March 21, 2010, 7:32 pm
There’s a discussion going on right now in the Project NExT email list about calculus textbooks, the merits/demerits of the Stewart Calculus textbook, and where — if anywhere — the “next wave” of calculus reform is going to come from. I wrote the following post to the group, and I thought it would serve double-duty fairly well as a blog post. So… here it is:
I’d like to add my $0.02 worth to this discussion just because (1) I’m a longtime Stewart Calculus user, having used the first edition (!) when I was an undergrad and having taught out of it for my entire career, and (2) I’m also a fairly consistent critic of Stewart’s calculus and of textbooks in general.
I try to see textbooks from the viewpoints of my students. From that vantage point, I unfortunately find very little to say in favor of Stewart’s franchise of books, including the current edition, all of the…
February 8, 2010, 7:00 am
I’m doing some research, if you can call it that, right now that involves looking at past editions of popular and/or influential calculus books to track the evolution of how certain concepts are developed and presented. I’ll have a lot to say on this if I ever get anywhere with it. But in the course of reading, I have been struck with how little some books change over the course of several editions. For example, the classic Stewart text has retained the exact wording and presentation in its section on concavity in every edition since the first, which was released in the mid-80′s. There’s nothing wrong with sticking with a particular way of doing things, if it works; but you have to ask yourself, does it really work? And if so, why are we now on the sixth edition of the book? I know that books need refreshing from time to time, but five times in 15…
April 6, 2009, 12:58 pm
You too can own a massive house if you sell enough calculus books.
There’s a new, five-story, 18000 square foot, $24 million house in Toronto that is built of curves and glass and boasts its own professional-quality concert hall. The owner? Not a billionaire financier, head of state, movie or sports star, or anything of the sort — it’s James Stewart, author of the Stewart Calculus franchise of books.
From the Wall Street Journal article:
As visitors descend into the house, the fins disappear and the views widen. On the first floor, push a button and a 24-foot wall of glass windows vanishes into the floor, opening the pool area to the outside. Curves are everywhere, down to the custom door handles and light fixtures. The architects are even working with Steinway to create a coordinating piano. [...]
February 26, 2009, 12:12 pm
In the Stewart calculus text, which we use here, the first chapter is essentially a precalculus review. The second chapter opens up with a treatment of tangent lines and velocities, with the idea of secant line slopes converging to tangent line slopes and average velocities converging to instantaneous velocities taking center stage.
Calculating average velocity is just a matter of identifying two time values and two position values and then performing two subtractions and a division. It is not complicated. Doing this several times for shorter and shorter time periods is also not complicated, and then using the results to guess the instantaneous velocity is a little complicated but not that bad once you understand the (essentially qualitative, not quantitative) idea behind shrinking the length of the interval to get an instantaneous value out of a sequence of…
May 5, 2008, 1:48 pm
Asking the following question may make me less of a mathematician in some people’s eyes, and I’m fine with that, but: How do you explain the meaning of the differential dx inside an integral? And more importantly, how do you treat the dx in an integral so that, when you get to u-substitutions, all the substituting with du and dx and so on means more than just a mindless crunching of symbols?
Here’s how Stewart’s Calculus does it:
- In the section introducing the definite integral and its notation, it says: “The symbol dx has no official meaning by itself; \(\int_a^b f(x) \, dx\) is all one symbol.” (What kind of statement is that? If dx has “no official meaning”, then why is it there at all?)
- In the section on Indefinite Integrals and the Net Change Theorem, there is a note — almost an afterthought — on units at the very end, where there is an implied connection between…