Welcome to the Math 208, Section 001, Calculus III (Fall 2005) home page. You're probably here for information, so let's start with the vital statistics of the course.

### Calculus III Course Resources

It's interesting to see how much information can be found on the web. Go to your favorite search engine (like the Google or Yahoo sites listed on my home page) and try searching on "vector field." See how many web pages you hit and visit a few interesting looking sites.

## Notes and FAQ

Final exams were graded this week. The median grade for the regular sections was about 128, while our median was 110. I'm at a loss to explain the apparent let-down since I do think, in view of class performance on earlier hour exams, that this class was capable of a better performance on the final. I'll have to rethink final exam preparation. Grades are posted outside my office and should be in the mail as well. If anyone wants to see their exam results, drop by my office. I look forward to seeing you again sometime, possibly in a future class. Have a great break!

(12/02/05) In our section (001) of Math 208 the final exam is worth 200 points, so it's equivalent to 2.5 hour exams. A number of people have been unhappy about their performance in one exam or another which was considerably lower than their other exam grades. I've been asked if there is a way to get some extra credit to make up for a poor score on a single exam. In response, I've decided to allow everyone to replace the score of their lowest hour exam by a score equivalent to what they obtained on the final. For example, if your low hour exam score is 60, and you scored 160 on the final, then I'll replace the exam score of 60 by 160/2 = 80. On the other hand, if your final exam score is 110, then your exam scores will be unchanged.

Lots of help is available to you as you review the course material and problems. For one, keys to all exams are available on our course homepage so that you can fix anything you missed on the hour exams. You should also get copies of recent finals from the Union and work through them. You can post questions on our message board. You can form or join study groups via the message board. Finally, I'll be available for help pretty much all day Monday and Tuesday until midafternoon. For more information on the topics in the unit final, be sure to look here. And, OF COURSE!, be sure to purchase and study copies of the two old unit finals that are available.

Here is our schedule for Dead Week:
• Monday: Review Chapters 10-11-12.
• Wednesday: Review Chapters 12-13.
• Thursday: Review Chapters 13-14 and do class evaluations.
• Friday: Review Chapter 14.

(9/19/05) In class today I gave an extra homework problem that I thought would provide a good application of tangent planes. In case you didn't write it down, here it is:
A laser beam is directed from the point (3,2,0) towards the point (1,1,3) on the elliptic paraboloid z = x2 + 2y2. It is reflected off this surface. Where, i.e., in what direction?
Hints: Use Snell's law (angle of incidence equals angle of reflection) and the fact that the laser beam sees a tiny (hence very flat) portion of the surface.
Answer: Any positive multiple of the vector <2,67,41> will do.

About polar angles for 2D vectors ...
... about the HW last night. When converting to polar form, am I correct in assuming it is just the reciprocal of ||a|| times the unit vector, and then just tan^-1 of y/x of the unit vector to get the angle?

Answer: ... you just about nailed it. There is one little detail to think about, and I don't think the book mentioned it. I haven't checked all the examples, but maybe they chose them to avoid this detail: atan = tan^(-1) has range -pi/2 to pi/2, which doesn't cover the range of possible angles like -pi to pi (or 0 to 2*pi) would. So, for example, if you wanted to put -i - j into polar form, you would get an anser of atan(-1/(-1))=0.78540 (really pi/4), but that wouldn't be right. Draw a graph with -i - j in it and you'll see why. You have to add pi to the answer to get the correct angle 5*pi/4.

### Gateway Information for Students of Math 208, Section 001, Fall 2005

#### Rules of the game:

1. All students of Math 208, Section 001, should take both the Differentiation (Test 1) and Integration (Test 2) Gateway exams.
2. The Gateways exams for credit are proctored (practice exams are not and do not have the limitations listed below.) 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 are listed at the schedule site and are as follows: Differentiation, August 24 - September 14; Integration, September 9 - 30.
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. Ten points will be given for each passed exam (Test 1 and 2) and one point per correct problem for less than passing scores giving a maximum of 20 points for the Gateways.

#### 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".
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.

#### Some Tips on Taking Gateway Exams:

1. Use the previewer to check your answers. Each answer section has a "Preview" button. Use it!
2. You can get a lot of useful help on how to enter answers by going to an exam page, say a practice exam, then clicking on the Help item at the top bar, then clicking on Math_Help in the contents column. You'll find there a very complete explanation on how to enter your answers into the computer.
3. Take your time and read the previewed answer carefully. If, e.g., you see "sinx" instead of "sin x" or "sin(x)", then you know that the computer is going to interpret what you wrote as a single symbol. This is one of the most common errors. Another: "2/3x" will be interpreted according to the same algebraic rules of precedence that your calculator uses, that is, as "(2/3)*x". So if you meant 2/(3x), write it that way.
4. If you think that an answer of yours has been graded incorrectly, make a copy of the disputed question and computer answer. Then open up a Gateway session and go to a practice exam. Type in your disputed answer (exactly as you see it on the printed sheet) as the answer to the first question and preview it (never mind what the on-screen question really is.) Does the previewed answer look like it is equivalent to the printed answer the computer gave to the disputed question? If not, bring the printed copy to me, but only after you have checked the previewer yourself.

Where do I stand right now?...

Well, that's easy enough. Here's a table to help you out. This table has all the possible grades for tests, gateways, etc, in this course. Notice there are zeros where an activity has not been completed yet. So if you are looking at this table and we've only done the exams through three, then the grade scales are based on this data alone.
Now all you need is your own scores. If you don't have them or simply want to see what grades I have recorded for you so far, email me with and give the the last 5 digits of your SSN. I will respond with the grades I have in my grade book. If you calculate your own grade remember that hour exams are prorated to 80 points, which accounts for the funny sums. Also note that the grade scales row gives the bottom score to attain the given grade.

### Grade Scales for Math 208, Section 001, Fall 2005

Activity: Gateways/ Project Exam 1 Exam 2 Exam 3 Exam 4 Exam 5 Exam 6 Final Exam Grade
Points: 20 100 100 100 100 100 100 200 700
Count: 27 27 26 24 24 24 23 23 25
Minimum: 0 35 17 43 43 36 43 55 83
Maximum: 20 100 100 100 99 95 99 181 675
Average: 10.19 76.37 67.88 75 79.42 70.17 73 115 460
StdDev: 6.75 13.98 18 16.48 15 15 14 38 132
Median: 8 79 66 80 79 71 72 110 464
D- 9 48 48 48 48 44 48 75 311
D 10 50 50 50 50 46 50 85 332
D+ 11 54 54 54 54 50 54 91 358
C- 13 57 57 57 57 53 57 98 380
C 13 60 60 60 60 56 60 105 403
C+ 14 64 65 65 65 61 65 117 439
B- 15 68 70 70 70 66 70 129 475
B 16 75 75 75 75 71 75 140 513
B+ 17 79 79 79 79 75 79 148 541
A- 18 83 83 83 83 79 83 158 571
A 19 86 86 86 86 82 86 165 594
A+ 20 93 93 93 93 89 93 182 647

Class Policy

Course: Math 208 - Section 001, Calculus III

Place/Time: 204 OldH, 8:30-09:20 MWRF, Fall 2005

Preq: Math 107 or equivalent.

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

Office Hours: Monday 2:00-4:00, Wednesday 10:30-11:30 and 2:00-3:30, Thursday 12:00-2:00, Friday 10:30-11:30, and by appointment. Office: 229 AvH

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 generally 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. Current information about the course will be available through the web (via the Math 208 homepage.) Using the web is strongly recommended for keeping track of current activities and resources for 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 80 points each. The final exam will count 200 points. All exams are closed book with calculators. The Gateway exams will account for 10 points and a writing assignment will account for 10 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 13, 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.)

Math 208, Section 001, Syllabus Fall Semester 2005

• 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.
• 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 exams on dates other than than those given below.
• 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 13, 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.
• ADVANCED PLACEMENT: If this is the first college mathematics course that you have attempted, then you may be eligible for 10 hours of free credit for Math 106 and Math 107, provided you earn a grade of P, C or better in Math 208 this semester. To be considered for this credit, you should register with the Department of Mathematics, 208 Avery Hall, by Friday, September 30, 2005.

•  WEEK DATES SECTIONS EXERCISES

 1 Aug 22-26 10.1 1, 9, 19, 21, 29, 32, 35, 36, 41, 42, 50, 53, 55, 57, 63 10.2 5, 8, 10, 19, 27, 34, 35, 41, 46, 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 7-9, 13, 21, 23, 29, 57-60, 68, 70-73, 75

 2 Aug 29-Sep 2 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, 8, 11, 13, 15, 17, 19, 22, 24,30,35,37,43,44,45,50,52,53,60 11.1 5-9, 11, 14, 19, 23, 26, 31, 35, 45, 48 11.2 6, 7, 9, 11, 13, 18-23,31,33,36,41,45,46,51,52

Friday, September 2, is the last day to withdraw from the course and not have it appear on your transcript.

 3 Sep 5 (no class) Labor Day Sep 6-9 11.3 5,9,12, 14, 25, 27, 28, 34-36, 43, 44, 46, 51 REVIEW EXAM 1

 4 Sep 12-16 12.1 5, 14, 19, 20, 21, 39, 40, 42, 44, 51-55, 60,65,66,68,70,72 12.2 1,3,4,7,12,14,15,19,24,27,30,35,38,39,43-45,49,51-58 Sep 14 Last day to take Differentiation Gateway 12.3 1, 4, 5, 9, 11, 14, 16, 19, 24, 35-38 12.3 41, 44-48, 51, 54, 59

 5 Sep 19-23 12.4 7-9, 12, 13, 16, 17, 20, 21, 24, 27, 29 12.4 32, 33, 35, 39, 40, 42-44, 50-53 REVIEW EXAM 2

 6 Sep 26-30 12.5 2, 4, 5, 8 , 7, 9, 12, 19, 19, 22, 24, 27-30 12.6 7-10, 13, 20, 23, 24, 27, 28 12.6 31, 33, 35, 36, 42, 43, 46-49, 52-58, 63, 68 12.7 1, 5, 6 , 15, 19, 26, 29 Sep 30 Last day to take Integration Gateway

 7 Oct 3-7 12.7 37-40, 45, 51-54, 61, 65, 66 12.8 1, 2, 5, 7, 8, 13, 14, 19, 23-25, 27, 34, 36-38, 47 REVIEW EXAM 3

 8 Oct 10-14 13.1 1, 5, 12, 13-16, 20, 25, 27 13.1 33-37, 41, 43, 47-51, 63, 68 13.2 5, 13, 16, 21, 27, 29, 30, 34, 35, 39, 47, 49, 55 13.3 1, 14, 15, 21, 25, 28, 34, 38, 45, 49, 52, 54

Friday, October 14, is the last day to change your grade option to or from ``Pass/No Pass''.

 9 Oct 17-18 (no class) Fall Break (no class) Fall Break Oct 19-21 13.5 5-8, 11, 16, 22, 24, 29, 34, 43, 44 13.6 6, 7, 14, 15, 18, 23, 25, 27, 33, 35, 37, 39, 43, 52

 10 Oct 24-28 13.7 2, 4, 7, 20, 25, 26, 31, 33-35 13.7 40, 41, 45, 48, 53, 54, 59, 60 REVIEW EXAM 4

 11 Oct 31-Nov 4 14.1 3, 5, 7, 10, 15, 18, 19, 27, 29-31, 33, 34 14.1 35, 36, 41, 42, 49-51, 54, 56 14.2 1, 6, 7, 11, 12, 17, 20-22, 28, 29 14.2 31, 33, 36, 37, 39, 43-45, 46, 48, 56, 59, 60, 65

 12 Nov 7-11 14.3 4, 5, 8, 15, 18, 19, 21, 25-27, 41, 45-49, 51 14.4 1, 5, 7, 11-15, 19, 21, 27, 36, 39, 41, 42 REVIEW EXAM 5

Friday, November 11, is the last day to withdraw from the course and receive a grade of W.

 13 Nov 14-18 14.5 6, 7, 10, 17, 21, 23, 25, 31, 35, 36, 38, 45, 47, 49,50,51 14.6 5-9, 13, 15, 19-21 14.6 24-28, 30, 31, 34 14.6 41-49 (odd), 52, 57, 58, 61

 14 Nov 22-23 14.7 1, 6, 7, 9, 12, 18, 21, 27, 28, 31 Nov 21-22 Thanksgiving Vacation

 15 Nov 28-Dec 2 14.8 1-3, 7-9, 11, 13, 14, 16, 17 14.8 21, 22, 24-27, 34 REVIEW EXAM 6

 16 Dec 5-9 REVIEW REVIEW REVIEW REVIEW

Final Exam: The time for the final exam is 6:00-8:00 pm, Tuesday, December 13, 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.