## Math 192, section 3, fall semester, 1996

Math 192 is second semester honors calculus. Its students have usually been self-selected from entering first-year students who have taken an AB calculus course in high school and gotten a 4 or 5 on the AB advanced placement exam. Most of the students in Math 192 have been students in the engineering honors track, together with a few high school students. The course has been viewed as a version of Math 152 with slightly more rigorous discussions in class, and with harder homework problems and test questions. Here is substantially all of the material handed out to students in this section of Math 192.

This year in section 3 the students were all first-year engineering students. I generally tried to follow the syllabus which was used in Math 152 in the spring, 1996, semester. The course also reflected the changes which were made last year in Math 152. The course had a somewhat different atmosphere from Math 152 because the class was small and the students had chosen a more challenging experience. The lectures were different. For example, a more thorough discussion of why the sum of a convergent power series was continuous was offered, an extended exposition of the volume of the unit ball in any finite dimension was given, and a derivation of the error estimate in the trapezoid rule was shown. All students in this rather small class gave oral presentations of workshop problems (please see the discussion of our changes in Math 151-152 for more on workshop problems).

Here are the two in-class exams (with solutions) which were given in the course, together with the final exam. We also show the more extended problems (many of which were taken from the Math 152 problem sets) asked of students. Most of the solutions were to be presented in written form with suitable exposition, but some were given orally. There's also some other material on volumes of balls and on sums of certain series which was handed out to students. The class made a one period (80 minutes)"field trip" to a computer lab where Maple was introduced using material shown here.

Review problems were handed out before each exam. The sets of these problems were the exams given in Math 152 during the spring, 1996, semester. See the Math 152 web site for these, please.

Please send mail to Stephen Greenfield if you have questions or comments about this material or if you use some of it in a course. An acknowledgment that the source of the material is the Rutgers Mathematics Department would be appreciated.