gulliet

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16 years, 238 days

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Well, when I said earlier that the solution was really huge, even Maple (in standard interface) thinks so :-) 97_lengthofoutputexceedslimit.jpg I shall try to find --- remember --- a way to increase this output limit (I am rather confident that this is possible, though I cannot remember what must be change right now). Regards, --Jean-Marc
Maple took about 18 minutes of cpu time to solve the system with the command line interface on my machine. Also, beware that the solution returned is really huge. (I can copy and past it from the terminal window to the web form, but the web server refuses to allocate enough memory for the post.) Regards, --Jean-Marc
Maple took about 18 minutes of cpu time to solve the system with the command line interface on my machine. Also, beware that the solution returned is really huge. (I can copy and past it from the terminal window to the web form, but the web server refuses to allocate enough memory for the post.) Regards, --Jean-Marc
You could enter your ode as follows (using the palettes), then use the command dsolve to solve it. See help("dsolve") for more info. 97_enteringandsolvingode.jpg Regards, --Jean-Marc
You could enter your ode as follows (using the palettes), then use the command dsolve to solve it. See help("dsolve") for more info. 97_enteringandsolvingode.jpg Regards, --Jean-Marc
Just to illustrate Alec's explanations with some Maple code, do not forget that one can check the limit of a function f(x) as x approaches x0, on both sides, on the right, or on the left of x0, thanks to the built-in function limit. (Note that for a limit to exist at a point, the limits on both sides must not yield an indeterminate form such as infinity - infinity, or infinity / infinity ) For instance,
> limit(1/x, x = 0);
                                  undefined
> limit(1/x, x = 0, right);
                                  infinity
> limit(1/x, x = 0, left);
                                  -infinity
One can also use the various palettes available on the left site of the standard interface to enter limits and integrals. 97_undefinelimitintegral.jpg 97_definedlimitintegral.jpg Regards, --Jean-Marc
Just to illustrate Alec's explanations with some Maple code, do not forget that one can check the limit of a function f(x) as x approaches x0, on both sides, on the right, or on the left of x0, thanks to the built-in function limit. (Note that for a limit to exist at a point, the limits on both sides must not yield an indeterminate form such as infinity - infinity, or infinity / infinity ) For instance,
> limit(1/x, x = 0);
                                  undefined
> limit(1/x, x = 0, right);
                                  infinity
> limit(1/x, x = 0, left);
                                  -infinity
One can also use the various palettes available on the left site of the standard interface to enter limits and integrals. 97_undefinelimitintegral.jpg 97_definedlimitintegral.jpg Regards, --Jean-Marc
Look for the function pdsolve, which finds the solutions for PDEs and systems of PDEs. See help("pdsolve") for more info. Sorry, but I could not fully understand your notation (looks weird on my system), but you can define a function of two variables as follows. Note that you differentiate with the diff function, that the exponential function is written expO, the logarithm ln(), and multiplication is denoted by *.
> z := proc (x, y) options operator, arrow; exp(y)*ln(x*y) end proc;

                        z := (x, y) -> exp(y) ln(x y)

> diff(z(x, y), x);

                                   exp(y)
                                   ------
                                     x   

> diff(z(x, y), x, x)

                                    exp(y)
                                  - ------
                                       2  
                                      x   

You can also use the palettes located on the LHS of the screen to enter your expressions. 97_pdesyntaxpalette.jpg Regards, --Jean-Marc
Look for the function pdsolve, which finds the solutions for PDEs and systems of PDEs. See help("pdsolve") for more info. Sorry, but I could not fully understand your notation (looks weird on my system), but you can define a function of two variables as follows. Note that you differentiate with the diff function, that the exponential function is written expO, the logarithm ln(), and multiplication is denoted by *.
> z := proc (x, y) options operator, arrow; exp(y)*ln(x*y) end proc;

                        z := (x, y) -> exp(y) ln(x y)

> diff(z(x, y), x);

                                   exp(y)
                                   ------
                                     x   

> diff(z(x, y), x, x)

                                    exp(y)
                                  - ------
                                       2  
                                      x   

You can also use the palettes located on the LHS of the screen to enter your expressions. 97_pdesyntaxpalette.jpg Regards, --Jean-Marc
Sorry, I posted it twice, so I deleted the content of the second post since I do not know how to delete a post entirely. Best regards, --Jean-Marc
Does anyone else has trouble seeing the picture that is supposed to be displayed at the bottom of the post? I have tried with Safari 3.2.1 for Mac OS X 10.5.6 and Firefox 3.0.5 for Windows XP Pro SP3, and I could not get the picture to be displayed. Here is what I see with Firefox: 97_missingpicturemaplehelpfirefox.jpg And here is what I see with Safari: 97_missingpicturemaplehelpsafari.jpg Also, If I try to dowload or open the picture in another window, I get the following message: 97_missingpicturemaplehelperrormessage.jpg Best regards, --Jean-Marc
I believe this is the command you are looking for. See help("dfieldplot") for more info. For instance, you could start with the following command, then add whatever is necessary to get the desired result.
DETools[dfieldplot](diff(y(x), x) = -4*x/y(x), y(x), x = -2 .. 2, y = -3 .. 3)
In addition, when looking for how to implement some mathematical method or concept, it is a good idea to browse the table of contents of the Maple's help system. For instance, 97_maplehelpdfieldplot.png Regards, --Jean-Marc
I believe this is the command you are looking for. See help("dfieldplot") for more info. For instance, you could start with the following command, then add whatever is necessary to get the desired result.
DETools[dfieldplot](diff(y(x), x) = -4*x/y(x), y(x), x = -2 .. 2, y = -3 .. 3)
In addition, when looking for how to implement some mathematical method or concept, it is a good idea to browse the table of contents of the Maple's help system. For instance, 97_maplehelpdfieldplot.png Regards, --Jean-Marc
Is this what you were looking for? 97_plotdiscontinuity.jpg Regards, --Jean-Marc
Sometimes, it might be hard to go from one form to another because Maple (like any other CAS) tries to return what it is deemed to be the simplest representation of an expression. You can try to use function such as convert, combine, factor, expand, simplify, etc. keeping in mind that many of them accept optional arguments specifying which kind of transformations is desired. For instance, 97_goingfromAtoB.jpg Regards, --Jean-Marc
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