MATH 220 - 54 -- Calculus
III -- Fall 2005
(a copy of this syllabus can be found at
http://cerebro.xu.edu/math/math220/05f54/syll.html)
| Professor | Bernd Rossa |
| Office | Hinkle Hall 132, phone: 745-3686, e-mail: rossa@xavier.edu |
| OfficeHours | TBA |
| Text |
"Multivariable Calculus from graphical, numerical and symbolic points of view", 2nd ed., by Ostebee and Zorn, Houghton Mifflin (2004) |
| Class meets | MF 12:30-1:20 and TR 1-2:15 in Hailstones 1. |
| Technology | You need to have access to (and use) Maple (either your own copy or in a computer lab) |
Course Web Page
To keep track of our day to day work please bookmark and check our
calendar daily. Homework assignments,
questions to guide your preparatory reading, dates, deadlines etc. will be
posted there. Give me about 1/2 hour after class before you check for latest
changes.
(http://cerebro.xu.edu/math/math220/05f54/calendar.html#current)
Course Content
The two major components of this course are "calculus of functions of more
than one variable" and "vector calculus". We begin with the geometry and
visualization of higher-dimensional space (3-space), an introduction to
vector-valued functions, vectors, and some important vector operations. After
this introduction (chapter 12), we develop the theory and techniques of
differentiation (chapter 13) and integration (chapter 14) of functions
of more than one variable. Chapter 16 provides a discussion of some famous
and important results in vector calculus, namely Green's and Stokes' Theorem.
We will talk about Chapter 15, Sec. 4 (constrained optimization) after Chapter
13, and omit the other sections of Chapter 15.
General Comments
The emphasis and ultimate goal of this course is not mastery of techniques
needed to solve calculus problems. The emphasis will be on learning where
those techniques come from. The ultimate goal is that you'll know why the
techniques lead to the desired results not only because someone (teacher,
colleagues, back of book) confirms that the answer is correct, but because
you firmly know that it is correct on your own, without a doubt, because
you have reasoned through all of the steps. To accomplish this, you will
always be asked to back up your work with reasons: In class as well
as on tests. It is therefore a good idea to do the same on homework exercises.
We will discuss "theory" (including proofs) in class. Of course we will have examples. But we will NOT go through ten examples and then assign homework for you to "practice the same". We will look at an example, or two, to try to understand a connection, or the logic behind a techniques. Once we believe we "know what's going on", we will back up our beliefs with solid reasoning.
For more about the philosophy I urge you to read the "Notes for Students" on p. xix of the text. The authors explain there what they had in mind about "how to use the text" when they wrote it.... So, yes, you are expected to read the book. Questions to guide your reading will be posted on our course web-page. Bookmark and regularly (daily!) check http://cerebro.cs.xu.edu/math/math220/05f54/calendar.html#current.
Read and understand the university's policy on academic dishonesty; any such
incidents will incur a harsh penalty.
If an assignment is submitted late (for ANY reason), the grade will drop
by one letter grade per 24 hour period.
Technology
MAPLE, a computer software package that handles mathematical
calculation - symbolic, numerical, and graphical - has been incorporated
into our mathematics program. Being able to ignore computational difficulty
(because Maple doesn't care how tricky calculations are) will allow us to
focus more on the question: "What needs to be done to solve the problem at
hand" rather than spending most of our time learning tricks to take the needed
mechanical hurdles.
While in the previous semesters MAPLE may have only been used occasionally, Maple will be more important in Multivariable Calculus since it is hard (or impossible) to visualize graphs of functions with more than one input etc. without some appropriate graphing tool. If you have not used MAPLE before, let me know and work through the following brief Maple-Intro ASAP. (You need the program MAPLE to access/view the above link.) I encourage you strongly to ascertain that you have access to a computer with Maple loaded. Preferably, you get a copy of Maple and put it onto your own machine. However, most computers in Xavier's computer labs should have Maple loaded.
Grades
Grades will be taken in each of the following categories:
homework/quizzes/journal (approx. 100pts. total)
two projects ( 50 pts. each)
semester exams (4 x 100 pts.)
final exam (100 pts.)
A total of approximately 700 pts. will be available. Your semester
grade is the percentage of points you took from the available total. I use
the standard 90-80-70-60 cut-offs for the various letter grades.
Remarks about +/- grading: There will be no A+.
There will be no D+ or D-.
70 - <73 will be C-
73-77 will be C
>77 - <80 will be C+
80 - <83 will be B-
83-87 will be B
>87 - <90 will be B+ 90
- <93 will be A-
In borderline cases regularity and quality of attendance and participation will be taken into account.
Collaboration
I expect you to work with one another in class, on homework, and on projects,
unless otherwise indicated. The grading of joint work will depend to some
degree on evidence of genuine collaboration. However, since you will have
to take the exams on your own, don't get too dependent on one another!
Attendance
I expect you to attend every class meeting! The material builds up
on all previous results and techniques and every hole in the overall train
of thought will eventually backfire. You'll be lost. If you don't show up,
it is entirely YOUR responsibility to do whatever it takes to avoid negative
consequences. (Trust me on this one, and expect no sympathy if you ignore
this advice). Exams and quizzes are to be taken at the scheduled times
(no make-ups). Exceptions may be made for good cause if arrangemants are
made in advance.
Important Dates:
| Sept. 5 | Labor Day -- no class |
| Sept. 16 | Exam 1 |
| Oct. 4 | Exam 2 |
| Oct. 6-7 | Fall Holiday -- no class |
| Oct. 25 | Academic Day |
| Oct. 28 | Exam 3 |
| Nov. 21 | Exam 4 |
| Nov. 24, 25 | Thanksgiving Holiday |
| Dec. 12 | Final Exam (1 - 2:50) |