D. J. Keenan:
That did the trick. Thank you.
Pages 69 and 70 of the Guide should have but seem not to have made an impression when I first read them. Thanks again.
I haven't been able to get The Assume Facility to help. I tried it on an integers only problem a while back and it didn't help there either.
Thank you for letting me know that Maple did not return a closed form solution but rather a 2nd order equation. I'm not yet able to read and understand all the math that Maple produced. I plan to keep trying.
Thank you for that elegant (I hope that's the word) presentation of the problem. Nahin is so fond of complex numbers that I am surprised that he did not have something similar in his book.
All that precedes this in this thread (topic) is about a numerical solution to a set of differential equations. I took a stab at typing in the differential equations and applying the Maple 11 ODE package and Maple produced an answer but I don’t know what to do next. I would like to use the closed form solution (assuming that that is what Maple has given me) to reproduce the graphs on page 88 of Dr. Euler’s Fabulous Formula
by Nahin. Nahin is a Matlab man and he says “To solve these differential equations analytically
for x(t) and y(t) is probably not possible, that is, I can’t do it!”
The differential equations and Maple's solution are in:
View 4937_Page_87_ODEs_3.mw on MapleNet
or Download 4937_Page_87_ODEs_3.mwView file details
The link can be found in the File Manager
Can anybody help me get a plot out of what Maple's answer?
How are the "Upload/Use File or Worksheet" things different from Maple document or worksheet files?
When I look at the post that I just made above. I don't see any of the structure that I see when I view the same files in Maple 11. In Maple, I see a section at the top. I see paragraphs and blocks.
I don't know how to show the things that I think are some of my problems.
If I start with this document file:
View 4937_Tim3.mw on MapleNet
and I cut the first math document block and paste it into the section above, which is, before the paste, all text, I get the following document file which produces error messages and no graph
View 4937_Tim4.mw on MapleNet
This seems to me to be a reasonable thing to do and so I must not understand enough about sections, blocks, paragraphs and perhaps other structural or scope features of document files.
I think that this identifies the version of Maple that I am attempting to use:
print(`output redirected...`); # input placeholder
Maple 11.00, IBM INTEL NT, Feb 16 2007 Build ID 277223
What version are you using?
I get error messages:
> for n to N-1 do x[n+1] := x[n]+`Δx`(n); y[n+1] := y[n]+`Δy`(n) end do;
Error, final value in for loop must be numeric or character
> C := seq([x[n], y[n]], n = 1 .. N);
Error, unable to execute seq
> M := seq([cos(t[n]), sin(t[n])], n = 1 .. N);
Error, unable to execute seq
I finally noticed "( includes worksheet link )" and "maple 11 worksheet download". I have your Maple 11 document and it works beautifully here. Thank you. Thank you. Thank you.
The difference that I first noticed is that you put the first 11 lines of Maple in the first paragraph and I put each line in it's own paragraph.
Also, I have been careless about putting a colon or semicolon at the end of each line or should I say expression. In document mode they didn't seem to be necessary. Perhaps they are only necessary if you want the thing to work.
You also have a lot of empty paragraphs at the end.
I like Paul J. Nahin's writing. I've read most of three of his books. There's a lot of math in his books but also a lot of history. I did know that Euler went blind, first in one eye and then totally but I didn't know about his orbital calculations. In Dr. Euler's Fabulous Formula Nahin quotes Charles Darwin as follows:
"During the three years which I spent at Cambridge my time was
wasted, as far as the academical studies were concerned, as
completely as at Edinburgh and at school. I attempted
mathematics, and even went during the summer of 1828 with a
private tutor (a very dull man) to Barmouth, but I got on very
slowly. The work was repugnant to me, chiefly from my not being
able to see any meaning in the early steps in algebra. This
impatience was very foolish, and in after years I have deeply
regretted that I did not proceed far enough at least to
understand something of the great leading principles of
mathematics, for men thus endowed seem to have an extra sense."
I retyped everything with care and it still doesn't work.
This is too hard for me.
Did you try my worksheet right above your last comment - it's 2-D
Yes, it's a thing of beauty but I can't seem to get it to run here like it runs there.
Tim Van Dusen,
You must be a wizard or guru. I'm not. I tried to duplicate your results and got the following
View 4937_Page_87Q.mw on MapleNet
or Download 4937_Page_87Q.mwView file details
I have something that works, my "P"th try.
View 4937_Page_87P.mw on MapleNet
or Download 4937_Page_87P.mwView file details
It's a worksheet rather than a document. There are two red prompts in it. The others are black or gray. Their color is out of my control. It's 1-D Math. When I convert it all to 2-D Math the graph will not display.
Can anyone show me the way out of this Maple darkness.
View 4937_Page_87L.mw on MapleNet
or Download 4937_Page_87L.mwView file details
This is FUBAR
> f := proc (`ϰ`) options operator, arrow; `ϰ`*`Δt` end proc;
I want a vector that contains floating point numbers that represent time. I get expressions.
When I try to plot, nothing happens because I have expressions and not floating point numbers.
I'm trying to get Maple to do a Matlab thing and all I can get from Maple is error messages and nothing plots.