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mehdi jafari

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12 years, 106 days
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plot output of an integral ...

mehdi jafari 749 Maple 2018
integration plotting
May 17 2021
2 14

how this integration can be computed and plotted? tnx in advance

 

> 

restart:Digits:=20:
> 

T := 10^(-6);
delta := 10;
m := 1;
alpha:= 75/10;
v := 65;
mu := 8;

1/1000000

  

10

  

1

  

15/2

  

65

  

8

 (1)
> 

z := sqrt((omega^2 - 4*m^2)/alpha^2 - v^2/alpha^2*(4 *delta/alpha*tan(theta)^2 - v^4/alpha^4*tan(theta)^4))

(2/135)*(81*omega^2-324-1825200*tan(theta)^2+1930723600*tan(theta)^4)^(1/2)

 (2)
> 

a := sec(theta)/sqrt(2)*sqrt((2 *delta)/alpha - v^2/alpha^2*tan(theta)^2 + z)

(1/90)*sec(theta)*2^(1/2)*(5400-152100*tan(theta)^2+30*(81*omega^2-324-1825200*tan(theta)^2+1930723600*tan(theta)^4)^(1/2))^(1/2)

 (3)
> 

f1 := 1/(exp(( omega/2 - mu)/T) + 1);
f2 := 1/(exp((- (omega/2) - mu)/T) + 1);

1/(exp(500000*omega-8000000)+1)

  

1/(exp(-500000*omega-8000000)+1)

 (4)
> 

A1 := evalf(-(f1 - f2)*abs(omega/(4*a*alpha*cos(theta)^2*(-delta+ a^2 *alpha* cos(theta)^2) + 2*a*v^2*sin(theta)^2 + 1/10000)))

-1.*(1/(exp(500000.*omega-8000000.)+1.)-1./(exp(-500000.*omega-8000000.)+1.))*abs(omega/(.47140452079103168293*sec(theta)*(5400.-152100.*tan(theta)^2+30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*cos(theta)^2*(-10.+0.18518518518518518519e-2*sec(theta)^2*(5400.-152100.*tan(theta)^2+30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))*cos(theta)^2)+132.77894002280725736*sec(theta)*(5400.-152100.*tan(theta)^2+30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*sin(theta)^2+0.10000000000000000000e-3))

 (5)
> 

b := sec(theta)/sqrt(2)*sqrt((2*delta)/alpha - v^2/alpha^2*tan(theta)^2 - z)

(1/90)*sec(theta)*2^(1/2)*(5400-152100*tan(theta)^2-30*(81*omega^2-324-1825200*tan(theta)^2+1930723600*tan(theta)^4)^(1/2))^(1/2)

 (6)
> 

f3 := 1/(exp(( omega/2 - mu)/T) + 1);
f4 := 1/(exp((- (omega/2) - mu)/T) + 1);

1/(exp(500000*omega-8000000)+1)

  

1/(exp(-500000*omega-8000000)+1)

 (7)
> 

A2 := evalf(-(f3 - f2)*abs(omega/(4*b*alpha*cos(theta)^2*(-delta+ b^2 *alpha* cos(theta)^2) + 2*b*v^2*sin(theta)^2 + 1/10000)))

-1.*(1/(exp(500000.*omega-8000000.)+1.)-1./(exp(-500000.*omega-8000000.)+1.))*abs(omega/(.47140452079103168293*sec(theta)*(5400.-152100.*tan(theta)^2-30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*cos(theta)^2*(-10.+0.18518518518518518519e-2*sec(theta)^2*(5400.-152100.*tan(theta)^2-30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))*cos(theta)^2)+132.77894002280725736*sec(theta)*(5400.-152100.*tan(theta)^2-30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*sin(theta)^2+0.10000000000000000000e-3))

 (8)
> 

plot(int(A1+A2,theta=0..2*Pi),omega=0..50);

Warning,  computation interrupted

  
> 

 


 

Download code.mw

sort an expression with order of a symbo...

mehdi jafari 749 Maple
sort
April 27 2021
2 0

How can this expression sorted in order of the symbol "y"? I want the terms with y locate at the beginnig.

> 

restart:
> 

f:=x^2+x^y+1-z

x^2+x^y+1-z

 (1)
> 

 

Download sort.mw

problem with finding roots of a function...

mehdi jafari 749 Maple
rootfinding numeric
March 27 2021
1 0

I want to find all roots of an function.we think there maybe 35 roots, but the commands


1. "SolveEquations" gives us 26 roots,

2."fsolve" gives us 10 roots,

3."Student[Calculus1]:-Roots" gives us 29 roots,

4.the proc "findroots" written by @acer 6 to 10 roots.

 I have tried everything but i cannot find all roots, what is th problem?
can anyone help?how many roots are there? and how to find all of them?

problem.mw

EDIT: the uploaded file is edited.

solve nonlinear integral equation...

mehdi jafari 749 Maple 2018
integral-equation
January 13 2021
1 0

Hi. i have a nonlinear integral equation. any idea for solving it? tnx in advance

integral-equation.mw

 

solve a nonlinear equation...

mehdi jafari 749 Maple
dsolve differential-equations bvp
November 28 2020
1 1

i have a nonlinear equation,W, which have two unknowns: x and b 
i want to solve W for b, and the x domain is : -4e-6<x<4e-6. can anyone help? tnx in advance


 

> 

restart; with(DirectSearch)
> 

E := (-7.29511346879067*10^9*b-12693.49752)*((D@@2)(phi))(x)+(5.36829162574305*b+0.3487242314e-3)*((D@@4)(phi))(x)+(2.02316788462733*10^17*b+4.107030812*10^12)*phi(x)+1.74615339888993*10^17*b

(-7295113469.*b-12693.49752)*((D@@2)(phi))(x)+(5.36829162574305*b+0.3487242314e-3)*((D@@4)(phi))(x)+(0.2023167885e18*b+0.4107030812e13)*phi(x)+0.1746153399e18*b

 (1)
> 

dsolve(E, phi(x))
> 

ivp := {E, phi(-0.406e-3) = 1, phi(0.406e-3) = 1, (D(phi))(-0.406e-3) = 0, (D(phi))(0.406e-3) = 0}

{(-7295113469.*b-12693.49752)*((D@@2)(phi))(x)+(5.36829162574305*b+0.3487242314e-3)*((D@@4)(phi))(x)+(0.2023167885e18*b+0.4107030812e13)*phi(x)+0.1746153399e18*b, phi(-0.406e-3) = 1, phi(0.406e-3) = 1, (D(phi))(-0.406e-3) = 0, (D(phi))(0.406e-3) = 0}

 (2)
> 

N := dsolve(ivp, phi(x))
> 

A := simplify(rhs(dsolve(ivp, phi(x))))
> 

W := evalf(subs(phi(x) = simplify(rhs(dsolve(ivp, phi(x)))), (2.74505742817409*10^8+3.18054074382591*10^8*phi(x))^2-(1.63833629390402*(2.74505742817409*10^8+3.18054074382591*10^8*phi(x)))*(diff(phi(x), x, x))+3*(6.98727355657655*10^7+32282.4885498329*(diff(phi(x), x)))^2+2.68414581287153*(diff(phi(x), x, x))^2 = 0.9e17))
> 

 

> 

``
> 

``

 

 
> 

 


 

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