Professor: Jeff Johannes Section 4 MWRF 1:30-2:20p Sturges 105

Office: South 326A

Telephone: 5403 (245-5403)

Office Hours: Monday 12:00N-1:20p, Tuesday 8:00 - 9:00p, Wednesday 11:30a - 12:30p, Thursday 4:30 - 5:30p, Friday 10:00 - 11:00a, or by appointment or visit.

Email Address: Johannes@Geneseo.edu

Web-page: http://www.geneseo.edu/~johannes

Course Materials

"Chapter 12 - Vector Calculus" from outboxes (can be accessed via your browser here after logging in)

Maple labs from outboxes (can be accessed via your browser here after logging in)

Exercise source and supplemental text

Purposes

- to learn how to represent the third dimension mathematically

- to apply the techniques of calculus to the third dimension

Overview

Calculus III is not really a continuation of Calculus I and II. It takes both of them to a whole new dimension - the third dimension. We will learn calculus that can be applied to the three dimensional world in which we live (but which we frequently ignore because it cannot be completely reproduced on paper or on screens).

Reading

I have intentionally chosen a very readable and interactive text. In addition to planning time to do homework, please take time to carefully read the sections in the book. Notice use of the words “time” and “carefully”. Read the sections slowly and actively. If you do not understand some statement reread it, think of some potential meanings and see if they are consistent, and if all else fails, ask me. If you do not believe a statement, check it with your own examples. Finally, if you understand and believe the statements, consider how you would convince someone else that they are true, in other words, how would you prove them?

Because the text is exceptionally accessible, we will structure class-time more as an interactive discussion of the reading than lecture. For each class day there is an assigned reading. Although it is possible we will have changes, I expect to stay close to the schedule. Read the section before coming to class. Complete the activities in the section to the best of your ability. We will spend class discussing the activities.

Learning Outcomes

Upon successful completion of Math 223 - Calculus III, a student will be able to:

- Represent vectors analytically and geometrically, and compute dot and cross products for presentations of lines and planes,
- Analyze vector functions to find derivatives, tangent lines, integrals, arc length, and curvature,
- Compute limits and derivatives of functions of 2 and 3 variables,
- Apply derivative concepts to find tangent lines to level curves and to solve optimization problems,
- Evaluate double and triple integrals for area and volume,
- Differentiate vector fields,
- Determine gradient vector fields and find potential functions,
- Evaluate line integrals directly and by the fundamental theorem, and
- Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of multivariable calculus concepts.

Grading

Your grade in this course will be based upon your performance on various aspects. The weight assigned to each is designated below:

Exam 1 13% Problem Sets (7) 42%

Exam 2 13% Reading Quizzes (as needed) 6%

Final Exam 26%

Assignments

There will be seven assignments. Each assignment will constitute three exercises per section of your choosing from the exercise source (relevant sections are indicated in parentheses), at most two problems per section of my designation, and one question of your choosing from a lab completed since the previous assignment. Assignments are due on the scheduled dates. You are encouraged to consult with me outside of class on any questions toward completing the homework. You are also encouraged to work together on homework assignments, but each must write up their own well-written solutions. A good rule for this is it is encouraged to speak to each other about the problems, but you should not read each other's solutions. A violation of this policy will result in a zero for the entire assignment and reporting to the Dean of Students for a violation of academic integrity. I strongly recommend reading the suggestions on working such problems before beginning the first set. Each assignment will be counted in the following manner: the exercises will be checked for completeness and will be worth half of the credit on the assignment. The remaining problems will be scored out of four points each:

0 – missing question or plagiarised work

1 – question copied

2 – partial question

3 – completed question (with some solution)

4 – completed question correctly and well-written

Each entire problem set will then be graded on a 90-80-70-60% (decile) scale. Late items will not be accepted as solutions will be posted at the time problem sets are due. Problem sets will be returned on the following class day. Because solutions will be provided, comments will be somewhat limited on individual papers. Please feel free to discuss any homework with me outside of class or during review. Points lost on problem sets may be reearned (or preearned) by finding errors in the textbook (there are a few - both mathematical and writing) as follows: The first student who notifies me via email of an error will receive one problem set point. I will keep the errors listed here for you to check.

Solutions and Plagiarism

There are plenty of places that one can find all kinds of solutions to problems in this class. Reading them and not referencing them in your work is plagiarism, and will be reported as an academic integrity violation. Reading them and referencing them is not quite plagiarism, but does undermine the intent of the problems. Therefore, if you reference solutions you will receive 0 points, but you will *not* be reported for an academic integrity. Simply - please do not read any solutions for problems in this class.

Reading Quizzes

You are responsible for reading the sections and activities before they are discussed in class. The schedule and links are given below. Occasionally - as I see it necessary - we will have short (five minute) reading quizzes to check that the reading is being done. As the class shows this is not necessary, they will become less frequent. Most will not be announced. If there are no questions from the activities, there will definitely be a reading quiz. The reading quizzes may be as straight forward as - "Write enough to convince me you did the reading." There will be no makeup reading quizzes.

Laboratory Activities and Writeups

We will regularly be spending parts of classes on Maple activities. Activity files are in my outbox in a folder called "MultiMaple". You may access them via a browser here (after logging in with your Geneseo account). Please come to class prepared for the activity (i.e. with a maple-installed computer and the file loaded), but without having completed it before. We will not use class time to prepare.

Exams

There will be two exams during the semester and a final exam during finals week. If you must miss an exam, it is necessary that you contact me before the exam begins. Exams require that you show ability to solve unfamiliar problems and to understand and explain mathematical concepts clearly. The bulk of the exam questions will involve problem solving and written explanations of mathematical ideas. The first two exams will occur in the evening so that you are not rushed to complete them. The final exam will be half an exam focused on the final third of the course, and half a cumulative exam. Exams will be graded on a scale

100 – 80% A

79 – 60% B

59 – 40% C

39 – 20% D

below 20% E

For your interpretive convenience, I will also give you an exam grade converted into the decile scale. The exams will be challenging and will require thought and creativity (like the problems). They will not include filler questions (like the exercises) hence the full usage of the grading scale.

Feedback

Occasionally you will be given anonymous feedback forms. Please use them to share any thoughts or concerns for how the course is running. Remember, the sooner you tell me your concerns, the more I can do about them. I have also created a web-site which accepts anonymous comments. If we have not yet discussed this in class, please encourage me to create a class code. This site may also be accessed via our course page on a link entitled anonymous feedback. Of course, you are always welcome to approach me outside of class to discuss these issues as well.

Social Psychology

Wrong answers are important. We as individuals learn from mistakes, and as a class we learn from mistakes. You may not enjoy being wrong, but it is valuable to the class as a whole - and to you personally. We frequently will build correct answers through a sequence of mistakes. I am more impressed with wrong answers in class than with correct answers on paper. I may not say this often, but it is essential and true. Think at all times - do things for reasons. Your reasons are usually more interesting than your choices. Be prepared to share your thoughts and ideas. Perhaps most importantly "No, that's wrong." does not mean that your comment is not valuable or that you need to censor yourself. Learn from the experience, and always try again. Don't give up.

Math Learning Center

This center is located in South Hall 332 and is open during the day and some evenings. Hours for the center will be announced in class. The Math Learning Center provides free tutoring on a walk-in basis.

Academic Dishonesty

While working on assignments with one another is encouraged, all write-ups of solutions must be your own. You are expected to be able to explain any solution you give me if asked. Exams will be done individually unless otherwise directed. The Student Academic Dishonesty Policy and Procedures will be followed should incidents of academic dishonesty occur.

Disability Accommodations

SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional, or cognitive disabilities. Accommodations will be made for medical conditions related to pregnancy or parenting. Requests for accommodations including letters or review of existing accommodations should be directed to Ms. Heather Packer in the Office of Disability Services in Erwin Hall 22 or disabilityservices@geneseo.edu or 585-245-5112. Students with letters of accommodations should submit a letter to each faculty member at the beginning of the semester and discuss specific arrangements. Additional information on the Office of Disability Services is available at www.geneseo.edu/dean_office/disability_services.

Religious Holidays

It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work. You are responsible for notifying me by February 4 of plans to observe a holiday.

Date Topic

January 23 Introduction

24 Maple basics lab

25 9.1

28 Multivariable functions lab

30 9.2

31 Vectors lab

February 1 9.3

4 Dot product lab

6 9.4

7 Cross product lab

8 9.5 PS1 due: 9.1-4 (13.1, 11.1, 11.3)

11 Lines and planes lab

13 9.6

14 9.7

15 Vector functions lab

18 9.8

20 Curvature lab (not on-line; follow link) (maple file with pasted commands)

21 overrun

22 Review PS2 due: 9.5-8 (11.2, 12.1-3)

25 Review

25 XM1 7-9p Sturges 221

27 XM return

28 10.1

March 1 XM discuss

4 10.2

6 10.3

7 10.4

8 10.5

11 10.6 PS3 due: 10.1-4 (13.1-3)

13 Gradient lab

14 10.7

15 10.8

25 Max/min lab

27 Review PS4 due: 10.5-8 (13.4-7)

28 Review

28 XM2 7-9p Sturges 221

29 XM discuss

April 1 XM return

3 11.1

4 11.2

5 11.3

8 Non-rectangular integrals lab

10 11.4

11 11.5

12 11.6 Problem Set 5 due: 11:1-4 (14.1-2)

15 11.7

17 GREAT Day

18 Triple integrals lab

19 11.8

22 11.9

24 12.1

25 12.2 Problem Set 6 due: 11:5-9 (14.2-4)

26 12.3

29 Line integrals lab

May 1 12.4

2 Fundamental theorem line integrals lab

3 overrun space

6 review Problem Set 7 due: 12: 1-4 (15.1-2)

8 review

Friday, May 10 final exam 12N -3:20p (probably not Thursday, May 16 12N-3:20p)