Professor: Jeff Johannes Section 3 MWTF 1:30-2:20p Sturges 113

Office: South 326A

Telephone: 5403 (245-5403)

Office Hours: Monday 2:30-3:30p, Wednesday 4-5p, Thursday 2:30-3:30p, 8-9p, Friday 2:30-3:30p and by appointment or visit

IM: JohannesOhrs

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

Course Materials

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

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 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 classtime more as an interactive discussion of the reading than lecture. For each class day there is an assigned reading. Read the section before coming to class. After completing questions from the reading we will discuss problems not a part of the problem sets during the class discussion.

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 (5) 25%

Exam 2 13% More (2) 10%

Final Exam 25% Lab Writeups (3) 15%

More may include extra problem sets, papers, or lab writeups.

*Problem set 3 is rather long and therefore worth 7%. Problem set 5 is rather short and therefore worth 3%.

Problem Sets

There will be five pairs of problem sets distributed throughout the semester. You must complete one of each pair. Problem sets 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 problem, 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 question will be counted in the following manner:

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. Problem sets will be returned on the following class day along with solutions to the problems. 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. **New: 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.

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. I strongly recommend reading the suggestions on writing lab writeups before submitting one. Follow-up questions are posted here and will be updated so as to include questions for each lab. Lab writeups may be turned in no more than three class days after the lab activity.

Reports

After attending a mathematics department colloquium (or other approved mathematics presentation) you may write a report. In your report, please explain the main point of the presentation and include a discussion of how this presentation affected your views on mathematics.

A – Well written, answers the questions, and is interesting and insightful

B – Well written and answers the questions

C – Well written or answers the questions (convinces the reader that

D – attempted

Papers are due within a classweek of the colloquium presentation. I will gladly look at papers before they are due to provide comments.

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 be an hour worth of material that I will two evening hours to complete. 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 learning disabilities. Students should consult with the Director in the Office of Disability Services (Tabitha Buggie-Hunt, 105D Erwin, tbuggieh@geneseo.edu) and their individual faculty regarding any needed accommodations as early as possible in the semester.

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 September 10 of plans to observe a holiday.

Date Topic

August 26 Introduction

28 Maple basics lab

29 9.1

30 9.2

September 4 Vectors lab

5 9.3

6 Dot product lab

9 9.4

11 Cross product lab

12 9.5

13 Lines and planes lab

16 10.1

18 Vector functions lab

19 10.2 Problem Set 1 due

20 10.3

23 10.4

25 Curvature lab (not on-line; follow link)

26 10.5

27 review Problem Set 2 due

30 review for XM

30 XM 1 7-9p in Welles 140

October 2 11.1

3 Multivariable functions lab

4 XM discuss

7 11.2

9 11.3

10 11.4

11 11.5

16 11.6

17 Gradient lab

18

21 11.7

23 11.8

24 Max/min lab

25 11.9

28 overrun space

30 review Problem Set 3 due

31 review

31 XM 2 7-9p in Welles 140

November 1 12.1

4 XM discuss

6 12.2

7 Nonrectangular integrals lab

8 12.3

11 12.5

13 12.6

14 Triple integrals lab

15 12.7

18 12.8

20 13.1

21 13.2

22 Line integrals lab

25 13.3 Problem Set 4 due

December 2 Fundamental theorem line integrals lab

4 overrun space

5 review

6 review Problem Set 5 due

9 review

Wednesday, December 11 final exam 12N - 3p