lab0 was due in lecture on Tuesday, September 25, and graded labs were returned on Friday, September 28. The grade on lab0 will not be used in determining grades for the course, but it will indicate the standards used in grading the other labs.
3. Maple Lab 1 was distributed on September 21 when everyone was expected to be present for the first exam. It was due in lecture on Tuesday, October 09.
4. Maple Lab 2 was distributed when Lab 1 was collected on Tuesday, October 09. It was due on Friday, October 26.
5. The second exam was given on Friday, October 12. It aimed for Green's theorem (Section 16.4). Along the way, maxima and minima for functions of several variables were considered.
6. Warning grades will be based on exams 1 and 2 and Maple Lab 1. Late labs will be accepted, although there may be a small penalty for not submitting it on schedule. The lab work is an important part of the course since Maple allows the study of important topics that need to be freed from computational difficulties.
7. Maple Lab 3 was distributed when Lab 2 was collected on Friday, October 26. It was due on Tuesday, November 13.
8. The third exam was given on Friday, November 09. This part of the course emphasized surfaces and ended with Stokes' Theorem (Section 16.8).
9. No further Maple Labs will be assigned this semester, although some other sections will have a fourth lab dealing with triple integrals.
10. Wednesday, November 21 follows a Friday schedule, and will be the only lecture in the first part of the week of the Thanksgiving break since Tuesday will follow a Thursday schedule. This makes it a poor time to introduce any new topics, so the class will be devoted to reviewing the role of Maple as a tool for understanding multivariable calculus. The class will meet in the PC IML, LOR-023, instead of the usual classroom.
11. The fourth exam was given on Friday, December 07. All topics dealing with three dimensional integrals will be in this part, and the goal will be the divergence theorem (Section 16.9) Changes of coordinates in integrals, including the use of polar coordinates in two dimensions and cylindrical or spherical coordinates in three dimensions will also be in this part.
12. Only one class remains after the last exam. This was used to highlight the big ideas of Multivariable Calculus using examples from the fourth class exam.
13. The final exam for this course is scheduled according to the class hour formula (exam code C), so will be held on Thursday, December 20 from noon to 3 PM in the regular classroom, RAB-207. It will be an exam for this lecture section only. You can expect problems very similar to those seen on the class exams, although those that seemed to be completely understood the first time won't need to be repeated. In particular, the best way to prepare for the final exam is to work through the problems from the class exams. If you missed the lecture comparing the work done on the exam questions to what was expected, you should find someone who was there and work together on filling all gaps revealed by the exam.

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.
• Lecture Schedule for these sections with homework problems through the next exam.
• Lecturer's Home Page

Directory

• Lecturer R. T. Bumby (Office hours: TF 9:00 - 9:45 in CHM-101B)
• Recitation Instructor (all sections), Madalena Chaves (Office hours: To be announced)

Course handouts

• Maple instructions distributed in IML on Thursday, September 6.
• Maple Lab 0. This was also distributed at the meeting in the computer lab on September 6.
• Maple Lab 1. This was distributed at the first exam on September 21.
• Maple Lab 2. This was distributed at the first exam on October 09.
• Maple Lab 3. This was distributed when Lab 2 was collected on October 26.

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.

If the current notes are delayed, there will be instructions for finding similar material from Spring 2001. Although it is planned to reorder the topics, the content should be similar, so those slides should be helpful.

• Lecture 1, Coordinates and vectors in three dimensions. Dot products. Sections 12.1, 12. 2 and 12.3, September 04. viewing and printing
• Lecture 2, Lines and Curves, September 07. viewing and printing
• Lecture 3, Space Curves, Partial Derivatives, September 11. viewing and printing
• Lecture 4, Gradients, Introduction to Line Integrals, September 14. viewing and printing
• Lecture 5, Computing line integrals, conservative vector fields, components of acceleration, September 18. viewing and printing
• Lecture 6, Cross product, Planes (including tangent planes), September 25. viewing and printing
• Lecture 7, Double integrals, September 28. viewing and printing
• Lecture 8, Maxima and minima, Lagrange multipliers. October 02. viewing and printing. There is also a Maple worksheet containing solutions of three exercises (use shift-click to download the worksheet, then load it in Maple to see how the solutions were computed. Note that Maple does not get along well with internet browsers, so you may need to exit your browser before trying to view the file in Maple).
• Lecture 9, Green's Theorem. October 05. viewing and printing.
• Lecture 10, Applications of double integrals. October 09. viewing and printing.
• Lecture 11, Examples of surfaces. October 16. viewing and printing.
• Lecture 12, Surface area. October 19. viewing and printing.
• Lecture 13, Parametric surfaces. October 23. viewing and printing.
• Lecture 14, Surface integrals. October 26. viewing and printing.
• Lecture 15, Stokes' theorem. October 30. viewing and printing.
• Lecture 16, The curl of a vector field. November 02. viewing and printing.
• Lecture 17, Polar coordinates. November 06. viewing and printing.
• Lecture 18, Triple integrals; the divergence of a vector field. November 13. viewing and printing.
• Lecture 19, The divergence theorem. November 16. viewing and printing.
• Lecture 20, Maple demonstration. November 21. This is still under construction since the worksheet shown in the IML was not completely saved. Anyone with notes or suggestions should contact me. A version for viewing is available that was printed and distilled from a Maple worksheet. A version stripped of output is available for experimentation (use shift-click to copy to your directory.).
• Lecture 21, Cylindrical and spherical coordinates. November 27. viewing and printing.
• Lecture 22, Changes of coordinates in multiple integrals. Jacobians. November 30. viewing and printing.
• Lecture 23, Review (An example of integrals computed by Green's theorem and by Jacobians). December 04. Maple output . This is the last lecture for which slides or other material is available.

Homework and Workshops

Watch this space. Information will be added frequently. The Lecture Schedule has a list of homework problems that should be the basis of discussion in the recitation classes. Some of these problems may be selected for grading. Solutions to these problems should be prepared carefully. The first set of four graded problems, due on October 04, is 12.4 #26, 12.5 #24, 15.3 #16, and 15.3 #40. Another set, due on November 01, is 15.6 #5, 16.6 #36, 16.7 #20.

Exam schedule:

• Exam 1: Friday, September 21. Lines, Curves, Gradients, Line integrals. Sections 12.1-3, 13.1-2, 14.1-6, 16.1-3.
• Exam 2: Friday, October 12. Maxima and minima, double integrals, Green's Theorem. Approximate sections 14.7-8, 15.1-3, 16.4.
• Exam 3: Friday, November 09. Surfaces, Stokes' Theorem. Approximate sections 12.4-6, 15.4-6, 16.5-8.
• Exam 4: Friday, December 07. Three dimensional integrals. Approximate sections 15.7-9, 16.9
• Final Exam: Thursday, December 20, Noon to 3 PM.

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.

The sharp contrast between the grades on problems 4 and 6 and the grades on the other 4 problems indicates that more practice with line integrals is needed. This topic is one of the ingredients in Green's theorem, which is the goal of the second part of the course, so a review of this topic will not be distraction from the main purpose of the second quarter of the course.

The average on the first exam was 71.2. Only the main clusters of grades are shown in the table. They reflect qualitative diffences, but do not easily translate into estimates of letter grades. The two grades below 40 should be considered unsatisfactory. Students with grades in this range may have gaps in the prerequisites for this course and should consider dropping.

The scatter plot compares the total of all classwork (4 exams at 100 each, 3 Maple labs at 30 each, and a recitation score scaled to 60 points) to the final exam.

The average on the final exam was 144 out of 200.

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. With Lab 1 there are important definitions in the seed file, but the little beyond formatting for the second half of the project.

• lab 0
• lab 1
• lab 2
• lab 3

There have been questions about how to use Maple on a PC while saving files in your eden account. Here is information about that beyond what was in the material distributed earlier.

One approach is to use the PC as a terminal to let you work on eden. This uses a program called eXceed to allow access to other machines using the usual conventions of the X-windows systems used on unix machines. You can use this program to start an xterm shell on eden from which you can start xmaple as described in the instructions for using Maple on eden. In this case, Maple really is running on eden, so its file operations will start from your home directory on eden.

You can also run Maple on the PC. In this case, you must run WebDrive to allow Windows to treat your eden directory as another drive on your PC. The WebDrive icon on the desktop will open an ftp connection to eden to transfer files. The logon program often starts minimized, so look for evidence of WebDrive logon program on the bar at the bottom of the screen, and force it to open on the desktop. The logon will ask for your eden username and password. If the connection is successful, your eden directory will be drive X: under ``My Computer'' in all Windows file operations. In particular, if you open the directory as a desktop folder, you will see icons for any previously saved Maple worksheets. Double clicking on such an icon will start Maple with this worksheet as initial file, and saving the worksheet will save the file to the original location (which is actually your home directory on eden). You will still need to execute the worksheet before Maple learns the content of any statements in the worksheet, even if there is output from a previous use of the worksheet.