How to learn how to apply calculus?
labyrinth
But even though I've taken and passed these courses, I still have little idea how to apply the knowledge. I can usually work out basic algebraic real-world problems, and estimate a simple probability when playing card games w/ the family, but most of my math goes unused.
I would especially like to use calculus more, but it seems like it only applies to throwing balls in a parabolic fashion, or maybe in gauging the rate of blood flow in an artery. I often feel like there are mins and maxes lurking behind the scenes as I push the brakes in my car going downhill, but on the whole, I feel like I could be having a lot more fun w/ applying math.
Are there some good books or resources that would give a lot of "story problems" like they did in high school for algebra? I think what would help me most would be a many exercises applying each method to a variety of seemingly different circumstances.
I'm open to suggestions if you found something that helped you.
thanks!
Frederick Williams
Maybe a physics book?
There's Polya and Szego _Problems and Theorems in Analysis_ in two
volumes. Their idea of what analysis is is very broad and some of the
problems are quite demanding.
Here's a problem for you: if gravity followed an inverse cube or inverse
fourth power law instead of an inverse square law, what would planetary
orbits look like? (Iirc, r^{-n} for n = 5, 6, ... leads to elliptic
functions, but n = 3, 4 are elementary.)
> I'm open to suggestions if you found something that helped you.
>
> thanks!
--
But you see, I can believe a thing without understanding it.
It's all a matter of training.
--Lord Peter Wimsey in Dorothy L Sayers' _Have His Carcase_
David Moran
"labyrinth" <laby...@operamail.com> wrote in message
news:16706655.1232425926...@nitrogen.mathforum.org...
You might consider buying an introductory ordinary differential equations
book and go through that.
Dave
Junoexpress
physics. Of course, when I was growing up, so to speak, the physics
applications that I learned about in school (planes, pulleys, and that
kind of thing), pretty much bored me to death. Wasn't till I got to
college and was exposed to a wide range of physics related research
that I found a particular field where math and physics can be applied
in which I was interested (biology and chemistry). One book that
really got my motor going was a slim little book by a Harvard
biophysicist called Howard Berg, entitled "Random Walks in Biology".
It requires nothing more than a decent background in calc and a little
prob stats and showss how physics and math can explain a a whole lot
of cool things (like how bacterial flagella work, how cells move,
etc.) Unfortunately however, there are not that many books that deal
with such a broad spectrum of interesting applications in the fashion
that you require.
Perhaps a good text to try out would be Courant's "Integral and
Differential Calculus". It is very much based in physics-related
applications and written in an exceptionally clear manner. You could
also try Feynman's Lectures on Physics, if you are really in the mood
for intellectual stimulation. He combines interesting physics problems
with clear calculus based analysis.
Good Luck,
Matt
Ken Pledger
<16706655.1232425926...@nitrogen.mathforum.org>,
labyrinth <laby...@operamail.com> wrote:
> ....
> I would especially like to use calculus more ....
>
> Are there some good books or resources that would give a lot of "story
> problems" like they did in high school for algebra? ....
In article
<8dd1d4b3-3581-4a09...@k1g2000prb.googlegroups.com>,
Junoexpress <MTBre...@gmail.com> wrote:
> ....
> Perhaps a good text to try out would be Courant's "Integral and
> Differential Calculus". It is very much based in physics-related
> applications and written in an exceptionally clear manner....
Agreed. Some of the old-fashioned books are stronger in
applications than most modern texts.
A little-known book about differential equations in the context of
their applications is Henry Margenau & George Moseley Murphy, "The
Mathematics of Physics and Chemistry", 1943. You may be able to find it
in a library.
For easier reading, a more recent text on elementary calculus is
Morris Kline, "Calculus: an Intuitive and Physical Approach".
Riding my own historical hobby-horse, I can also suggest an easy
little book which shows how elementary calculus originated: Otto
Toeplitz, "The Calculus: a Genetic Approach".
Ken Pledger.