Mariusz Iwaniuk

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These are replies submitted by Mariusz Iwaniuk

@Rouben Rostamian

See attached file.
 

Download integral_ver2.mw

 

Yes, I also want  find many things?

Please post a clear example of input and desired output. Nobody likes to guess...

Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images.

 You can upload a worksheet by using the green up-arrow on the toolbar of the MaplePrimes editor.

@golnaz 

You say:

 ((sqrt(a*e^(-2*x)+a))-sqrt(a)));

# Error, unable to match delimiters ???

You wrote in the question: (sqrt(exp(-2*x) + a) - sqrt(a)) then you wrote:  ((sqrt(a*e^(-2*x)+a))-sqrt(a))),it's not same expression ? 


 

In Mathematica it's ease to do:

 

Improvement to the mathematics engine(sum) ?

Simple example:

sum(1/k^z, k = 1 .. n) assuming n::'nonnegint'

Maple does not know that this is a harmonic(n, z) ?

See files attached.

Weakness_in_sum_Examples.mw

Weakness_in_sum_Examples_2.mw

Weakness_in_sum_Examples_3.mw

Weakness_in_sum_Examples_4.mw

Weakness_in_sum_Examples_5.mw

@nm 

Answer is in attached file.

This_is_Abel_eq..mw

 

@nm 

dsolve convert second order ODE to first order ODE(to Abel).

Without a reproducible example, we can't say much.

@reza gugheri 

You should copy and paste all your code and definition of U to this thread.

Please paste copy&pastable code instead of screenshots. It is not fair to the people who are trying to assist to make them need to retype all your content based on some images.

@Stretto 

Solution for Numeric Fourier transform for sigmoid function.

For_sigmoid_function.mw

@Stretto 

 

My answer works for erf(x) function and if Maple can finds fourier transform symbolically, then works for general.

Give an example of a function for which a derivative can not be calculated symbolically ?

@9009134 

You can decrease steps in seq command to make plots more accucurate,but the calculation time will increase.


 

restart

Digits := 20

20

(1)

F := proc (s, x) options operator, arrow; exp(-(1/20)*sqrt(2)*sqrt(s)*sqrt(49*s^2+280*s+800)/sqrt(s+4))*exp((1/20)*sqrt(2)*sqrt(s)*sqrt(49*s^2+280*s+800)*x/sqrt(s+4))/((-exp((1/20)*sqrt(2)*sqrt(s)*sqrt(49*s^2+280*s+800)/sqrt(s+4))+exp(-(1/20)*sqrt(2)*sqrt(s)*sqrt(49*s^2+280*s+800)/sqrt(s+4)))*s)-exp((1/20)*sqrt(2)*sqrt(s)*sqrt(49*s^2+280*s+800)/sqrt(s+4))*exp(-(1/20)*sqrt(2)*sqrt(s)*sqrt(49*s^2+280*s+800)*x/sqrt(s+4))/((-exp((1/20)*sqrt(2)*sqrt(s)*sqrt(49*s^2+280*s+800)/sqrt(s+4))+exp(-(1/20)*sqrt(2)*sqrt(s)*sqrt(49*s^2+280*s+800)/sqrt(s+4)))*s) end proc

INVLAP := proc (F, tau, x) local oldDigits, n, r, k, t, result, Y, B, W, G; n := 80; oldDigits := Digits; Digits := oldDigits+max(80, 2*n); t := evalf(tau); Y := Vector(1 .. 2*n, proc (k) options operator, arrow; F(k*ln(2.0)/t, x) end proc); B := Matrix(1 .. n, 1 .. 1+n, proc (i, j) options operator, arrow; binomial(i, j-1) end proc); W := Vector(1 .. n, proc (k) options operator, arrow; (-1)^(n-k)*k^n*factorial(2*k)/(factorial(k)*factorial(n-k)*factorial(k)*factorial(k-1)) end proc); G := Vector(1 .. n, proc (k) options operator, arrow; add((-1)^r*B[k, r+1]*Y[k+r], r = 0 .. k) end proc); result := ln(2.0)*add(evalf(W[k]*G[k]), k = 1 .. n)/t; return Re(evalf[oldDigits](result)) end proc

INVLAP(F, 0.84e-1, 1/2)

-0.43468229756029945212e-11

(2)

plots:-pointplot({seq([x, INVLAP(F, 0.84e-1, x)], x = 0 .. 1, 0.1e-1)}, connect = true)

 

data := [seq([seq([i, j, evalf(INVLAP(F, i, j))], i = 10^(-9) .. 1, 0.5e-1)], j = 0 .. 1, 0.5e-1)]

plots:-surfdata(data, axes = frame, labels = [t, x, z])

 

``


 

Download INV-LAPLACE_-3.mw

@Melvin Brown 

For solving  PDEs use extreme powerfull pdsolve command ,will do the job for you.

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