Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Request for a text



At 16:36 7/8/00 -0400, Tom McC wrote:
Hello phys-listers,
I have two students who would like to study difeqs one semester and
linear algebra during the other. These are seniors in high school. I have
been given the task of introducing them to these subjects. I would like to
put a heavy physics/application twist to the material. Do you have any
suggestions for texts that would serve all these purposes? They have both
gotten 5's on the AP BC Calculus and the Physics C in Mechanics and E+M.
Thanks for your help.
Tom McCarthy


I hope Tom will forgive me for using his request as a stimulus for
plumbing the depths of my ignorance of various components of the
physics syllabus.

His question (above) easily led me to a simpler question to pursue:
What is a strong physics application of the differential equation
methods accessible to a college freshman?

I took an old Barnes & Noble College Outline "Differential Equations"
off the shelf to get an impression of the scope.

I see that in the nineteenth of twenty chapters, titled "Elementary
Scientific Analyses" there was some mention of applications:

Pursuit Courses:
what course does a dog follow in running towards his master walking
a straight path?
what course does a fighter pilot fly in level flight at constant speed
to fire a gun to hit a target flying a straight line at constant
height and speed?

Ballistic Trajectories:
what is the free fall motion of a body in a gravitational field of
a spherical Earth - the ballistic trajectory of a missile, as
an example?

My impression is that these three samples of the topic space are
not calculated to consume the student's interest, especially not
a female student's curiosity, I imagine.

I next consulted the introductory college physics text I had on hand:
"Crummett & Western's University Physics, Models & Applications".

I have remarked before on its attractive presentation and
sympathetic feel. I have no conception how respectible it is in
academic terms however.

In back it carries an appendix (2) of useful numerical methods.

Under A2.1 Solving Equations there are three methods noted;
Binary Search, Iteration and Brute Force.

I will take the liberty of quoting a little of this last topic.

"Although frowned on in polite circles, there's really nothing
wrong with brute-force calculation for one-time problems.
Such calculations are specially handy if you have a spreadsheet
handy. Write your equation in the form h(x) = 0
In column A of your spreadsheet write 100 equally spaced values
that seem reasonable for x (Use the FILL command of your spreadsheet)
Then in column B write the function g(x) in the 100 cells next to the
x-values in column A (Use the COPY command, of course!)

"Now just scan column B and look for the place(s) where g(x) changes
sign. Refill column A new x-values starting with a value just less
than than that for which g(x) changed signs and using a smaller
incremental delta x-value in the FILL command. Once again scan the
g(x) column for the sign change and repeat the process until you
find a value of x for which g(x) = 0 to sufficient accuracy.
Inelegant as it is, this method is fairly quick and just the ticket
when you're not feeling clever."

Is there a high school senior who would not be attracted to such an
immensely practical tutelage, couched in such student-friendly terms?

Passing on to A2.4 Differential Equations, I see mention of N2 and
Runge-Kutta, then A2.5 Simultaneous Overrelaxion (delightful sounding
prospect!) with Laplace given boundary conditions applied in
electrostatics, and Jacobi's method with a spreadsheet again,
and tentative values for an over relaxation parameter for quicker
convergence. All this in four pages.

THAT'S the kind of text your students could use - though I hesitate to
advocate a 4 cm thick four color production for the sake of the
relatively few pages that would serve your present purpose.

Sincerely


brian whatcott <inet@intellisys.net>
Altus OK