Friday, January 23, 2009

Friday floobydust

posted by db at 4:08 PM 1 comments

Wednesday, January 21, 2009

Wednesday flooby

posted by db at 1:54 PM 0 comments

Tuesday, January 20, 2009

Faster numeric arc lengths on the Voyage 200 and TI-89

The built-in arclen() function will return a numeric result for an arc length if a symbolic solution cannot be found. For example,

arclen(-x^3 + 3*x^2 - 2x + 2/x - 2/x^2 + 1, x, .769, 2.428)

returns 4.2413 in about 62 seconds in APPROX mode. We can speed this up by using nint() to numerically integrate the arc length integrand, as follows.

First define a simple function to find the arc length integrand:

: arcleni(f,x)
: Func
: sqrt((d(f,x))^2+1)
: EndFunc

where f is the function of the desired arc length and x is the independent variable. d() is the built-in derivative function. We then find the arc length with

nint(arcleni(-x^3+3*x^2-2x+2/x-2/x^2+1,x),x,.769,2.428)

which returns the arc length in about 27 seconds, saving 35 seconds.

It is likely that arclen() spends the extra time trying to find a symbolic solution before falling back to the numerical integration.

posted by db at 4:44 PM 0 comments

A little math reading today

posted by db at 2:42 PM 0 comments

Monday, January 19, 2009

Lotus Symphony lives

I'm a PC dinosaur, so I spent many pleasant hours learning and using Lotus Symphony before MS Office took over. It turns out that Symphony is still available, and free, to boot.

Short article here

IBM download page here

posted by db at 4:18 PM 1 comments

Worth reading today

posted by db at 4:07 PM 0 comments