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How to simplify multiple definite integrals...

Asked by: sunit 105
integral simplification combine
May 02 2020
0  2

Hi Guys,

I need help regarding simplifying definite integrals. I have following expression

2*s^2*(int(Phi[1, 1](x, T[2])*(diff(Y1(x), x, x)), x = 0 .. x1))+int(Phi[1, 1](x, T[2])*(diff(Y1(x), x, x, x, x)), x = 0 .. x1)-omega_y^2*(int(Y1(x)*Phi[1, 1](x, T[2]), x = 0 .. x1))

As we can notice the limit for each integral is same, so I should be able to take these integral limit outside. I am trying to use collect and simplify, but both of these command are not working. It would be really helpful for me if I can get the solution for it.

Please find the attached example sheet also.example.mw

With Regards

Sunit

 

How to use factor elementwise?...

Asked by: sunit 105
factor elementwise
May 01 2020
1  2

Hi Guys,

It might be a very basic question, but I am struggling with it for a quite a time.  I have an expression in a form of

f(x)=h(x)+g(x);

and I want to use factor operation elementwise, i.e., it can individually act on h(x) and can give me

f(x)=h1(x)*h2(x)+g1(x)*g2(x). But whenever I am putting factor operation with elementwise it is not giving me desired answer. It would be really helpful and great if someone can help me out.

I am attaching maple sheet for reference also.

Thanks in advance and regards

Sunit.
example.mw
Download example.mw

 

Solving a Quadratic Diophantine Equation with 3 va...

Asked by: aiewabgalbd 10
isolve diophantine_equation
February 02 2020
2  1

How do I find integer solutions to this non-linear equation:

 

8= 7(x^2+y^2+z^2)+2x+4y-8z.

 

Tried isolve and it wasn't working. (I guess too many variables?)

 

Also, if f(x,y,z) is the RHS, how do I write a loop that finds integer solutions to f(x,y,z)=c for |x|,|y|,|z|< N, say?

error: fsolve unrecognized form...

Asked by: susanhl 5
fsolve rootof
October 30 2019
1  7

Hello,

I don't understand why Maple gives me the following error:

Error, (in fsolve/Iterators) unrecognized form

The full maple file:


 

> 

restart
> 

mbal := 0.28e-2:
> 

rbal := 0.2e-1:
> 

Cw := .47:
> 

g := 9.81:
> 

A := Pi*rbal^2:
> 

beta := 3.33*Pi*(1/180):
> 

s0x := .2:
> 

s0y := .25:
> 

rho := 1.293:
> 

l := 2:
> 

vx := diff(sx(t), t);

diff(sx(t), t)

 (1)
> 

vy := diff(sy(t), t);

diff(sy(t), t)

 (2)
> 

ax := diff(sx(t), `$`(t, 2));

diff(diff(sx(t), t), t)

 (3)
> 

ay := diff(sy(t), `$`(t, 2));

diff(diff(sy(t), t), t)

 (4)
> 

v0x := cos(beta)*v0;

cos(0.1850000000e-1*Pi)*v0

 (5)
> 

v0y := sin(beta)*v0;

sin(0.1850000000e-1*Pi)*v0

 (6)
> 

`&Sigma;Fx` := -Fdx = mbal*ax;

-Fdx = 0.28e-2*(diff(diff(sx(t), t), t))

 (7)
> 

`&Sigma;Fy` := -Fz-Fdy = mbal*ay;

-Fz-Fdy = 0.28e-2*(diff(diff(sy(t), t), t))

 (8)
> 

Fz := mbal*g;

0.27468e-1

 (9)
> 

Fdx := .5*rho*vx^2*A*Cw;

0.1215420e-3*(diff(sx(t), t))^2*Pi

 (10)
> 

Fdy := .5*rho*vy^2*A*Cw;

0.1215420e-3*(diff(sy(t), t))^2*Pi

 (11)
> 

ics1 := sx(0) = s0x, (D(sx))(0) = v0x;

sx(0) = .2, (D(sx))(0) = cos(0.1850000000e-1*Pi)*v0

 (12)
> 

ics2 := sy(0) = s0y, (D(sy))(0) = v0y;

sy(0) = .25, (D(sy))(0) = sin(0.1850000000e-1*Pi)*v0

 (13)
> 

verplaatsingx := dsolve({ics1, `&Sigma;Fx`}, sx(t));

sx(t) = (1400000/60771)*ln((60771/1400000)*cos((37/2000)*Pi)*v0*exp((60771/7000000)*Pi)*t*Pi+exp((60771/7000000)*Pi))/Pi

 (14)
> 

verplaatsingy := dsolve({ics2, `&Sigma;Fy`});

sy(t) = (1/243084)*(60771*Pi+2800000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*t)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*t))^2))/Pi

 (15)
> 

eindy := rhs(verplaatsingy) = rbal;

(1/243084)*(60771*Pi+2800000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*t)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*t))^2))/Pi = 0.2e-1

 (16)
> 

eindx := rhs(verplaatsingx) = l;

(1400000/60771)*ln((60771/1400000)*cos((37/2000)*Pi)*v0*exp((60771/7000000)*Pi)*t*Pi+exp((60771/7000000)*Pi))/Pi = 2

 (17)
> 

t := solve(eindy, t);

RootOf(1397733*Pi+70000000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z))^2))

 (18)
> 

t := evalf(t[1]);

RootOf(1397733*Pi+70000000*ln((1/92736546000)*(20257*Pi^(1/2)*sin((37/2000)*Pi)*v0*sin((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z)+20*231841365^(1/2)*cos((3/70000)*231841365^(1/2)*Pi^(1/2)*_Z))^2))[1]

 (19)
> 

v0 := fsolve(eindx, v0)

Error, (in fsolve/Iterators) unrecognized form

  
> 

``
> 

``


 

Download ttbuddymaple.mw

 

Thank you!

 

How to display each vector turn on the same axis o...

Asked by: smiths 25
vector animation homework
October 05 2019
0  3

How do I draw three vectors on the same axis of coordinates, I see this vector appear after the previous vector one second  and on the screen when this vector appears, the previous vector remains on the screen and on the last screen I see all three vectors with the Maple command?

Example : plottools :- arrow( [1, -2], [4, -1], 0.001, 0.05, 0.1), plottools :- arrow( [-1, 3], [2, 1], 0.001, 0.05, 0.1), plottools :- arrow( [0, 2], [-3, 0], 0.001, 0.05, 0.1).

Thanks so much for the help of everyone!

How to display each chart turn on the same axis of...

Asked by: smiths 25
animation plotting
September 30 2019
1  4

How do I draw three graphs on the same axis of coordinates and I see this graph appear after the previous graph one second with the Maple command? Example : y = x, y = x2, y = 1 - x.

Thanks so much for the help of everyone!

How to use the add command in this scenario...

Asked by: Alejo 30
homework add
September 15 2019
1  2 
Lecture 4 - Problem 2
a)
> a := -2100; b := 2100; N := 8; h := (b-a)/N; C := 4491; x := [seq(h, h = -2100 .. 2100, h)]; y := proc (x) options operator, arrow; sqrt(1+((1/2)*exp(x/C)-(1/2)*exp(-x/C))^2) end proc; evalf(y(x[1])); evalf(y(x[N+1])); L := (1/3)*h*(y(x[1])+4*(y(x[2])+y(x[4])+y(x[6])+y(x[N]))+2*(y(x[3])+y(x[5])+y(x[N-1]))+y(x[N+1])); evalf(L);
                             -2100
                              2100
                               8
                              525
                              4491
     [-2100, -1575, -1050, -525, 0, 525, 1050, 1575, 2100]
         /                           2\
         |    /1    /x\   1    /  x\\ |
x -> sqrt|1 + |- exp|-| - - exp|- -|| |
         \    \2    \C/   2    \  C// /
                          1.111332350
                          1.111332350
                                           (1/2)
         /                               2\    
         |    /1    /-700\   1    /700 \\ |    
     175 |1 + |- exp|----| - - exp|----|| |    
         \    \2    \1497/   2    \1497// /     

                                               (1/2)
              /                              2\    
              |    /1    /-175\   1    /175\\ |    
        + 700 |1 + |- exp|----| - - exp|---|| |    
              \    \2    \499 /   2    \499// /     

                                                (1/2)
              /                               2\    
              |    /1    /-175\   1    /175 \\ |    
        + 700 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                                (1/2)
              /                               2\    
              |    /1    /175 \   1    /-175\\ |    
        + 700 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                               (1/2)
              /                              2\    
              |    /1    /175\   1    /-175\\ |    
        + 700 |1 + |- exp|---| - - exp|----|| |    
              \    \2    \499/   2    \499 // /     

                                                (1/2)     
              /                               2\          
              |    /1    /-350\   1    /350 \\ |          
        + 350 |1 + |- exp|----| - - exp|----|| |      + 350
              \    \2    \1497/   2    \1497// /           

                                                (1/2)
              /                               2\    
              |    /1    /350 \   1    /-350\\ |    
        + 350 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                                (1/2)
              /                               2\    
              |    /1    /700 \   1    /-700\\ |    
        + 175 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /    
                          4354.742601
> L := (1/3)*h*(y(x[1])+4*add(y(i), i = y(x[2]) .. y(x[N]), 2)+2*add(y(i), i = y(x[3]) .. y(x[N-1]), 2)+y(x[N+1])); evalf(L);
Error, invalid input: add expects 2 arguments, but received 3
                          4354.742601

How do i get my computation time...

Asked by: babajeay 5
performance linear-algebra homework
September 12 2019
1  1

I am trying to compare time taken in minutes for each iterative model(Jacobi, Gauss-Seidel and SOR) to complete, so as to figure out the iterativre model with a faster time of convergence but i don't know the command to initiate.

How to convert a function expressed by the hyperge...

Asked by: ahmadtalaei 25
dsolve differential-equations legendre
June 07 2019
2  8

Anyone can help me to convert the following maple solution expressed by the hypergeom function to the LegendreP(n,b,x) or Q function?


 

> 

restart
> 

with(PDETools):
> 

infolevel[pdsolve] := 3:
> 

sol[1] := dsolve((1-x^2)*(diff(y(x), x, x))+n(n+1)*y(x) = 0)

y(x) = _C1*(-1+x^2)*hypergeom([3/4+(1/4)*(4*n(n+1)+1)^(1/2), 3/4-(1/4)*(4*n(n+1)+1)^(1/2)], [1/2], x^2)+_C2*(x^3-x)*hypergeom([5/4+(1/4)*(4*n(n+1)+1)^(1/2), 5/4-(1/4)*(4*n(n+1)+1)^(1/2)], [3/2], x^2)

 (1)
> 

convert(sol[1], LegendreP)

y(x) = _C1*(-1+x^2)*hypergeom([3/4+(1/4)*(4*n(n+1)+1)^(1/2), 3/4-(1/4)*(4*n(n+1)+1)^(1/2)], [1/2], x^2)+_C2*(x^3-x)*hypergeom([5/4+(1/4)*(4*n(n+1)+1)^(1/2), 5/4-(1/4)*(4*n(n+1)+1)^(1/2)], [3/2], x^2)

 (2)
> 

``

 

Download convert-Legendre.mw

 

https://math.stackexchange.com/questions/3254765/how-to-convert-a-hypergeom-function-to-the-legendre-function

I just want y(x) to be expressed in the form of LegendreP(n,b,x).

maple dosent solve my problem?...

Asked by: byrktr 10
optimization sum numeric
May 14 2019
2  12

i have a assignment problem to optimize with 1200 variables and almost 1000 constraints. but maple couldnt solve it. anyone who can help me is welcome

or may i try another app?

thanks

this is the my model
tam2.mw

 

> 

restart;
> 

 

> 

 

> 

we:=[1,2,8,9,15,16,22,23,29,30];

(1)
> 

wd:=[3,4,5,6,7,10,11,12,13,14,17,18,19,20,21,24,25,26,27,28];

(2)
> 

#printlevel :=3;
> 

for j from 1 to 30 do
#her gündüz vardiyasında en az 4 hemşire bulunsun
a[j]:=sum(x[i][j][1], i=1..20)>=4:
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(3)
> 

A := [seq(a[j],j=1..30)];

(4)
> 

#her gece vardiyasında en az 4 hemşire bulunsun
for j from 1 to 30 do
b[j]:=sum(x[i][j][2], i=1..20)>=4:
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(5)
> 

 

> 

B := [seq(b[j],j=1..30)];

(6)
> 

#her hemşire ayda en az 4 hafta içi gündüz vardiyasında çalışsın
for i from 1 to 20 do
c[i]:=sum(x[i][wd[k]][1], k=1..20)>=4:
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(7)
> 

C := [seq(c[i],i=1..20)];

(8)
> 

#her hemşire ayda en az 4 hafta içi gece vardiyasında çalışsın
for i from 1 to 20 do
d[i]:=sum(x[i][wd[k]][2], k=1..20)>=4:
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(9)
> 

dd:= [seq(d[i],i=1..20)];

(10)
> 

#her hemşire ayda en az 2 hafta sonu gündüz vardiyasında çalışsın
for i from 1 to 20 do
e[i]:=sum(x[i][we[k]][1], k=1..10)>=2;
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(11)
> 

E:= [seq(e[i],i=1..20)];

(12)
> 

#her hemşire ayda en az 2 hafta sonu gece vardiyasında çalışsın
for i from 1 to 20 do
f[i]:=sum(x[i][we[k]][2], k=1..10)>=2;
end do;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(13)
> 

F:= [seq(f[i],i=1..20)];

(14)
> 

#gece vardiyasında çalışan hemşire ertesi gündüz ve gece vardiyalarında izinlidir
for i from 1 to 20 do
for j from 1 to 29 do
g[i][j]:=2*x[i][j][2]+x[i][j+1][1]+x[i][j+1][2]<=2
end do;
end do;
> 

for i from 1 to 20 do
g[i] := seq(g[i][j],j=1..29)
end do;
> 

g:= [seq(g[i],i=1..20)];
> 

with(Optimization);
> 

Minimize( sum(t[m], m=1..20),{A[],B[],C[],dd[],E[],F[],g[]}, assume = binary );


 

Download tam2.mw

 

Maple: How to solve the given Partial Differential...

Asked by: ahmadtalaei 25
pde differential-equations duplicate-question
April 08 2019
1  6

I need help on solving the following PDE by Maple:

https://math.stackexchange.com/questions/3177491/how-to-solve-the-given-partial-differential-equation

I couldn't write the partial differential equation in Mapleprimes so provided the link from somewhere else. Please help. Thank you.

Ordinary differential equations...

Asked by: Gabriel samaila 35
ode dsolve numeric
February 14 2019
1  22

Hi guys,

This is the first time of solving partial differential equation, can some please help me point out some errows in my code. 
 

> 

restart
> 

ODEs := `<,>`(diff(v(y), y, y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, diff(theta(y), y, y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0, diff(phi(y), y, y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(theta(y), y, y)+(diff(theta(y), y))/y)/Nb = 0)

ODEs := Matrix(3, 1, {(1, 1) = diff(diff(v(y), y), y)+(diff(v(y), y))/y-(Ha^2/(1-eta)^2+1/y^2)*v(y)-Re*v(y)*(diff(v(y), y)) = 0, (2, 1) = diff(diff(theta(y), y), y)+Ec*Pr*(diff(v(y), y)-v(y)/y)^2-Pr*Re*v(y)*(diff(theta(y), y))+Nb*(diff(theta(y), y))*(diff(phi(y), y))+Nt*(diff(theta(y), y))^2 = 0, (3, 1) = diff(diff(phi(y), y), y)-Re*Sc*v(y)*(diff(phi(y), y))+Nt*(diff(diff(theta(y), y), y)+(diff(theta(y), y))/y)/Nb = 0})

 (1)
> 

BCs := `<,>`(phi(eta) = 1, v(eta) = 1, theta(eta) = 1, phi(1) = 0, theta(1) = 0, v(1) = 0)

BCs := Matrix(6, 1, {(1, 1) = phi(eta) = 1, (2, 1) = v(eta) = 1, (3, 1) = theta(eta) = 1, (4, 1) = phi(1) = 0, (5, 1) = theta(1) = 0, (6, 1) = v(1) = 0})

 (2)
> 

param_names := [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr];

[eta, Ha, Ec, Nt, Nb, Re, Sc, Pr]

 (3)
> 

pdSolve := subs(_P = param_names, proc ({ eta::realcons := .5, Ha::realcons := 1, Sc::realcons := .8, Nt::realcons := .1, Nb::realcons := .1, Re::realcons := 2, Ec::realcons := 0.1e-1, Pr::realcons := 10 }) userinfo(1, Solve, `~`[`=`](param_names, _P)); dsolve(eval(`union`(convert(ODEs, set), convert(BCs, set)), `~`[`=`](param_names, _P)), numeric) end proc);

proc ({ Ec::realcons := 0.1e-1, Ha::realcons := 1, Nb::realcons := .1, Nt::realcons := .1, Pr::realcons := 10, Re::realcons := 2, Sc::realcons := .8, eta::realcons := .5 }) userinfo(1, Solve, `~`[`=`](param_names, [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr])); dsolve(eval(`union`(convert(ODEs, set), convert(BCs, set)), `~`[`=`](param_names, [eta, Ha, Ec, Nt, Nb, Re, Sc, Pr])), numeric) end proc

 (4)
> 

infolevel[Solve] := 1:

Fig. 3 (changing values of Ha):

> 

P:= Ha:
vals:= [1, 5, 10, 20]:
sols:= [seq(Solve(P= v), v= vals)]:
colors:= [red, green, blue]:
for F in [v,theta,phi](y) do
   print(plots:-display(
      [seq(
         plots:-odeplot(sols[k], [y,F], color= colors[k], legend= [P= vals[k]]),
         k= 1..nops(vals)
      )],
      labeldirections= [horizontal,vertical]
   ))
od:

Error, pdeplot is not a command in the plots package

  
> 

``


 

Download chapter5.mw

 

problem solve a system in maple...

Asked by: Aissam 5
solve
February 03 2019
1  1

i have a problem to solve this system ?

How to transform a function plot by "shifting" hor...

Asked by: Iza 35
transform plotting
January 09 2019
2  5

Hello,

I will explain my problem on a simple function and some data.

mg:=78.54*7.85*1e-9*1000*9.81;l:=10000;l0:=12000;h:=0;H := 28.399;
eta:=mg*l/(2*H);
zeta:=arcsinh(mg*h/(2*H*sinh(eta)))-eta;
z:=H/mg*(cosh(mg/H*x+zeta)-cosh(zeta));
plot(z,x=0..l);

Above is a definition of an initial plot. Now I would like to draw a new plot in which every x coordinate is shifted horizontally by a function:

deltax:=H*arcsinh(x)-x;

As you see I can't use translate or scale so I've tried to use a transform function but I can't do it the right way.

I would be grateful for any ideas.

 

Greetings,

Iza

Background Images...

Asked by: leikf 15
plot image background
December 10 2018
2  3

Hei!

In my Maple project I want to put a simple sin graph on top of an image. But how do I create a background image with a graph on top?

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