Mathematics 233 Calculus III
Fall 2003
Dr. Carol Browning
Pearsons 102
873-7268
cbrowning@drury.edu
Office Hours
Monday
10-10:50 a.m.
Tuesday
10-10:50 a.m.
2:00-2:50 p.m.
Thursday
10-10:50 a.m.
Friday
10-10:50 a.m.
Contents of Syllabus:
1. Letter to the student
2. Learning goals
3. Learning activities
4. Learning assessment

Course requirements

Evaluation

Test rewrites

Absence policy
5. Helpful hints

Supply list

Problem solving strategies

Study skills
6. Disclaimers and special arrangements
7. About the professor
8. References used to create this course
Syllabus
Dear Students,
I am so pleased to be directing your study of Calculus III. This is my favorite
class to teach because I think calculus in 3 dimensions is a fun theory with exciting
applications: spacecraft trajectory models, roller coaster design, etc. I would be delighted
if some of you go on to work for Disney Imagineering or for NASA in spacecraft
navigation!
We will consider the calculus of functions which give position in 3 dimensions
over time and functions which describe surfaces in three-dimensional space. Most
students can visualize these curves and surfaces fairly easily with a little practice, but
some students need extra help to be able to "see" and draw three-dimensional objects on a
flat piece of paper. If you do need help with visualizing or representing 3-space, please
let me know. We will work together to make sure you can see it.
What is the equation of a line in three-dimensional space? That’s hard to say
given just the slope intercept concept of a line in two dimensions. We will start the
semester by looking at two dimensional geometry in a different way – a way that will
extend to three dimensions easily.
For the most part, the differential and integral calculus that you already know
extends naturally to functions in multiple dimensions. The development of the theory
this semester will be powerful and largely straightforward. We will hit a couple of
complicated topics, such as parameterizing by arc length in order to compute curvature,
but for the most part you will find big payoffs this semester for all the hard work you did
to learn Calculus I and Calculus II.
Dr. Allen and I are being supported by the National Science Foundation and the
Educational Advancement Foundation to develop discovery materials for the calculus
sequence. This semester we will study from a draft of the Calculus III text. Our
classroom activities will integrate problem solving and communication skill development
as well as the concepts of Calculus III. Our pedagogical theory is that if you understand a
concept well enough to explain its application to classmates, then you have truly learned
that concept. Your constructive comments and suggestions on the course are always
welcome.
I hope you enjoy the semester. I welcome you to visit my office and look forward
to working with you throughout this semester.
Sincerely,
Carol Browning, Associate Professor
Department of Mathematics and Computer Science
2. Learning Goals
The primary goal for this class is to gain an understanding of the concepts of
differential and integral calculus of functions in multiple dimensions. Additional goals
are to
 increase clarity and precision in reading, listening, thinking, and expression
 develop critical thinking and problem solving skills
 understand the history and applications of multi-dimensional calculus
in the context of group work and cooperation. One reason we have these additional goals
is that employers hire and promote people who not only know a particular technical area,
but can apply that knowledge to solve problems, communicate their results, and work
well with others.
This course is designed for mathematics majors and minors to complete the study
of calculus. Most of the further courses in mathematics are more theoretical and less
computational in nature. The selection of topics for this course reflects the varied reasons
for the students who are taking the course: preparation for more theoretical study in
mathematics, preparation for engineering applications of calculus per se, and personal
fulfillment in studying a beautiful theory.
Here are the ten communication skills we will focus on this semester:
1. Full statement of the problem;
2. Correct solution content;
3. Articulate statements;
4. A conclusion;
5. An introduction;
6. Clear presentation;
7. Connective sentences;
8. Subtleties of communication;
9. Pictures and diagrams; and
10. Definition of all symbols and variables.
3. Learning Activities
To achieve our primary goal of learning about multi-dimensional calculus,
students will read and see explanations, work problems, present solutions to problems,
write up problem solutions, work projects and answer reflective questions. To encourage
you to keep current with the class, I will collect some of the assignments and give tests.
As a class we will study problem solving skills and communication skills.
On all written work and oral presentations, each step of the process of getting the
answer needs to be shown and complete explanations of your work are required. I am
interested not only in the right answer but also the thought process that went into it as
well as your communicative skills in explaining your work. If you understand how you
think to solve a problem, then you will be better able to solve future problems.
I require that you keep a three-ring binder with all of our class papers included.
This will help you see the development of the theory and of your problem solving and
communication skills. I will collect your notebook periodically to check your problem
solutions.
We will have three tests and final presentations. Before each test we will review.
4. Learning Assessment
One of the conflicts we face as teachers is the desire to use homework and tests to
help you learn from your mistakes and the tradition of using homework and tests to
determine your grade. We have researched various approaches both in the literature and
in our classes. The plans we have for this class emphasize using homework and tests to
help you learn.
Course requirements

Come to class every day.

Keep a notebook.

Read all assigned material.

Work assigned problems and projects.

Make presentations.

Listen actively to other student presentations.

Write up results as assigned.

Take 3 tests and make a final presentation.
Evaluation
Your grade will be determined as follows:
attendance, participation, presentations
15%
notebook, written assignments
15%
3 tests
60%
final presentation
10%
Oral and written presentations
Presentations and written work will be graded on all 10 objectives for
communications given above. Each presentation will be given by a group or individual
and graded by classmates. For each presentation, the graders will assess whether or not
each objective has been met. The final presentation will be individual and will be graded
by the professor.
If your written work meets the communications criteria and provides a correct
solution, it will be graded and returned. Otherwise, you may be asked to make changes
and resubmit for a grade.
Your course grade will depend upon your trend in achieving the communication
goals and your ability to maintain a high level of performance once it has been achieved.
Notebook
Periodically during the semester, the professor will review your notebook for
effort, neatness, and completeness. Each problem will be reviewed, and those that were
assigned for written submissions will be assessed using the communication goals.
Participation
Your group members will write an informal summary of your group
contributions. Your participation grade will be based upon the consensus of those
summaries and the observations of the professor.
 Make sure you do the following:
 Do your fair share of the writing for your group
 Ask questions when you are unsure, and pursue a question until you understand fully
 Answer questions in a manner that helps your classmate understand the concepts
 Attend all group study sessions
 Arrange study sessions that everyone in your group can attend
 Be well-prepared for class each day
 Contribute to class and group discussions
 Participate helpfully in planning group presentations
 Be easy to work with
Evaluation of Projects
Your grade on each project will fall into two categories. Your participation and
presentation grades will be part of your attendance, participation and presentation score.
The grade on your written project will be part of your notebook and written assignments
grade. Be sure to follow the communication objectives for your written work and your
presentation. In addition, be sure to do the following:
 Cite any sources you use, including Internet sources.
 Provide a nice presentation of your written project, either typed or very nicely written
and in a nice folder.
Tests and final presentations
The questions will be similar to problems worked in class.
Test rewrites
It is important that you understand all of the concepts we study since this material
builds. So if you miss a question on a test, make sure you understand the underlying
concepts.
If you score below a B on one of the first two tests, you may choose to rewrite
that test to make sure you understand the concepts well enough to continue your studies
this semester. If you rewrite your test, you will receive the average of the two grades for
that test. Here are the conditions:
 Do not make any marks on the original test after it is returned.
 Resubmit the original test with the rewrite.
 Include a full explanation of the correct solution for each problem on the test,
following the 10 communications criteria.
 Submit the rewrite within one week of the return of the original test.
Absence policy
In this class it is very important that you come to class each day. There will be
significant information that is not in the handouts that you need to know, and coming to
class is the way to find out what that is! Also, the people that you work with will depend
upon you to show up every day.
I know that sometimes students get sick, and if you are very sick, please stay
home and get well. Some of you must travel for sports or for academic reasons. If you
have to miss class for any reason, please do all of the following:

Before your absence, if at all possible, contact the people you work with in class to let
them know you will not be there. Make arrangements for any responsibilities you
have for joint work.

Work ahead so you will be on top of the material when you return to class.

After the class session you miss, contact your group members to find out what we did
in class, what we talked about, and what you need to have completed before the next
class.

Schedule a time with me to come in during my office hours and present solutions to
the problems that were presented in class during your absence. It is important to me
that you learn all of the concepts that we will study this semester. By having you
present missed material to me, we can both be sure that you understand it.

Come to the next class. If at all possible, come prepared to contribute and to learn the
material we will be studying that day.
SNOW DAYS: IF SPRINGFIELD PUBLIC SCHOOLS ARE CLOSED FOR
SNOW, THIS CLASS WILL NOT BE HELD.
5. Helpful hints
Supply list
Required
- a 3-ring binder
- notebook paper
- pencils and erasers
Suggested
- a graphing calculator
Optional
- playdough
- pipe stem cleaners
- colored pencils
- a ruler
- a protractor
Problem solving strategies
∙ Getting Started on a Problem
1) Read the problem carefully.
2) Draw a Picture.
3) Believe that you can solve the problem.
4) Develop a game plan.
5) Write about relevant concepts.
∙ Finishing the Problem
1) Execution. Double-check your execution of your solution plan.
2) Expression. Write your answer as a complete sentence, using appropriate units.
3) Evaluation. Is your solution complete and does it make sense?
∙ The Example Strategy
To solve a problem stated in general terms, first substitute in simple numbers for the
constants and solve the example problem. Then follow the same steps for the general
case.
∙ Five Approaches to Problem Solving
1) Graphic - using features of a graphical picture of a function,
2) Numeric - using a table of values,
3) Symbolic - using algebraic manipulation of expressions,
4) Algorithmic - applying a sequence of theorems, and
5) Verbal - using a precise verbal description.
The analytic approach is any combination of symbolic and algorithmic steps.
∙ The Context Strategy
First get the question firmly in mind. Then look back through the recent material you
have studied. For each concept, ask yourself whether or not it could apply to the current
situation.
∙ The Know-Show Strategy
Write what you know at the top of the page and what you want to show at the bottom.
For each part, write as many different equivalent expressions as you can until you can see
how they meet in the middle. Then write up your solution from top to bottom.
∙ The Salami Strategy
Slice the problem into small pieces and solve each piece.
∙ The Analogy Strategy
Have we ever seen a problem like this one? If we have, then we can use the same
method to solve this problem.
∙ Document your Toolbox
Each time you solve a problem, write notes to yourself on how to solve this type of
problem.
∙ The Fishing Expedition
Start by putting all of the information from the problem into equation form and then
play with the equations until the solution jumps out.
∙ The Modeling Process
1) Analyze the problem and describe it mathematically
2) Solve the math problem
3) Figure out what your answer means in terms of the real-world situation
If you've tried several of these ideas and still can't make progress on your problem,
here are three other good ideas:
1) Take a brisk walk
2) Call a friend
3) Talk to your professor
Study skills
Successful students set aside particular study times for each course they take. The
Dean of the College suggests two hours out of class for every hour in class. When it is
your time to study for this class, what exactly should you do? Here are some ideas.
First, read over your notes from class that day. Fill in the sketchy parts and
clarify them. Make a list of questions you have about things that still don't seem clear.
Pay particular attention to any feedback you have received from your classmates about
your presentations and from your professor about your written work.
Then review the problems that have been worked recently. Make sure you
understand the solutions well enough that you could explain it to someone else. In fact,
you may find it useful to spend at least part of your study time for this class with a study
partner or with your group, taking turns explaining past solutions to each other.
You will want to spend most of your time with the problems that you and your
group are currently working. As you solve a problem, practice giving a presentation of
your solution. For the written problems, make sure your written solutions are clear to
others and have the style of a textbook example solution. Be sure to work ahead so you
will be well prepared to make good use of class time.
When you finish, make sure your notebook is well organized. Review your list of
questions and decide which ones to ask in class, which to ask the professor in private, and
which to discuss with your friends. Have your written assignments printed and ready to
turn in the night before they are due.
6. Disclaimers and special arrangements
The particular topics, assignments, dates, number of tests, etc., are subject to
change at the discretion of the professor.
If you have any physical, emotional, or psychological conditions that may inhibit
your ability to learn in this class, please notify me immediately so that we can make
arrangements that will make it easier for you to learn the material.
7. About the Professor
Dr. Browning began teaching college-level mathematics in 1978. She has eight
years of experience working for NASA on interplanetary exploration, including the
Voyager mission to Neptune, the Ulysses mission to the polar regions of the Sun, the
Galileo mission to Jupiter, and the Cassini mission to Saturn. In addition, she led
research in robotics which has been applied to the Martian robotic rovers.
Dr. Browning came to Drury in August 1995 as Chair of the Department of
Mathematics. She designed and implemented the new computer science major at Drury
and led the establishment of a program in statistics. She and Dr. Allen wrote a text for
Calculus I which was published in June 2000 and revised in August 2003. They have
grants from the National Science Foundation and the Educational Advancement
Foundation for completing the Calculus I, II, and III series in May 2005.
8. References used to create this course
Howard Anton, Calculus – A New Horizon, Volume Three, Sixth Edition, Wiley 1999
Howard Anton, Calculus, Fifth Edition, Wiley 1995
Ostebee and Zorn, Multivariable Calculus from Graphical, Numerical, and Symbolic
Points of View, Preliminary Edition, Harcourt Brace 1997
Ostebee and Zorn, Multivariable Calculus from Graphical, Numerical, and Symbolic
Points of View, Revised Preliminary Edition, Harcourt Brace 1998
A. Wayne Roberts, Editor, Calculus – The Dynamics of Change, MAA Notes Number
39, 1996
Rogers, Reynolds, Davidson, and Thomas, Cooperative Learning in Undergraduate
Mathematics – Issues that Matter and Strategies that Work, MAA Notes Number 55,
2001