Math 251:05--06 Spring 2003
Announcements
- The first recitation class on Wednesday, January 23 met in the InstructionalMicroLab in ARC instead of the scheduled location. This meeting was devoted to an introduction to the Maple Symbolic Computation program. Printed copies of the Maple Instructions and the description of Maple Lab0 were distributed at this meeting. In this class, the seed file for the lab was obtained from the course web page, Maple was started and work on Lab0 was begun. Students were shown how to recognize common mistakes encountered in Lab0 and shown how to save work in an eden directory in order to continue working on the lab. For subsequent labs, no printed material will be distributed. Students will be responsible for printing the lab description from the file on the web site.
- 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 is due in lecture on Tuesday, February 4., and returned on Tuesday, February 11. 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 four labs. Lab 1 was due on Friday, February 21. The functions defined at the beginning of Lab 1 allow vectors to be represented as lists. This makes some things easy, but it requires that these functions be used for all operations, including multiplying vectors by scalars of scaling the vector r' to get the unit tangent vector T. If this is not done, the formulas for curvature will not simplify even though it appears that you are correctly representing the formulas in Maple. To allow some time for evaluation of the results of lab 1 without falling too far behind schedule, the due date for lab 2 was extended until the first class after Spring Break, Tuesday, March 25. Lab 3 was due on Friday, April 11. Lab 4 will be due on Friday, April 25.
- 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. The first exam is scheduled for Tuesday, February 11. It aims 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 and the exam schedule below for a list of topics for all exams.
- The final exam for this course is scheduled according to the class hour formula (exam code C), so will be held on Monday, May 12 from 8 AM to 11 AM in the regular classroom, SEC-117. 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.
- See Lecturer's Home Page and Recitation Instructor's Home Page for office hours during Reading days, May 6 and 7.
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
- Recitation Instructor's Home Page
Directory
Electronic addresses are collected here for your convenience. You should seek help as soon as you notice a need. An exam is always coming soon.- Lecturer R. T. Bumby (Office hours: M 4:30 - 7:00, or by appointment, in Hill Center 438)
- Recitation Instructor (all sections), Aaron Lauve (Office hours: M 2:50--4:10PM Hill Center Rm 605-B)
Course handouts
Adobe Acrobat format. You should be able to view and print from your browser.
- Maple instructions distributed in IML on Wednesday, January 23.
- Maple Lab 0. This was also distributed at the meeting in the computer lab on January 23.
- Maple Lab 1.
- Maple Lab 2.
- Maple Lab 3.
- Maple Lab 4.
Copies of slides shown in lecture.
Since we meet in an Enhanced Classroom, lecture demonstrations will normally (after the first week) use a computer, and the same files can be posted here for re-viewing. This format is not practical for printing. Printable summaries will be produced before each exam.
Similar material from Spring 2001 or Fall 2001 produced from the source of the transparencies used in those lectures is also available. Although it is planned to reorder the topics, the content should be similar, so those slides should be helpful.
Current material is delayed due to the change in format. Lectures 1 and 2 will be here soon. Lecture 3 is available as basic slides. The format will evolve during the semester to make better use of the projection equipment. Watch this space!
A printable digest of all lectures in the second quarter of the course will be posted along with the lecture on Tuesday, March 4. No new examinable material is expected to be included in the lecture of March 11, so it need not be included in the digest.- Lecture 3, space curves; tangent vectors; introduction to line integrals. Sections 13.1, 13. 2 and 16.2, January 28, as shown in lecture.
- Lecture 4, More line integrals; arc length. Sections 13.3 and 16.2, January 31, as shown in lecture.
- Subsequent slides will be password protected. The purpose is only to remove the temptation to copy or print these slides. A printable summary will be posted at the end of each segment of the course. The password for all files will be the University's designation of lecture room in the format XXX###. Try it with Lecture 4.
- Lecture 5, Partial derivatives, chain rule, gradients. Sections 14,3, 14.5, 14.6, February 04, as shown in lecture (password protected, as described above).
- Lecture 6, Curvature, velocity and acceleration, the fundamental theorem for line integrals. Sections 13.3, 13.4, 16.3, February 07, as shown in lecture (password protected, as described above).
- Lecture 7, Equations of lines and planes, intersections, cross products. Sections 12.4, 12.5, February 14, as shown in lecture (password protected, as described above). The prepared slides did not get as far as I intended, but a future augmented summary is planned.
- Lecture 8, Tangent planes, gradients, maxima and minima. Sections 14.4, 14.6, 14.7, February 21, as shown in lecture (password protected, as described above). One slide listed the exercises done at the end of Lecture 7. Towards the end of this segment of the course, a printable version of the material on these slides will be posted that will include corrections.
- Lecture 9, Lagrange Multipliers, Iterated integrals. Sections 14.8, 15.3, February 25, as shown in lecture (password protected, as described above).
- Lecture 10, Calculation of iterated integrals, polar coordinates, applications. Sections 15.4, 15.5, February 28, as shown in lecture (password protected, as described above).
- Lecture 11, Green's Theorem. Sections 16.4, March 04, as shown in lecture (password protected, as described above).
- Printable file with all slides from lectures 7 through 11.
- Lecture 12, Examples of Surfaces. Sections 12.6, March 07, as shown in lecture (password protected, as described above). An application of Green's Theorem to the change of variables in double integrals is also included here. The proof was done in the generalityof section 15.9 because it is no more difficult than the special case of polar coordinates, which is the only alternate coordinate system we have introduced at this point of the course.
- Lecture 13, Surface Area. Sections 12.4, 15.6 March 14, as shown in lecture (password protected, as described above). The cross product gives areas of plane polygons. This leads to a relation between areas of figures and the areas of their projections. For any plane figure, area is then given are the integral of a constant function over a projection of the figure. It seems reasonable to assume that the area of pieces of tangent planes over a projection of a part of a general surface will approximate susrface area. For smooth surfaces, these expressions are Riemann sums of an integral that we define to be the surface area integral.
- Lecture 14, Parametric representation of surfaces; Surface (flux) integrals. Sections 16.6, 16.7. March 25, as shown in lecture (password protected, as described above).
- Lecture 15, Stokes' Theorem, Section 16.8 (and curl, part of Section 16.5). March 28, as shown in lecture (password protected, as described above). There are some misprints that should be obvious on these slides that will be corrected when they are combined into a summary.
- Lecture 16, A look back at surface area, surface integrals, and parameterization of surfaces, April 01, as shown in lecture (password protected, as described above).
- Printable file with all slides from lectures 12 through 16.
- Lecture 17, Introduction to triple integrals, Section 15.7, with a review of methods used for double integrals, April 08, as shown in lecture (password protected, as described above). There is also a Maple worksheet that will show you how one of the figures was obtained and allow you do further experiments with graphing figures from this type of description.
- Lecture 18, The divergence theorem, Section 16.9, (and the divergence of a vector field, part of Section 16.5), April 11, as shown in lecture (password protected, as described above).
- Lecture 19, Cylindrical and Spherical Coordinates, Sections 12.7 and 15.8, April 15, as shown in lecture (password protected, as described above).
- Lecture 20, Changes of Coordinates and Jacobians, Section 15.9, April 18, as shown in lecture (password protected, as described above).
- Lecture 21, Integrating over a general tetrahedron, April 22, as planned to be shown in lecture (password protected, as described above). This example ties together the different topics in this segment of the course.
- Printable file with all slides from lectures 17 through 21.
- Lecture 22, More changes of coordinates, April 25, as shown in lecture (password protected, as described above).
- Lecture 23, Overview of integrals, May 02, as shown in lecture (password protected, as described above).
Homework and Workshops
The Lecture Schedule has a list of homework problems that should be the basis of discussion in the recitation classes. There will also be quizzes in recitation. Quiz questions should be similar to homework exercises.
Exam schedule:
- Exam 1: Tuesday, February 11. Lines, Curves, Gradients, Line integrals, the fundamental theorem for line integrals. Sections 12.1-3, 12.5 (part), 13.1-2, 13.3 (part), 14.3, 14.5-6, 16.2-3.
- Exam 2: Tuesday, March 11. Planes, cylinders, quadric surfaces, tangent planes, max-min for functions of at least variables (including constrained extrema), double integrals in rectangular and polar coordinates and their applications, Green's theorem. Sections 12.4-6, 14.4, 14.6-8, 15.3-5, 16.4. Here is a printable file of all relevant slides.
- Exam 3: Friday, April 04. Surface area, surface (flux) integrals, Stokes' theorem. Sections 12.4, 15.6, 16.5-8. Here is a printable file of all relevant slides.
- Exam 4: Tuesday, April 29. Triple integrals, the divergence theorem (including additional work on the surface integrals appearing in its statement), changes of variable, cylindrical and spherical coordinates. Sections 12.7, 15.7-9, 16.5 (divergence), 16.9, and supplementary notes. Here is a printable file of all relevant slides.
- Final Exam: Monday, May 12, 8 - 11 AM. Exam questions will be based on questions from the class exams. No new topics will be introduced.
Information on grades.
The course grades will be based on a ranking on a 700 point scale composed of the following items:
- Four class exams, 80 points each, total 320. Expected time for each class exam will be 60 minutes. This allows time before the exam for last minute questions and a preview of the next segment of the course. This buffer will protect the exam from being disrupted by students arriving a little late.
- One three hour final exam, total 200.
- Four graded Maple Labs, 20 points each, total 80.
- Recitation grade, graded homework and possibly some quizzes, total 100.
An effort will be made to respect any clustering of grades in assigning course 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.
Exam 1 has been graded. If you want to check the grades that I have recorded for you, you can find exam scores in the FAS Gradebook. The average on exam 1 (including only those taken at the scheduled time) was 58 and the median was 59.
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Exam 2 has been graded. If you want to check the grades that I have recorded for you, you can find exam scores in the FAS Gradebook. The average on exam 2 (including only those taken at the scheduled time) was 47.9 and the median was 49. The grade distribution will be shown using the attained grades in clusters of irregular size.
The scatter plot shows the comparison of grades on the first two exams with a trend line (of positive slope) and a line (of slope -1) distinguishing unsatisfactory performance (leading to W1 or W3 warnings) from satisfactory performance.
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Exam 3 has been graded. If you want to check the grades that I have recorded for you, you can find exam scores in the FAS Gradebook. The average on exam 3 (including only those taken at the scheduled time) was 41.24 with a median of 39.
The scatter plot shows the comparison of grades on the third exam with the sum of the first two exams with a trend line (of positive slope) and a lines (of slope -1) distinguishing several levels of performance. A total of 195 marks the bottom of a possible A-B+ cluster; 170 is the bottom of the B range; 155 the bottom of the C+ range; and 100 separates C from unsatisfactory grades.
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Exam 4 has been graded. If you want to check the grades that I have recorded for you, you can find exam scores in the FAS Gradebook. The average on exam 4 (including only those taken at the scheduled time) was 40.6 with a median of 43.
The scatter plot shows the comparison of grades on the fourth exam with the sum of the first three exams with a trend line (of positive slope) and a lines (of slope -1) with totals of 275, 225, 180 and 140 distinguishing several levels of performance.
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Another scatter plot has been prepared showing the role of Maple in
preparing for exams. The horizontal axis shows the total of the four
Maple labs and the vertical axis the total of four exams. Beyond the
simple trend line, the plot reveals that very high score on the labs
(around 70 out of 80) correspond to exam totals above 260. Otherwise,
the trend line follows a concentration of grades, although there is a
wide range of exam scores on both sides of the trend line.
The Final Exam has been graded. If you want to check the grades that I have recorded for you, you can find exam scores, together with the course grade in the FAS Gradebook. The average on the exam was 116 out of 200.
The scatter plot shows the comparison of grades on the final exam with total of all classwork with a trend line (of positive slope) and a lines (of slope -1) with totals of 585, 520, 455, 390, 320, and 290 distinguishing the letter grades: A, B+, B, C+, C, D, F. Grades of D are given only in special cases. In this course, the grade is recorded as TD, signifying that completion of the Maple labs would allow a satisfactory grade to be assigned.
Note that final exams are kept on file for one year. You should contact the lecturer to review your exam during this time.
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Maple Lab seed files.
You will need to save a copy of the seed file to open in Maple. There are several ways to get this copy: (1) click the right mouse button on the link to get a context menu and select save to disk; (2) press the shift key and click the left mouse button to get the save to disk dialog directly; (3) if your browser shows you the file as text, use the SaveAs item on the file menu to save a local copy. There is a better method, introduced in December 2002, but it requires some preparation. The math department web server now defines all files with extension mws as mime-type application/x-maple. This means that you can configure your web browser to do something useful in response to an ordinary left click on the link to such a file. In Netscape, select preferences from the edit menu, expand the Navigator submenu an select Applications. This will allow you to add this type and instruct the browser to Save to Disk. (It is also possible to have the browser start xmaple, but this is not recommended on eden because Netscape reserves too many colors for its own use and this causes Maple to behave strangely.)
This page changes frequently. If you don't see what you expect, use the "refresh" command of your browser to get a fresh copy. Uploads are sometimes delayed, but the aim is to get everything here when it is needed.
Comments on this page should be sent to: bumby@math.rutgers.edu
Last updated: May 14, 2003