Hi everyone,

I have a question about surface fitting. I tried to follow the step of application "Fitting an Ellipse to Data" to fit the ellipsoid surface but got the incorrect result:

It seems that the convergence condition can be modified but I have no idea. 

The related Maple file is attached:

Ellipsoid_Surface_Fitting.mw

I'd appreciate any help on this topic. Thank a lot.

Some years ago member William Fish started a long discussion in part about a numeric integral involving high parameter (high oscillation) Bessel J0. That numeric integration task appeared in a Bitwise Magazine article.

At that time even obtaining numeric results involved extra effort such as handling real and imaginary components of the integrand separately, and requesting particular methods (sometimes hacked, to bump up the subinterval limit, for very high parameter values).

That led to a post where I showed that the result could be obtained quickly by using a fast compiled BesselJ (J0) from an external library along with a modified low-level call to a particular evalf/Int solver.

And sometime after that a numeric result for the real & imaginary split integrand became much more readily (if not quickly) available by using a new `maxintervals` option of evalf/Int to specify the maximal number of subintervals for the particular solver.

Maple 18 has its own compiled implementations of the Bessel functions for "hardware" (double) precision arguments. So now the numeric evaluations of the integrand are computed much faster.

Using Maple 18.00 on 64bit Windows 7 the same numeric results obtain in under a second, in a simple, single call to evalf,Int.

restart:

CodeTools:-Usage(
  evalf(Int(BesselJ(0, 50001*x)*x*exp(I*(355*x^2*1/2)), x = .35 .. 1))
                 );
memory used=9.28MiB, alloc change=32.00MiB, cpu time=437.00ms, real time=441.00ms, gc time=0ns

                           -8                 -8  
             3.181753502 10   - 7.798301124 10   I

restart:

CodeTools:-Usage(
  evalf(Int(BesselJ(0, 10000*x)*x*exp(I*(355*x^2*1/2)), x = .35 .. 1))
                 );
memory used=6.83MiB, alloc change=32.00MiB, cpu time=218.00ms, real time=211.00ms, gc time=15.60ms

                            -7                 -7  
             -2.007752340 10   + 4.275388462 10   I

Of course the ramifications of fast, compiled Bessel functions at double precision extend much farther than just this one example. But I like seeing the speed improvement in terms of a concrete example.

acer

What is the set of the points (x,y) s. t.

y^2+y^3+(y^3-x^2-3*x*y)^(1/4) <= 5*x*y ?

How to draw it with Maple?

Using the Fourier convolution theorem to solve f(t) =sin (t)

f(t)=R dJ(t)/dt+J(t)/C

R dJ(t)/dt+J(t)/C=f(t)

where f(t) is a driving electromotive force. Use the fourier transform to analyze this equation as follows.

Find the transfer function G(alpha)  then find g(t) .

 Thanks ....

Hi , everyone who love Maple and dsolve command, 

my ODE is :

sys_ode := diff(d11(m), m) = -(3*sin(m)^2-1)*d31(m)/a^(3/2)+(-3*cos(m)*sin(m)/a^(3/2))*d41(m), diff(d21(m), m) = (-3*cos(m)*sin(m)/a^(3/2))*d31(m)-(3*cos(m)^2-1)*d41(m)/a^(3/2), diff(d31(m), m) = -a^(3/2)*d11(m), diff(d41(m), m) = -a^(3/2)*d21(m)

using " dsolve([sys_ode]) " command could get the solution easily, and the solution contains "I" (imaginary domain).

However, when we substitute the solution into the ODE "sys_ode", find not correct !

we use the following command to check the solution :

 simplify(  -diff(d11(m), m) -(3*sin(m)^2-1)*d31(m)/a^(3/2)+(-3*cos(m)*sin(m)/a^(3/2))*d41(m)  )

the upper expression is supposed to be zero, but not ! Is it a bug in Maple dsolve ?

How can I plot multiple numeric plots, such that numeric solutions belong to different differential equations?

For solving problem sets, I have a pdf template I created for myself that has a header with a blank for the class name, TA, professor, date, etc. In addition to this header, I had a margin on the left to scribble questions I had and to holepunch. 

I used to print out the template and write on the template and turn in that as my pset.

I am nowthinking of doing everything on the computer. Writing out all of the problem set on the computer. Combining stuff from maple, combining handwritten stuff from the computer using a digitizer. However I want to write it all on top of the my template that I created, which is a pdf file. I can turn the pdf into an image file if need be. 

What would be the easiest way to do what I want? To open a program that automatically sets that pdf as the template and easily lets me handwrite stuff I want and paste in maple code? 

Right now if I tried my idea, I would basically be constantly copying and pasting stuff from maple and my digitizer drawn pictures/equations into one file and it would be very clumsy.

Basically there are problems that I do partially on maple and I just want to unify all my work into one easy, printable file. 

I'm doing a pset in maple.

I paste in a block of text in maple. I put an asterik at front and end, and hit enter and it spits out an error. Why? I thought two *'s around it comment it out. 

I also can't see the file I uploaded while I preview my post. 

Hai everyone.

I try to double integrate this generalized extreme distribution.

q[p] := 6.256: h := .8; t[c] := .45: S[di] := 0: k[v] := .32639: mu[v] := -0.1786e-1: sigma[v] := 2.1694: k[t] := .36132: mu[t] := .63543: sigma[t] := 3.1183:

int(exp(-(1+k[v]*(v-mu[v])/sigma[v])^(-1/k[v]))*(1+k[v]*(v-mu[v])/sigma[v])^(-1-1/k[v])*exp(-(1+k[t]*(t-mu[t])/sigma[t])^(-1/k[t]))*(1+k[t]*(t-mu[t])/sigma[t])^(-1-1/k[t])/(sigma[v]*sigma[t]), [v = q[p]/(2*h*t)+q[p]*t[c]/(2*h)+S[di] .. infinity, t = 0 .. infinity]);

however, I got an error, as follow:

Error, (in assuming) when calling '`root/fraction`'. Received: 'numeric exception: overflow'

Any recomendations and tips to solve this integration? or this integration may cannot solve?

Thank you.

I have an expression like this:

Since it is linear I want Maple to rewrite it into this:

(with the benefit that Maple then can solve it at least up to a point). i have tried to conceive a rule to do that but got stuck relatively quickly. Does anybody have a way to do this (in some genrality)?

Thanks,

Mac Dude.

Hi, I want to define functions recursively... 

I don't know how to do it with the for loop in Maple.

I have a[0](t)=0, a[1](t)=t, and then some recursion connecting a[j+1](t) = f( a[j](t), a[j-1](t)) for some explicit function f. 

Then I want to plot the graph of a[N](t) as a function of t. 

Thanks!!

Hi, please a Need a help.
I have an error in my code: Error, (in collect) cannot collect 0
Here, is the code:
Question8X.mw

Many thinks.

Hello,

I am a student and using Maple to type homework assignments because of the math symbols available.  I was using Maple 17 but upgraded to 18, and its not as easy to use as 17.  For right now I am using it in text mode, because that is what I need.  But I can't figure out an easy way to do subscripts and superscripts in text mode.  Also, the "element symbol," where is it?  I feel like a lot of stuff is missing.  For instance, the arrows, the sideways triangle, lots of symbols I used before the upgrade I cant find.  Can someone help please???

After using Simplify the indices are are arranged in the tensor.  I am using the April 14th update from the Physics R&D page.

Download Vacuum_Solutions_(Kerr-Schild)_3.mw