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
Active Calculus
- Multivariable: 2018 Edition by Steve Schlicker, David
Austin, and Matt Boelkins
"Chapter 12 - Vector Calculus" from outboxes (can be
accessed via your browser here
after logging in)
Maple software from software.geneseo.edu
(login and select the category Academic)
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:
Exams:
Assignments: (6% each)
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 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.
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.
Schedule (subject to change)
The section numbers in the .html version of the book are offset from the
.pdf version. In the .html version they start at one, while in the
.pdf they start at 9. Please feel free to subtract 8 as needed.
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)