Introduction:
Calculus, developed over 300 years
ago, is an incredibly powerful tool with applications in a wide variety
of disciplines from engineering to the social sciences. The key ideas are
those of instantaneous rate of change, or derivative, and area under the
curve, or integral. These ideas will be developed fully. In addition
we will investigate the theoretical underpinnings of these ideas and some
of their practical applications.
Goals:
You will come to understand the basics
of calculus. You will learn to solve problems and communicate your
solutions clearly orally and in written form.
How the course will be conducted:
A common experience in many math classes
is that the professor shows the students how to work certain problems.
The solution is quite slick and is made to appear easy. The
students are often given the impression that either; 1. there is
no need for them to work any problems on their own since the solution methods
have been so clearly demonstrated, or 2. anything short of the slick
solution is of no value. Neither of of these impressions is correct.
Having watched someone else solve a problem does not guarantee that you
will be able to solve similar problems. You learn how to solve problems
only by actually working on them yourself. If you must watch someone
else, it is far better that it be someone who is at your own level.
In order to become better problem
solvers and also to help you better retain the essentials of calculus we
will spend most of our class time working problems at the board and discussing
these solutions.
In case you are a little suspicious
about the legitimacy of all of this, I want to assure you that the style
of teaching I am using has a long and distinguished tradition. My
teaching style is influenced by what is often referred to as the Moore
Method, Inquiry Based Learning, Discovery Based Learning, or the Socratic method. For more
on this (no pun intended) go to http://www.mathnerds.com/mathnerds/texan/index.asp
.
Problems will be posted
at
http://www.aug.edu/~cstallmann/M2011F09MM.pdf
. You will not be given all the problems at once, but only enough
to keep you busy for the next few class meetings. There are several
reasons for this. First, it gives me a chance to tailor the problems to
the class. Second, it gives you a chance to contribute problems by
making your own conjectures and asking questions in class. And finally,
it keeps me from spoiling your fun by giving away something that you might
have discovered on your own. Because I am generating problems as
we go, please don't hesitate to let me know about typos, errors, or anything
that you have trouble understanding. You will be doing us all a favor
if you bring such matters to my attention. I am open to any suggestions
as long as they don't distract us from our goal of becoming better problem
solvers and mathematicians.
Grades:
Board work and class participation
33%
Written work 33%
Final Exam 33%
I also plan to give two mastery of basic skills tests. This my way of checking whether you are ready for second semester calculus. I will insist that you get 70% or better on both of these tests before I give you a C or better in the class. I allow you two attempts to pass each test. The second attempt will have to be scheduled outside of class time. Let's all see if we can pass the first time.
Attendance:
I expect you to attend every single
class meeting. The nature of the course requires you to be present,
both to present your work to others and to respond to the work other students
have presented (and hence to earn the points that constitute your grade). Of
course, if urgent circumstances require your absence, you will be responsible
for any work that you miss. In such cases, please get in touch with me
as soon as possible. If you miss more than 5 class periods you are
subject to being withdrawn from the class.
If you are withdrawn before midterm you will receive a W. If you are
withdrawn after midterm you will receive a WF.
More details on grades:
The board work and class participation
grade will be based on a point system. You get 1 to 3 points for
working a problem at the board and 1 to 2 points for contributing to someone
else's solution. All points are counted in a positive sense.
No one will ever get points taken away. You are never penalized for
trying.
The point scale for board work is
as follows:
0-You really have nothing. You
are just winging it.
1-You have major errors.
2-You have some minor errors, your
solution is not complete, or your presentation is not clear.
3-You have a clear, correct, and complete
solution.
An unsuccessful first attempt with a score above 0 may be redeemed at a subsequent meeting. This will potentially allow you to get full credit for the problem in the end. While I will try to be as fair as possible in calling on students to present to the class and in awarding points for this work, I must ask you to respect my judgment on these matters.
You can also earn points by contributing in a significant way to class discussions.
Written work will primarily consist of careful write-ups of problems that you or someone else has presented in class. You will be expected to write thorough, correct, and clear solution to every problem that is worked at the board. Each Thursday I will collect one or more of these written solutions from the previous week's in-class work to grade and return to you. You are to work on these write-ups alone: I will not accept written work on which you collaborated with someone else or that you copied from a book or the internet. These written solutions should contain considerably more detail and explanations than solutions presented at the board. Expect my standards to be quite high.
Written work is graded on a 0 to 5
scale, with point values as follows:
0-The work you handed in is not your
own.
1-The work you handed in does not
make sense or is irrelevant to the problem
2-The work you handed in contains
major errors that cannot be fixed without a complete overhaul.
3-Your idea is productive, but the
details are incorrect or incomplete.
4-Your solution is essentially correct. What is keeping you from earning a 5 is either poor or imprecise wording
or notation or minor computation or algebra errors.
5- Your solution is both correct and
written in a clear and precise manner.
For more on what constitutes good
written work go to goodwrittenexplanations.htm
.
The grades are necessarily somewhat subjective, but I will do my best to make sure that you understand my assessment of your work.
Textbook:
At the beginning of the semester I
would prefer that you not consult any calculus textbooks, but I have no
objection to you consulting algebra, trigonometry, or precalculus textbooks.
For many this will be a relief and for others a burden. I want us
talk and work with concepts and symbols that we all understand and to develop
our own techniques for solving problem. Reading textbooks will, at
least at the beginning, distract us from these aims.
Later on in the semester I see no
harm in your using a textbook as a reference. Pretty much any calculus
book will do, and it doesn't matter if it's old. You can probably
pick one up for less than $10.
Withdrawal:
The deadline for withdrawal with a
grade of W is October 12 . Any withdrawal after that date will result
in a WF. If you feel that you must withdraw please try to do so on or before
October 12 .
Important Dates
Mastery
Test 1:
Thursday October 1
Mastery Test
2: Tuesday November 24
Final
Exam: Tuesday December 8 (10:00-12:00)