BC Calculus at IMSA

Note: We're redoing our web site, so these pages do not yet link to the rest of our web site. That will be changing soon. Thanks for your patience.

Here at IMSA, we use the text Calculus from Graphical, Numerical, and Symbolic Points of View, 2nd edition, by Arnold Ostebee and Paul Zorn. We've been using the text since the fall of 1995, I think, in one edition or another. The text has served us well.

At IMSA, we also believe that it is very important to have the students working together to share ideas and approaches. We see the teacher as a guide rather than a lecturer. To this end, we have created a lot of worksheets to supplement the book. Some of these merely offer a little more practice on a particular topic. Most are meant to introduce and/or extend an idea. These worksheets are intended to be done (or at least begun) during class. They do not simply hand the concepts and skills to the students, but with other students and with hints from the teacher as necessary, students are able to think through a lot of mathematics. When they do the work, they will understand and remember the concepts more fully. That is, of course, the goal.

ImpInt1.pdf ImpInt2.pdf	More problems for students to justify convergence or divergence of improper integrals. The first sheet does not assume limit comparison test, but the second one does.
GeomSeries.pdf	A review of geometric series -development of formula for the sum and some problems.
UpperBounds.pdf	This sheet talks about bounds and develops a proof of the divergence of the harmonic series.
AltSeries1.pdf AltSeries2.pdf	These worksheeets introduce the idea of alternating series as well as upper and lower bounds.
Series1.pdf Series2.pdf Series3.pdf Series4.pdf Series5.pdf Series6.pdf Series7.pdf Series8.pdf Series9.pdf Series10.pdf TaylorReview.pdf	These include a development of Maclaurin and Taylor series. These worksheets are intended to be done with help available - from the teacher and from other students. There are jumps and clarifications and hints will need to be given. This is intentional. It is suggested that an intro is given before Series 1. (Suggestion: Look the the graphs and the derivatives of both y = sin(x) and y = x - x3/6 to see what they have in common. Series 6 deals with the Lagrange error bound and e help in advance. Series 8 and 9 show how to create new series from old.
SlopeFields.pdf TI89EulerSlope.pdf EulerEtc.pdf	This set of matching slope fields is noticeably harder than the earlier, intro version. The TI-89 instructions are longer than the earlier set, including analytic solutions. Euler, Etc. extends earlier work with Euler's Method, showing a chart.
Coffee.pdf Population.pdf	Coffee looks At Newton's Law of Cooling and Population considers logistic DE's. Both assume slope fields and Euler and analytic solutions.
Vectors.pdf	A detailed example of vectors and trajectory motion.
Polar1.pdf Polar2.pdf Polar3.pdf	Polar 1 and 2 do a review of polar coordinates and basic graphs. Polar 3 is a substantive collection of problems.