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I have a quote on my teaching room along the lines of .......
"There are three physics courses taught at most universities: physics with calculus, physics without calculus and physics without physics."
It sounds like Physics First could be a prerequisite for "physics without physics."
Speaking of physics without calculus, is this calculus without calculus?
I've been cruising this course for a long time....
11 comments:
Hey! I just bought that!
Having received "Chicago Calculus" in college (All Modeling Deer Populations on TI-81s All the Time!), it should be right up my alley.
(Have I told the story yet about the physics prof who team taught the course with the calc guy getting utterly steamed in January when we couldn't integrate yet? We'd only done derivatives to that point, but yeah, we kinda needed to know a little more to move ahead in physics. So he stopped the physics lecture and started an impromptu calculus one.)
The calculus text you linked to appears to be calculus appreciation. Content free calculus and physics for the 21st century!
It's definitely calculus appreciation -- but there are a couple of engineering & math major types who say the course was useful to them as an adjunct to a real course.
I'm planning to teach myself calculus using Saxon Calculus.
Of course, first I have to get through Saxon Advanced Math.
BUT: first I have to get proficient in logarithms.
AND: this summer, it's ALEKS geometry.
As soon as I finish ALEKS Algebra 1.
(Does that sound like a lot?)
When I was an undergraduate there was a course entitled (informally) "Physics for Poets." It was not a course for the lazy but apparently it required much less math expertise than "regular" Physics 100 or whatever it was called then, and it didn't qualify you for more advanced courses in physics. At that time you needed 2 or 3 lab science credits to graduate, even if you were in the humanities. I took zoology, geology and I think botany. Really loved geology and had I taken it before junior year might have decided to change fields.
High school physics was fascinating (and well-taught in my case; I loved it) but for some reason I didn't get seriously interested in sciences until much later. Too many competing interests.
Do many colleges still require a cross section of courses -- some math, some science, etc even if you are in sociology or comparative literature?
Incidentally, there really is a rigorous, mathematically correct class on Calculus without Calculus: Limits.
Calculus was the natural end product of studying limits; it's an elegant unification of all the different methods used in limit problems, and generalizable well beyond the original, uh, limits of Limits. In HS, we had to take a year of Precalculus before Calc; arrogant schmuck that I was, I was insulted by the notion at the time, but, in retrospect, I think it saved my mathematical future. I think we spent close to half of the year picking apart limits and continuity in seemingly every way imaginable.
Unfortunately, I'm pretty sure that's not what this book is about.
"Formulas are important, certainly, but the course takes the approach that every equation is in fact also a sentence that can be understood, and solved, in English."
so why do these folks
think they call it "calculus"?
--i.e., collection of techniques
for *performing calculations*.
careful study of limits
(and of continuity; much the same)
was historically much *later*
than derivatives and integrals.
and probably for most students
it'd be easier to *delay*
limits rather than (as in almost
every calculus *book*)
putting 'em first.
"handwaving" was good enough
for newton, leibniz, and euler.
"epsilon-delta" is a 19th century
thing; calculus got started
in the 17th. this was no accident.
i've long felt that the "natural"
intro to calculus is *series*.
something along the lines of
konrad knopp's classic.
Yeah, I'd agree with vlorbik here. When I first hit calculus, I didn't see the point of limits (just like I didn't see the point of logarithms when I hit Algebra II). The mathematicians love limits, but I wonder if students would get more out of them if they started with series, derivatives, and integration, and then talked about the underlying theory and "epsilon-delta."
I recall that limits were introduced in order to define what a derivative is. There wasn't extensive work done with limits--just general operations and some derivations, but not a whole bunch. After Calc III, there was a "bridge course" that I had to take which was fundamentals of real analysis which then gets into sequences, limits thereof, Caucy sequences, continuity, epsilon delta, etc. We had a smattering of epsilon delta in freshman calc, but I was not up to it at that point.
It varies. I know that at my school, they spend nearly half of Calc I on limits, which is overkill. The order Barry Garelick describes makes a lot more sense to me.
I'd agree with Barry and Vlorbik also.
I studied my Math in the UK where the idea of using limits as a substantive introduction to calculus is almost unheard of. The common approach can be found here.
The usual approach would be differentiation from first priciples leading onto optimisation and integrating to find area under curves in grade 11.
In Grade 12, we'd stretch calculus methods (chain rule, integration by parts, etc ....) .... a rigorous approach to limits is saved for undergraduate level work.
Using limits as an introduction to calculus would be akin to using Peano's axioms as an introduction to consecutive numbers.
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