 Overview
This course is a continuation of the topics covered in Calculus I.
One of the most fundamental, and most slippery, topics in mathematics
is the relationship between the finite and the infinite.
A recurring theme throughout the semester will be the
relationship between an approximation and the exact value.
We will spend quite a bit of time this semester trying
to determine just how good any approximation is.
One of the most beautiful aspects of calculus is that by taking
better and better approximations and extending from the finite to the
infinite, we will often be able to find a precise solution.
Many of the topics we will cover this
semester allow us to solve many problems that do not seem to be
immediately related to calculus. Here are just a few:
- How much foam goes into a Nerf football?
- If you look in the front cover of the text, it will tell you
that the volume of a sphere of radius r is 4/3 * Pi r3.
Why is this correct?
- If you ask Maple (or your calculator) for the value of
Pi , it will tell you that PI is approximately 3.141592654.
How do we know that?
In the same way, e is approximately 2.718281828. Why?
- A company manufactures corrugated tin for roofing by taking a
flat piece of tin and pressing it until it is wavy. If it wants
to produce corrugated pieces that are 10 feet wide, how wide should the
flat pieces be to begin with?
- We will show how to design an apartment building that has a
center wall which is infinitely long (and has infinite area), but the building
itself has finite volume. In other words, all the tenants can move
into the building, but the workers will never finish painting the
hallway!
Course Goals and Expectations
Two of the goals of this course are that you learn to read a math text
and that you learn to communicate mathematics with other students.
Mathematics is a very personal discipline that is best learned by doing
rather than by observing.
Therefore, the class will be structured with some lectures to emphasize particular
topics, but much of the time will be spent on in-class work. The
class meetings are not intended to be a complete encapsulation of the
course material - There will be material in the text for which you are
responsible that we will not cover in class.
You will have a reading assignment for nearly every class meeting, and
it is extremely important that you complete the reading before the
next class meeting!
You should expect to put in approximately 2 hours outside of class for
each hour in class. In other words, expect to spend at least 8 hours
per week on Calculus II outside of class. There will be some weeks
where you spend more time (e.g. working on projects or preparing for exams),
and there may be some weeks where you do not spend the full 8 hours.
Working with Other Students
Many of the assignments this term will be group assignments where
you will work in groups of two or three (of your choosing). Each
assignment will receive a grade, and the group will
determine how the points are allocated to each member.
For example, if a group of
three receives an 85 on an assignment, then the group will have
3 x 85=255 points to distribute among them.
I will be available to mediate this process, if necessary.
Evaluation
Your final grade will be determined by
| Reading Assignments | 5% |
| Three Group Projects | 20% |
| Three In-Class Exams | 40% |
| Antidifferentiation Exam | 10% |
| Comprehensive Takehome Final Exam | 15% |
| Homework | 10% |
Reading Assignments
I will put a copy of each reading assignment on the Math 104 homepage.
Each assignment will indicate which parts of the section are especially
important and which can be skipped. Each assignment will also have
two or three questions that you should be able to answer after you have
read the section.
See the Guidelines for Submitting Reading Assignments for more information.
Group Projects
There will be three group projects assigned during the semester. You will
have two class periods to work together on the project, and your
written report will be due a week or so later
(see the syllabus for specific dates).
One of the main goals of the projects is that you learn to communicate
mathematics precisely, both verbally with your group and in
writing. The reports should be written in complete sentences explaining
the results and major ideas involved.
You may divide the writing of the report in whatever way is
agreeable to the group, but everyone should completely understand
the whole of the paper. Further, each member should proofread the
entire paper for consistency and typos.
I will give you a handout that explains my expectations for the
written reports in more detail.
Exams
The dates for the exams are given on the syllabus. I will give you a set
of sample problems before each exam, and we will have a question and
answer session before each exam to discuss the sample problems.
For each exam, you will be allowed to bring an 8.5 x 11 piece
of paper, handwritten on one side, which you will turn in with the exam.
The final will be a takehome exam and is due Monday, May 17.
Antidifferentiation Exam
One of the fundamental skills you will learn this semester is
antidifferentiation, or finding an antiderivative of a function.
The Antidifferentiation Exam will consist of four or five problems
and is graded with no partial credit. You
either get every problem correct, or you get no credit for the exam.
However, you may retake a similar exam as many times as you need
until you pass.
The Antidifferentiation Exam will be given in class on
March 5. If you pass
the Exam (or any version of it) on or before March 26, you will receive
the full 10% credit. After that date (until the end of classes
on May 11),
you will receive 5%. You are not allowed to take the exam after the end
of classes.
Homework
Homework will be collected every Wednesday. Three
or four problems will be graded from each assignment, with each problem
graded fairly leniently and assigned a score of 0, 1, or 2. The most important
aspect of the homework is that you make an effort on every problem.
The homework assignments will alternate between Individual
assignments and Group assignments. For the Group assignments,
each group will turn in one paper. On each assignment, one student will
be designated as the
primary author who writes-up the solutions. The role of primary
author must rotate among the members of the group.
For the Individual assignments, I encourage you to work with other
students, but each person must turn in a separate paper.
Here are a few guidelines for the presentation of your homework.
If you do not follow these, I reserve the right to return your homework ungraded!
- Your writing must be clear and legible.
- Your homework should be well-written,
using complete sentences to justify your results where necessary.
A list of answers without explanation is not acceptable.
- Here is a good rule of thumb to follow when writing up your
homework:
Write your solutions so that you could hand them to a student in a
different section of Calc~II and she could understand your
explanation.
- If you write in pen, there should be no scratch-outs.
- Do not turn in paper torn from a spiral notebook with ragged
edges.
- Clearly label each problem.
In order to give you some time to look over your assignment after you
have asked questions, I will leave 10 minutes of class on
Monday for homework questions.
The homework is due in my office by 4:00 on Wednesday. Be aware
that
Late homework is not accepted!! No exceptions!!
You will be allowed to drop one individual assignment and one group
assignment at the end of the semester.
Class Attendance
Although class attendance is not a specified percentage of your grade,
I will keep a class roll to help me determine borderline grades at the
end of the semester. If you do miss class, you are responsible
for the material that was covered.
Getting Help
Please come see me during my office hours! If you have a conflict
and cannot make my office hours, please call or email me and we can set up
an appointment for another time.
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