I was introduced to the geometric interpretation of correlation and linear regression recently.
Orignially due to the famous statistician R.A.Fisher, the idea is that the correlation between
two variables is the cosine of the angle between the 2 vectors in n-dimensional space.
This can be demonstrated in Maple as follows:
First, we represent each variable as a vector and transform it so that it is centred at its
mean and has a length equal...
In a reply to Markiyan Hirnyk's recent question on this topic, Alec Mihailovs posted solutions
for n=1..7 for the mean distance between random points in an n-cube.
I also
Why is it possible for http://www.mapleprimes.com/users/abraham to continue posting spam ? It is incredibly irritating for me, and I presume it must be for other bona fide users. Why can't the account be disabled, made inactive, or whatever is necessary to stop this ridiculous activity ?
In this post I will describe a little about the OU course MS325: Computer Algebra, Chaos and Simulations, which I took last year.
MS325 is a level 3 OU applied mathematics course, which means, roughly that it is pitched at the level of a final year mathematics undergraduate. It is split into three components: Computer Algebra, which teaches the use of Maple and Maple programming; Chaos, which teaches dynamical systems, deterministic chaos and fractals, with an emphasis...
Greetings all
I'm currently using an AMD Athlon system, 2GHz with 4GB Ram with 64 bit windows 7
I'm considering an intel Core i7-720QM (1.6GHz, 4 Cores/8 Threads, turbo up to 2.8 GHz) with 8GB Ram with 64 bit windows 7
Do you think I'll see a noticable improvement over what I'm seeing now, with Mapl 13.
Thanks
LR
This is an update to my earlier post on the Rossler system, one of the simplest examples of a dynamical system in 3 dimensions that can exhibit deterministic chaos.
restart;
interface(displayprecision=10):
PDEtools:-declare(prime=t,quiet):
ross_x:=diff(x(t),t)=-y(t)-z(t):
ross_y:=diff(y(t),t)=x(t)+a*y(t):
ross_z:=diff(z(t),t)=b+x(t)*z(t)-c*z(t):
rossler_sys:=ross_x,ross_y,ross_z;
#Find fixed points:
So it appears that using subscripts in Maple is not a good idea.
I ran into this problem for the first time yesterday, and is documented here:
http://www.mapleprimes.com/forum/drivenharmonicoscillatoramplitudephaseangle#comment-32780
And now it seems I've run into it again. Or possibly I have made a mistake ;)
This is part of an implementation of Newton-Cotes method of numerical integration:
restart:
NCcoef := proc(N::integer)
# procedure returns the Newton-Cotes coefficients for an
# appoximation with N+1 points
local a,c,p,h,B,LH,RH,eq,seqeq,seqco:
h := B/N:
Here is the Rossler system, one of the simplest examples of 3 dimensional deterministic chaos (under certain conditions according to "params"). Thanks to Doug and Joe for various assists. Comments and critiques most welcome !
restart;
interface(displayprecision=10):
ross_x:=diff(x(t),t)=-y(t)-z(t):
ross_y:=diff(y(t),t)=x(t)+a*y(t):
ross_z:=diff(z(t),t)=b+x(t)*z(t)-c*z(t):
rossler_sys:=ross_x,ross_y,ross_z;
#Find fixed points:
sol:=solve({rhs(ross_x...
Here's a simple rocket model
I came across this issue on my course today, and found it somewhat surprising:
restart:Digits:=7:
foo:=1/2*sqrt(3):
evalf(foo);
0.8660255
evalf[5](%);
0.86603
evalf[5](foo);
0.86605
I suppose this means that whatever algorithm Maple uses to compute the square root also works to the specified level of accuracy and the above is a result of accumulated rounding errors.
This blog will contain postings documenting some of my mathematical travels. In particular it will chronicle my experiences and problems in learning maple and the mathematics I am studying along the way.
Excuse me, I'm very new here, but what's the main purpose behind users blogs on mapleprimes ? I see many (perhaps most ?) blog postings that could just as easily (and perhaps more usefully, for other members, that is) be posted in forums since they are often asking for advice on various matters.....
