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

This material is also available in GIF format.

### Starting with the syllabus

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

### Exams

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.

### Workshops

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.

### Maple

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.