## Index to course material for Math 192:03, fall, 1996 (in GIF)

This material is also available in Postscript format.

Syllabus and textbook problem assignments
The course did not follow this syllabus in detail, but the sequence of
topics described here was usually followed.

The first exam and
solutions with some comments

The second exam and
solutions with some comments

The final exam

Exams given in
Math 152 last spring were handed out for review before each of
the exams in this course. Review sessions were scheduled during
evenings before exams.

Workshop 1
This problem was designed to show students the sort of non-routine
work that would be required - finding the common tangent line(s?) to
two parabolas. Solution of the problem "only" requires "easy"
differential calculus, but organized exposition of the solution
is usually difficult for students.

Workshop 2
The toxic waste problem - the work done emptying containers
with different shapes (taken from Math 152).

Workshop 3
Three problems using integration by parts (taken from Math 152).

Workshop 4
Some problems on improper integrals and some integration problems
(taken from Math 152).

Workshop 5
Some more improper integral problems (taken from Math 152).

Workshop 6
Some problems on sequences, mostly taken from Math 152.

Workshop 7
A problem on a quickly convergent Fourier series (note that I
used Fourier series to emphasize that one couldn't differentiate
convergent series of functions with impunity - power series inside
their intervals of convergence are special). Solutions to the
festival of series were presented orally by students at the next
class meeting.
I handed out
a graphical "solution" to the Fourier series problem after
students had worked on it, emphasizing that for engineering purposes,
this solution was likely to be "good enough", showing such features as
max/min behavior and approximate range. See also the comment (not
discussed in class) that equates this Fourier series with a
combination of familiar classical functions.
A few other handouts using problems derived from Math 152 workshops
were given out and discussed in class.

### Notes on topics

Some more elaborate discussions were accompanied by notes usually
produced after the lectures.
Balls in *n-*dimensional space
A discussion of what the volume of such a ball should be, along
with related problems such as Wallis's formula and the Gamma function.

Sums of certain series
A discussion of the expectated winnings in a gambling game with an
infinite number of outcomes is used to investigate the sums of certain
series which turn out to be integer-valued and computable!

Deducing the Fundamental Theorem of Calculus from the Mean Value Theorem
This was intended to remind students beginning the course of some
important material which may have been forgotten over the summer, using
a presentation likely to be different from what had been seen before.

The aims of the ** Maple ** lab session This is what I wanted
to do and why, and what happened. There's also some comments on the
current Rutgers environment for ** Maple **.

Here's the instructional material handed out in the computer lab,
improved by the correction of misprints caught by the students. Thanks
to them for this.

Arithmetic and ** Maple **

Algebra and ** Maple **

Calculus and ** Maple **

Graphs and ** Maple **

### Ending with some advice

During the last week of the course, I impetuously wrote a
short note about giving oral
presentations. I wanted to help students acquire some confidence and
knowledge about this important skill which is necessary in any
academic or business environment.
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