Mathematics 222 :  Calculus II
Fall 2012

Introduction

Professor:          Jeff Johannes                                 Section 1    MTWF  9:30-10:20a    Sturges 113
Office:               South 326A
Telephone:         5403 (245-5403)
Office Hours:    Monday 3-4p, Wednesday 4-5p, Thursday 12N-1p, 8-9p, Friday 1-2p, and by appointment or visit
Web-page:         http://www.geneseo.edu/~johannes

Course Materials
Thomas' Calculus, Twelfth Edition by Weir and Hass

Required:  TI-89 (or higher) or TI-nSpire Calculator
Additional handouts of problems and activities will be provided

Purposes
• to develop some fluency and comfort with the techniques of the calculus in order to use those techniques to solve routine exercises and nonroutine problems
• to appreciate the cultural significance and consequence of the calculus

Overview
Calculus is the culmination of high school mathematics and the entryway to higher level college mathematics.  The discovery of the calculus was a turning point in the history of mathematics and society.  As the mathematics of change, calculus is widely applicable in all fields of study that have quantifiable change.  It is for these reasons that we will be studying not only how to do calculus, but why calculus is done the way it is, and why it is done at all.

Learning Outcomes
Upon successful completion of Math 222 - Calculus II, a student will be able to:
• Define, graph, compute limits of, differentiate, and integrate transcendental functions,
• Examine various techniques of integration and apply them to definite and improper integrals,
• Approximate definite integrals using numerical integration techniques and solve related problems,
• Model physical phenomena using differential equations,
• Define, graph, compute limits of, differentiate, integrate and solve related problems involving functions represented parametrically or in polar coordinates,
• Distinguish between the concepts of sequence and series, and determine limits of sequences and convergence and approximate sums of series, and
• Define, differentiate, and integrate functions represented using power series expansions, including Taylor series, and solve related problems.

Your grade in this course will be based upon your performance on various aspects.  The weight assigned to each is designated below:
Exams:                                                                  Assignments: (5% each, complete 10)
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.

Exercises
With each day of lecture, I will suggest several exercises that are relevant for practising from that day's lesson.  I will not grade these exercises, but will gladly discuss or look at them.

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.

Laboratory Activities and Writeups

We will regularly be spending classes on activities.  Activity descriptions will be distributed in class the day before the lab.  Please come to class prepared for the activity (i.e. complete the section labeled "Before the Lab" if there is one), 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.  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 you were there)
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's worth of material that I will allow two hours to complete.  Tentatively they are scheduled for a Thursday and a Monday at  7 – 9p.  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 approximately (to be precisely determined by the content of each individual exam) given by
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.

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.

Schedule (subject to change)

August 27    introductions
28     review
29    7.1
31    Lab 15

September 4    7.2
5    Lab 16
7    7.3

10    Lab 10
11    7.5
12    7.6
14    Problem Set 1 due; Lab 17

17    8.1
18    8.2
19    8.3
21    8.4

24    8.5
25    Lab 18
26    8.6
28    8.7

October 1    review
2    Problem Set 2 due; review
3    review
4    XM1 (7-9p Welles 140)
5    XM discuss

10   XM discuss
12    10.1

15    Lab 19
16    10.2
17    Lab 20
19    10.3

22    10.4
23    Lab 21
24    10.5
26    Problem Set 3 due, 10.6

29    10.7
30    Lab 22
31    10.8
November 2    Lab 23

5    10.9
6     review
7    10.10
9    Problem Set 4 due, review

12    review
12    XM2 (7 - 9p Welles 140)
13    XM discuss
14    7.5
16    XM discuss

19    9.1
20   Population Project

26   11.1
27   Lab 14
28   11.2
30   11.3

December 3    Lab 24
4    11.4
5    11.5
7    Problem Set 5 due, review

10    review

Monday, December 17    8 - 11a    Final XM

Assignments at beginning of the semester for Calculus 222:

The most important topics to review from 221 for 222 are differentiation and integration.  While I will assume that you know all of chapters 1-6, focus your review thoughts on Chapters 3 and 5.

Opening day exercises (remember exercises are not graded)

If you want a taste of things, here are some sample questions of review nature to think about:
p. 176-182
p. 301-307
For Friday, September 14

Read “Suggestions to the Students” first
required to complete at least one of two options:

Problem Set 1A
Problem Set 1B