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Fall 2003 Math 208H Home Page

Welcome to the Math 208H, Honors Calculus III, home page. You're probably here for information, so let's start with the vital statistics of the course.

Essential Information

Honors Calculus III Course Resources

You might be surprised at how much information can be found on the WWW. Go to your favorite search engine (like the Yahoo site listed on my home page) and try searching on "vector-valued function". See how many web pages you hit and visit a few interesting looking sites.

Announcements

Notes and FAQ

12/27/03: About Final Exam and Grade Results...
Final exams were graded last week. The median grade for the regular sections was about 143, while our median was 167. I'm very pleased with the class performance. It was quite comparable to performance in the hour exams, so evidently there was no let-down for the final. Great job, everyone! Grades are posted outside my office and should be in the mail as well. If anyone wants to see their exam or project 2 results, drop by my office sometime. In the meanwhile, have a great break!

11/20/03: About Our Dead Week Schedule...
Here is a schedule for Dead Week. Hopefully, this will help you focus your review efforts. The topics are not set in concrete, and I'll answer questions on any problems if the class so wishes. However, I'll give preference to questions relating to the topic to be covered according to the following schedule:
  • Monday: Chapters 10-11.
  • Wednesday: Chapter 12 (we will also do class evaluations on this day.)
  • Thursday: Chapter 13.
  • Friday: Chapter 14.
11/20/03: About Sample Unit Exams...
I received this message from the convenor of the course:

"There are two old exams now available at the two bookstores (not Kinko's). ... Note that the old finals were written for the Hughes-Hallett (HH) text. The topic list has changed only marginally. In particular, HH did not do integrals of scalar functions over curves and surfaces, so these topics are not represented on the old exams. Vectors in HH are always given with the i,j,k notation. The spherical coordinate system is the same, although HH list theta before phi and SM list phi before theta. There may be some other notational differences as well. There could also be problems involving contour plots that would be less likely to appear on a final written for the SM text. HH also did more with global extrema on unbounded regions and less with global extrema on bounded regions."

11/20/03: About Project 2...
Several students have asked me about item 2 of the Project. The idea here is to identify a simple region in uvz-space (like a box with sides parallel to the u- , v- and z-axes). Now work backwards to the image of this simple region in xyz-space. Get a region in xyz-space that would be hard to integrate because of the boundary. Since the z variable is the same in both coordinates, you need only focus on u,v.
Regarding item 3, you don't need to know how to find the inverse of a jacobian matrix. Your calculator understands matrices, vectors and their arithmetic. For example, on the 86 you could type

[[1,5][3,7]] STO A [ENTER]
[[3][4]] STO b [ENTER]
A[2ND x^-1]*b [ENTER]

You'll get the output of inverse of A times b. There is even a matrix editor. Look at the documentation. The 89 is just as easy, if not easier. In fact, there's a bonus with the 89: It does symbolic matrices, so you could actually use the explicit Jacobian. In either case, you might want to write a simple program to automate the calculations, although in the case of the 89 it's fairly easy to do the whole thing symbolically.

Along these lines I was asked other questions by email, and I'm going to post them and my answers:

We know that we have to work backwords from uv space and we have set an easy shape there but we are having touble getting what the shape should look like in xy space. Are we just supposed to plot points using the conversions to find the region or are we missing an easier (more mathematical) way of finding what that region should look like. Any help you can offer or pages in the book we could look at to refresh our memories on a process we are missing would be very helpful.

No, you shouldn't just plot points. The simplest example of what I want you to do would be analogous to a double integral over a circle centered at the origin. When you convert to polar coordinates, it becomes an easy iterated integral in r-theta space over a rectangle. Look in Section 13.3 for other conversions from "hard" xy-integrals to "easier" rtheta-integrals. You should look for the same sort of thing except in parabolic coordinates. You have to work backwards from a simple shape in uv-space to something in xy-space. For example, if you start with the unit square 0 <=u,v <k=1 in uv-space, then the segment along v=0 corresponds in xy space to the segment 0<=x<=1/2, and the vertical segment u=0 corresponds to the segment -1/2<=x<=0. The point is, when you choose a particular curve in uv-space, you can often figure out what it corresponds to in xy-space. Use this to make an irregular plane area in xy-space that simplifies in uv-space and then set up the "hard" integral in xy-space.

I was wondering how much you were looking for with the introduction, as far as defining determinants and the Jacobian matrices.š I can see that there is the possibility of having a pretty short to the point description and explanation of the two terms, but I can also see the possibility of trying to go pretty in depth also.š I was wondering which route you were looking for us to take on the subjects.

"Short to the point" is sufficient provided it is lucid and complete.

Project 1

Rules of the game:

  • Due Date: Wednesday, October 8
  • Points: 18 (2 for each part of exam)
  • Get a copy of the Project Hour Exam if you don't already have one (click on URL above).
  • Work out all problems on the exam correctly. Put your complete answersin the space provided.
  • Write neatly and clearly.
  • Use complete mathematical sentences and clear explanations.
  • Give some indication of point values for parts, thus making your solutions suitablefor a grading key.
  • Your target audience for readability is not the instructor, but fellow students.

Gateway Information for Students of Math 208H Fall 2003

Rules of the game:

  1. All students of Math 208H must take both the Differentiation and Integration Gateway exams.
  2. The Gateways exams for credit are proctored. For information on times and places check the Gateway schedule. However, you may take a practice exam from any location.
  3. In order to take a Gateway exam for credit you must sign up first. See the signup directions below.
  4. The times for our exams differ from the times listed at the schedule site and are as follows: Differentiation, September 8-18; Integration, September 8-25.
  5. Only one attempt for credit per day is allowed.
  6. There is a 60 minute time limit on exams for credit.
  7. A score of at least 8 out of 10 is considered passing on the Differentiation exam and 5 out of 6 is passing on the Integration exam.
  8. Your highest score on any attempt is the one that will be counted.
  9. A maximum of 20 points will be given for each exam according to the following formula: let X be the number of incorrect answers and Y the number of questions. Then the resulting points earned are (whether you passed the Gateway or not):
        POINTS = 12*(Y-X)/Y + 8*min(1,max(100*(Y-X)/X - 79,0))

Signup Directions:

  1. Go to this URL. (This is our home website for the Gateway. You might want to bookmark it.)
  2. On the student menu, click "Register for this class".
  3. Fill in the form. Note that you choose your own login and password.
  4. Click "OK" and verify or correct your entries.
  5. If you happen to forget your password, register again using the same name and new login. Your instructor can use the system to combine your old records with the new ones.

Class Policy Statement

Course: Math 208H - Section 001, Honors Calculus III

Place/Time: 304 OldH, 9:30-10:20 MWRF, Fall 2003

Preq: Math 107 or equivalent, and invitation or admission to UNL Honors Program.

Objectives: This is basic skills course whose goals are to help students achieve competence in these areas:

  • Understanding concepts of vector and multivariate calculus.
  • Proficiency in the mechanics of vector and multivariate calculus.
  • Use of vector and calculus concepts in mathematical modeling.
  • Expression of mathematical ideas through writing.
Instructor: Dr. Thomas Shores

Telephone: Office 472-7233 Home 489-0560

Email: tshores@math.unl.edu

Web Home Page: http://www.math.unl.edu/tshores/

Office Hours: Monday 2:00-3:30, Wednesday 10:30-12:00, Thursday 1:00-3:00, Friday 8:00-9:30, and by appointment. Office: 834 OldH

Class Attendance: Is required. If absent, it is incumbent upon the student to determine what has been missed as soon as possible. It is advisable to consult with the instructor. There will be no makeup exams.

Homework/Projects: Everyone is expected to master the syllabus homework assignments. These will not be graded, but at least one question on each exam will come directly from these problems. Therefore, students are strongly encouraged to work them and ask questions about them in and outside of class. There will be two writing projects to be done in groups of two. Students will be given an account in the Mathematics Computer Lab and are expected to attend a lab orientation session if they have not already done so. Current information about the course will be available through this lab account and the WWW (via the Math 208H homepage or my home page.) Using the web is is recommended for keeping track of due dates for projects and current activities in the course.

Reading Assignment: Read the sections of the text as, or before, they are covered in class lectures. This is a standing assignment throughout the semester.

Grade: Six 50 minute exams will be given and these will account for 70 points each. The final exam will count 200 points. All exams are closed book with calculators. The projects will count 40 points and Gateway exams 40 points. See the syllabus for a schedule of events. The final grade will be based on these 700 points.

Final Exam: Will be comprehensive. To be given on Tuesday, December 16, 6:00-8:00 pm in a room TBA.

Grades of "I", "W" or "P": These grades will be given in strict accordance with University policy. (See any Schedule of Classes for the relevant information and dates.)

Keep This Information!!!

Syllabus for Math 208H, Fall 2003

  • [TEXT:]Calculus, 2nd Ed., Smith and Minton, McGraw-Hill.
  • [SCHEDULE:]Unless announced otherwise in all sections, all topics listed herein will be possible topics on the common final. However, the daily schedule in your section could well be different from that listed below. In particular, the schedule assumes that your class meets MWRF and not MTWF.
  • [DAILY WORK:]Do the reading from the sections to be covered before coming to class each day. Your instructor will be planning class activities assuming you have done the reading. The exercises suggested below represent a minimal assignment and should also be done as the material is covered. Some students may have to work additional exercises from the text to attain sufficient mastery of the material.
  • [OTHER ASSIGNMENTS:]Your instructor may assign a group project or other take-home work for grade. Your instructor may collect homework, give quizzes, or schedule more than the three exams listed in the schedule.
  • [CALCULATORS:]You will be permitted to use any calculator on the final exam. Your instructor will decide whether or not calculators are allowed on hour exams.
  • [FINAL EXAM:]The time for the final exam is 6:00-8:00 pm, Tuesday, December 16, Room TBA. You are expected to arrange your personal and work schedule to allow you to take the exam at the scheduled time. Students with conflicting exam schedules may be allowed to take an alternate final, which is always given after the regularly scheduled final. No student will be allowed to take the final exam early. A picture ID (driver's license or student ID) is required to take the final exam.

       
WEEK DATES SECTIONS EXERCISES
1 Aug 25-29 10.1 3, 19, 20, 27, 32, 35, 36, 41, 42, 53, 55, 57, 62
    10.2 5, 8, 11, 21, 28, 35, 41, 44, 51, 53, 63
    10.3 5,13,15,18,21,24,29,33,38,39,41,44,47,49,50,53,56,61,66
    10.4 9, 13, 19, 25, 27, 57-60, 67, 69-72, 77
       

2 Sept 1 (no class) Labor Day
  Sept 2-5 10.5 2, 5, 8, 9, 17, 24, 26, 27, 30, 33, 35,41,45,46,49,55,57,62,67
    10.6 2, 5, 7, 15, 17, 22, 24, 37, 44, 45, 50, 52, 53, 60
    11.1 5-9, 11, 18, 22, 28, 31, 35, 45, 47
    11.2 5, 7, 9, 11, 14, 17, 19, 20, 22-24,29,31,32,36,40,44,46,51,52
       


Friday, September 5, is the last day to withdraw from the course and not have it appear on your transcript.

3 Sept 8-12 11.3 11, 14, 25, 27, 28, 34-36, 43, 44, 45
    12.1 7, 13, 19, 20, 21, 39, 40, 42, 44, 51-56, 60,65,66,68,70
    REVIEW  
    EXAM 1  
       

4 Sept 15-19 12.2 3, 5, 11, 14, 15, 19, 24, 35, 38, 49
    12.2 1, 4, 27, 30, 39, 43, 44, 45, 51-56,58,59
    12.3 3, 4, 7, 9, 11, 12, 16, 22, 24, 35, 36
    12.3 43, 44, 45, 46, 47, 48, 51, 54, 58
       

5 Sept 22-26 12.4 5, 8, 9, 12, 13, 16, 17, 20, 21, 24, 27, 30
    12.4 31, 34, 35, 38, 39, 42-44, 49-53
    REVIEW  
    EXAM 2  
       

6 Sept 29-Oct 3 12.5 1, 5, 8, 9, 12, 20, 21, 23, 26, 27, 30
    12.6 5-8, 15, 20, 21, 24, 28, 30
    12.6 31, 34, 35, 38, 42, 45-49, 51-58, 63, 65
    12.7 1, 5-12, 15, 19, 26, 29,37-40,61,64,65
       

7 Oct 6-10 12.8 1, 2, 7, 9, 12, 13, 16, 17, 20
    12.8 21, 24, 25, 33, 35, 37, 38, 47
    REVIEW  
    EXAM 3  
       

8 Oct 13-17 13.1 1,5,6,12,13,15,17,18,20,23,28
    13.1 32-34,36,38,41,43,46,47,49,51,52,54
    13.2 5, 12, 16, 19, 27, 29, 30, 33, 34, 37, 47, 49, 56
    13.3 3, 14, 16, 21, 25, 30, 34, 36, 45, 52, 54
       


Friday, October 17, is the last day to change your grade option to or from ``Pass/No Pass''.

9 Oct 20-21 (no class) Fall Break
    13.4 2, 3, 7, 13, 17, 19
    13.5 7, 9, 13, 16, 22, 24, 27, 34, 41, 44
    13.6 7, 14, 15, 18, 21, 23, 29, 31, 33, 37, 41, 43, 51
       

10 Oct 27-31 REVIEW  
    EXAM 4  
    13.7 1-5, 19, 23, 26, 29, 32, 36, 38, 41, 45, 48, 53, 60
    13.8 1, 2, 3, 9, 15, 25, 29,31
       

11 Nov 3-7 14.1 5-7, 15, 18, 19, 27, 29, 30, 31, 33, 34
    14.1 3, 35, 37,40,41,49-51,54
    14.2 5, 8, 11, 12, 17, 24-26, 28
    14.2 29, 31, 34, 36, 37, 39, 41-43, 46, 56, 59, 60, 65
       

12 Nov 10-14 14.3 6, 9, 13, 18, 19, 21, 24, 25, 27, 41, 45-49
    14.4 5, 8, 10, 13, 14, 19, 21, 36, 37, 41, 42
    REVIEW  
    EXAM 5  
       


Friday, November 14, is the last day to withdraw from the course and receive a grade of W.

13 Nov 17-21 14.5 5, 7, 12, 17, 19, 23, 25, 31, 35, 36, 40, 45, 47, 49,50,52
    14.6 6-10, 13, 15, 18, 19, 21
    14.6 23-26, 28, 30, 31
    14.6 41, 43, 45, 47, 49, 52, 57, 60
       

14 Nov 24-25 14.7 6, 7, 9, 12, 16, 21, 25, 28
  Nov 26-28   Thanksgiving Vacation
       

15 Dec 1-5 14.8 5, 8, 9, 11, 14, 16, 17
    14.8 1-3, 21, 24-27
    REVIEW  
    EXAM 6  
       

16 Dec 8-12 REVIEW  
    REVIEW  
    REVIEW  
    REVIEW  
       

Final Exam: The time for the final exam is 6:00-8:00 pm, Tuesday, December 16, Room TBA.

Department Grading Appeals Policy: The Department of Mathematics and Statistics does not tolerate discrimination or harassment on the basis of race, gender, religion or sexual orientation. If you believe you have been subject to such discrimination or harassment, in this or any math course, please contact the department. If, for this or any other reason, you believe that your grade was assigned incorrectly or capriciously, appeals may be made to (in order) the instructor, the department chair, the departmental grading appeals committee, the college grading appeals committee and the university grading appeals committee.