tomleslie

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These are answers submitted by tomleslie

evalf(int(ln(z)^6/(1+z^3), z=0..infinity));

returns 725.5729630 - so what exactly is the problem?

 

as in


1*Unit(m)+d*Unit(m)=2*Unit(m);

Before applying numerical solution methods (I mean why bother?), one can show that the supplied PDE is inconsistent with the supplied boundary conditions. See attached

pdeProb.mw

 

Consider the value of the integran at the lower limit (u=1) - it is infinite. Still think this integral can solved for arbitrary n?

By the way - is this a typo, lousy cut-and-paste, double integral, whatever - why does 'du' occur twice?

Given the pde

eqn:=0.3846153846*(diff(F(x, y), y, y))+diff(F(x, y), x)-(diff(w(x), x, x))*y-(1/2)*(int(diff(F(x, y), x), y = -1 .. 1))
        +diff(F(x, y), x, x)-(diff(w(x), x, x, x))*y-(1/2)*(int(diff(F(x, y), x, x), y = -1 .. 1));

the command

sol:=pdsolve(eqn, F(x,y));

will produce the "solution"

sol:= F(x, y) = (diff(w(x), x))*y-_C1*y/exp(x)-(1923076923/5000000000)*_c[2]*x*y+_C2*y+
                       (1/6)*_c[2]*y^3+_C4*y+_F1(x)

In this expression _C1, _c[2], _C2, and _C4 are arbitrary numeric constants: not functions of anything. There are a couple of "interesting" aspects to this equation:

  1. The existence of the sub-expression _C2*y+_C4*y: since both _C2 and _C4 are arbitrary and numeric, then they can be combined into _C3*y: why didn't Maple do this - don't really know
  2. The existence of the "indexed" arbitrary constant _c[2]: why is this an "indexed" constant? - particularly given that there is no _c[1] or _c[3]. I haven't seen an indexed constant returned by a call to pdsolve() before: and I have no idea why it is occurring in this case

You should laso be aware that the last term _F1(x) represents an arbitrary function of 'x'. preceding terms in the solution are functions of 'y', (or 'x' and 'y'), but the existence of _F1(x), means that any function of 'x' alone *ought* to be OK

Tidying the given solution, means that

sol:=F(x, y) = (diff(w(x), x))*y-_C1*y/exp(x)-(1923076923/5000000000)*_C2*x*y+_C3*y+
               (1/6)*_C2*y^3+_F1(x)

ought to be a valid solution: and in fact checking this with

pdetest(sol, eqn);

confirms, that the "tidied" version of the solution is still a solution.

I have laso tried the tidied version when substituting various functions for _F1(x), and pdetest() confrims that each of these is a solution (NB, I only tried functions which were continous, and differentiable)

Overall a very interesting PDE - idle curiousity: does it arise as a result of some "physical, real world" type of problem, or is more or less an "exercise in mathematics"?

Do you just want the parametric plot?

If you do then checkthe help at ?Parametric Plots. The simple command

plot( [2*t*(3*t^4+50*t^2-33)/(t^2+1)^3,
         2*(7*t^6-60*t^4+15*t^2+2)/(t^2+1)^3,
         t=-100..100
       ]
     );

would appear to produce the plot you want.

If you want the corresponding space curve, you could use

plots:-spacecurve( [ 2*t*(3*t^4+50*t^2-33)/(t^2+1)^3,
                                  2*(7*t^6-60*t^4+15*t^2+2)/(t^2+1)^3,
                                  t
                                ],

                                t=-100..100
                             );


 

depending exactly on what you want the result to look like.

Try playing with the following

restart;
g := proc(z)
               local w;
               w := Re(z)*exp(Im(z)*I);
               return 1/(1-z);
       end proc:
changecoords(plots:-complexplot3d(g, 0..1+2*Pi*I, axes=boxed), cylindrical);

 

As the expression is written, the existence of the multiplying factor cos(x)*exp(-t) means that the expression is zero whenever cos(x)=0. Given that x=0..2, this will be true whenever x=Pi/2.

In a similar fashion, the integral in the numerator will return 125*sin(L), which will therefore be unconditionally zero whenever L=An_Integer*Pi - and hence the whole expression wiil be zero

Having considered the above carefully - when you ask "how can i find the lambda " - do you mean pairs of lambda[1], lambda[2]. As written, lambda is an indexed variable in your expression - is this intentional?

So far as I know there is are such concepts in Maple as "text mode" or "math mode".

There are however two choices called "Document Mode" and "Worksheet Mode"

So far as I am aware

  1. if you select "Document Mode" then 2-D Math Input is mandatory
  2. if you select "Worksheet mode" then you have the choice of 1-D or 2-D Math Input

Now I'm strictly a "worksheet mode", with "1-D math input" kind of guy, cos I (personally) find this most convenient,

However you can *play* with these settings using

Tools->Options->Display->Input Display

and

Tools->Options->Interface->Default format for new worksheets

until the find you the one you want

 

 

Rather obviously, by ensuring that when you specify a floating point format specification (probably one of %e, %f, %g, %y), then the corresponding expression either is (or can be evaluated) to a floating point number.

Integers or rationals will be automatically coerced to a floating point number, so whatever the expression you are formatting is - you can guarantee that it is not

  1. a floating point number
  2. an integer
  3. a rational (ratio of integers)

For example, in the equation definition above

S:= 1 + 2.sin(t) - 1.9.t ;

you appear to think thaat the '.' character can be both a decimal point (as in 1.9) and a multiplication symbol!

There are several other syntax errors.

The above expression has only one root, which can be found using

   S:= 1 + 2*sin(t) - 1.9*t ;
#
# Plot the function just to show that
# there is only one root
#
   plot(S, t=-2..2);
#
# Compute root
#
  Result:= Student[Calculus1]:-Roots(S)

I see three possibilities

  1. Mapleprimes does not accept uploaded files
  2. Your browser settings do not allow file uploads
  3. Your firewall/security processes do not allow file uploads

I'll deal with each of these in turn

  1. All(?) Mapleprimes users, including me, are able to upload files with no problem, so I think we have to accept that there isn't a real problem with the Mapleprimes site
  2. Depending on you browser (and its settings) certain things may be "forbidden". For example, my default browser is Firefox, and it *really* does not like me copying hypertext links around the Mapleprimes site (or any other site for that matter).. I know how to switch off this Firefox restriction, but I choose not to. I can usually work around it. In order to check whether you have a browser restriction, I can only suggest that you experiment with a different browser. When I decide that I really *really* need a hypertext link in a post on Mapleprimes, then I just use either Chrome or IE11 (either of which will work because their default security options are a bit more "relaxed". So does the same problem occur with all browsers - if not then you need to adjust the security settings on your default browser (or use a browser which works)
  3. If no browsers allow file uploads to Mapleprimes, then I would recommend that you try file uploads to other "similarish" websites. For example download a matlab .m file from somewhere and try uploading to http://www.use-matlab-online.com/matlab-user-forum.html#/ (you will probably have to register first). Or do the same with Mathematica. Basically can you upload any files to anywhere? If you can't then the problem is with your site security processes.

For the first part of your question, the easiest way is probably to generate two plots and then display them together, as in the 'toy' example below

ymax:=10:ymin:=5:fn:=x*sin(y):
a:=plot3d( fn, x=-5..5, y=-ymax..-ymin, color=red):
b:=plot3d( fn, x=-5..5, y=ymin..ymax, color=blue):
plots[display]([a,b]);

I don't really understand the second part of your question (and some of it is missing anyway)

 

Carl is correct, but actually you don't even need a display() command, because plot3d() will accept a list of plots as its first argument, so

plot3d( [seq(srr[j], j=1..n)], +whatEverPlotOptionsYouWant)

ought to work. I have tested this with

srr[1]:=r^2*sin(theta):
srr[2]:=r+theta^2:
plot3d( [ seq(srr[j], j=1..2)], r=0..1, theta=0..2*Pi, color=[red,blue]);

and it works perfectly

Assuming 'A' is some kind of sequence, then [A] will produce a list

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