AWK, LaTeX, and Maple
In rewriting the ODE Manual with Maple, I discovered that, while
preparing the manuscript demanded that I include LaTeX commands in the text
areas, the Export to LaTeX command of the new release translated the commands
to make them print, instead of having them remain as executables. I then had
to learn AWK to write a script that would reverse the translation. The
following book was very helpful.
SED & AWK
by Dale Dougherty
Here is the actual script, which Phil Yasskin and I used to automate
the translation as the ODE Manual and the Stewart Calculus extensions were
prepared. It has been updated to Maple 6.
NAWK Script
For those individuals wanting to use the script in MS-DOS/Windows, the following
URL shows a source of the MS-DOS binary executable for GAWK (The GNU version).
GAWK Binary File When downloaded and unzipped, the file gawk.exe will appear in the
bin subdirectory.
Using Maple for Proofs
Like most mathematicians, I am aware of the formula due to the 1st century A.D.
Greek mathematician Heron for finding the area of a triangle from the lengths
of its sides. On the other hand, I have never seen a proof by synthetic
geometry; so , just for fun, I did one based on analytic geometry, using the power of Maple
to reduce the calculations to a reasonable level.
Maple Proof of Heron's Formula
Lagrange Multipliers
Maple has a very nice command for computing constrained maxima and minima.
However, it is often difficult for a beginning student to visualize what
the command produces. As an amusing exercise, I modified the implicitplot
command so that one can graph a space curve over an arbitrary implicitly
defined planar curve, showing the locations of the extrema in a third dimension.
Space Curve Over Implicit Function
Newton's Method
Many students treat Newton's Method for finding the zeros of a function as just
an exercise in memory, rather than understanding what the method does. I wrote a
Maple animation to accept arbitrary functions and iteratively follow the tangent line
approximations as the procedure either does or doesn't converge.
Newton's Method Animation