MaplePrimes Questions

im refering to the reason why a maple andriod application hasnt shown up or at least one of the big ones (preferably a java based on since thats the only thing i know for making any apps fluently) but yep cannot be the only one who has felt that need to get out of the house but wants to keep mathing when there is nothing to do which is pretty much always for me anyway

How can one find out when a Maple command or package became part of Maple? i.e. which Maple version first had this command or package?

For example, I'd like to know when applyrule https://www.maplesoft.com/support/help/Maple/view.aspx?path=applyrule was introduced. But this applies really to any command I see.

In Mathematica, this is easy to find out, since it is documented in the help page for the command, at the botton of each page when the command was added. Is there a command or a web page that shows this type of information about Maple commands and packages?

 

I have some data

> X:=[291.3301386,349.9410125,420.7945287,490.0836935,558.1365585,623.6824877,688.6344191,752.1359797,814.1871695,874.7879884,933.8452525,991.0023402,1047.88822,1102.687556,1156.036521,1207.200419]:

>
> Y:=[0.008923638,0.010336322,0.012031554,0.013676089,0.01527851,0.016809936,0.018315901,0.019777093,0.021194266,0.022568158,0.023897399,0.025174796,0.026437267,0.027645069,0.02881302,0.029925828]:

to which I am trying to fit a function

U:=(m,d,Theta,T)-> (((3*(6.62607e-34)^2*T)/(4*Pi^2*m*1.36085e-23*Theta^2))*((T/Theta)*int(x/(exp(x)-1),x=0..Theta/T) + (Theta/(4*T))))/1e-10^2 +d^2;

where Theta≈200 and d≈0.035. T, Theta, d, m > 0

 When I try and solve

> NonlinearFit(U(0.15036/6.022e23,d,Theta,T),X,Y,T,initialvalues=[Theta=200, d=0.035]);

I get the error "Error, (in Statistics:-NonlinearFit) complex value encountered"

 

I can plot the function with Theta=200 and d=0.035, I get approximately the right curve and no errors about complex values.

 

How can I solve for Theta and d without encountering this error?

Hello,

Lets say I have some expression F that is a function of n and N like, F=n+N-1 and I want to express that in terms of x, where x=n/N. How would I do this in maple? Thanks in advance. 

Hi, I am trying to plot a parabola in spherical coordinates using the command spacecurve, using 

 

>with(plots);

>spacecurve([cot(phi)/sin(phi), 1.61, phi], phi = -3.14 .. 3.14, numpoints = 3000, axes = normal, coords = spherical, color = red, linestyle = dash, axes = normal)

 

(I know it is easier in Cartesian coords, but I am doing this as a first version of a more complicated curve, given by the sol. of a system of differential equations). 

Maple plots the parabola correctly but it joins the initial and the final points of the plot with a straight line, yielding something that looks like a U with a bar on top (I cannot upload the image). Is there any way to get rid of the line?

 

This came up in another language. I tried to solve it in Maple, but I am newbie so did not know how to.

The problem is to remove all products of  "a^n*b^m" that shows up in an expression, including any powers of "n,m". For example, given these three expressions

f0 := a^4+4*a^3*b +6*a^2*b^2+4*a*b^3+ b^4;
f1 := 3*(a*b -2*c);
f2 := (a*b -2*c)/(c - a*b);

Then applying the transformation needed, will result in

f0:= a^4+b^4;
f1:=-6*c;
f2:=-2;

Becuase the transformation will detect any a^n*b^m and simply replace this product by zero
from the resulting expression. So "a*b^2 + 2" will become "2", and so on.

I assume a function such as "patmatch" or "match" is needed. I tried, but could not figure how.
I also tried algsubs. How would this be coded in Maple?


Hi,

1st post. I'm trying to integrate the following function:

h:=t->(2*t-1)*cos*sqrt(3*(2*t-1)^2+6)/(sqrt(3*(2*t-1)^2+6));

h:=t->(2*t-1)*cos*(sqrt(3*(2*t-1)^2+6))/(sqrt(3*(2*t-1)^2+6));

h:=t->(2*t-1)*(cos*(sqrt(3*(2*t-1)^2+6)))/(sqrt(3*(2*t-1)^2+6));

h:=t->((2*t-1)*(cos*(sqrt(3*(2*t-1)^2+6))))/(sqrt(3*(2*t-1)^2+6));

int(h(t),t); ** Integration command. I've also replaced the "h(t)" with the entire function.

I've tried the following:

1. Changed the "t" to "x" throughout function.

2. Added parens around sqrt portion.

3. Added parens to include "cos" and then added to include the beginning (2*t-1).

4. I've added brackets around the numerator but this just causes Maple to reprint the function with the inegration sign in front of the function.

5. I've also tried using the Integration tutor. It returns that maple is unable to calculate.

6. Repeat all the above in Maple 2015, same answer.

I always get cos(t^2-t).

The math book claims the answer is 1/6*sin*sqrt(3*(2*t-1)^2+6). When I perform the inegration on paper I get the same answer.

Any suggestions or corrections would be great.

Thank you,

Jay.

 

hi every one...

how i can simplify this result (R_arm_F2 $  Twflex) via tringular relations.

where Ixflex & tetadot and other... are constants

thanks

matrix_f.mw


NULL

NULL

R := (Matrix(3, 3, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = cos(teta), (2, 3) = -sin(teta), (3, 1) = 0, (3, 2) = sin(teta), (3, 3) = cos(teta)})).(Matrix(3, 3, {(1, 1) = cos(phi), (1, 2) = 0, (1, 3) = sin(phi), (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (3, 1) = -sin(phi), (3, 2) = 0, (3, 3) = cos(phi)})).(Matrix(3, 3, {(1, 1) = cos(si), (1, 2) = -sin(si), (1, 3) = 0, (2, 1) = sin(si), (2, 2) = cos(si), (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1}))

R := Matrix(3, 3, {(1, 1) = cos(phi)*cos(si), (1, 2) = -cos(phi)*sin(si), (1, 3) = sin(phi), (2, 1) = sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si), (2, 2) = -sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si), (2, 3) = -sin(teta)*cos(phi), (3, 1) = -cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si), (3, 2) = cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si), (3, 3) = cos(teta)*cos(phi)})

(1)

NULL

RT := simplify(1/R)

RT := Matrix(3, 3, {(1, 1) = cos(phi)*cos(si), (1, 2) = sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si), (1, 3) = -cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si), (2, 1) = -cos(phi)*sin(si), (2, 2) = -sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si), (2, 3) = cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si), (3, 1) = sin(phi), (3, 2) = -sin(teta)*cos(phi), (3, 3) = cos(teta)*cos(phi)})

(2)

R_I_F2 := Matrix(3, 3, {(1, 1) = sin(phi)^2.(1-cos(si))+cos(si), (1, 2) = -(sin(phi).cos(phi).sin(teta))*(1-cos(si))-cos(phi).cos(teta).sin(si), (1, 3) = (sin(phi).cos(phi).cos(teta))*(1-cos(si))-sin(teta)*cos(phi).sin(si), (2, 1) = -(2*sin(phi).cos(phi).sin(teta).cos(teta))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2), (2, 2) = (2*cos(phi)^2.(sin(teta)^2).cos(teta))*(1-cos(si))+cos(teta).cos(si)-sin(teta).sin(phi).sin(si), (2, 3) = -(2*cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-sin(phi).cos(teta).sin(si)-sin(teta).cos(si), (3, 1) = (sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*cos(phi).cos(teta).sin(teta).sin(si), (3, 2) = (cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+sin(phi).cos(teta).sin(si), (3, 3) = (cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-sin(phi).sin(teta).sin(si)+cos(teta).cos(si)})

R_I_F2 := Matrix(3, 3, {(1, 1) = sin(phi)^2.(1-cos(si))+cos(si), (1, 2) = -(`.`(sin(phi), cos(phi), sin(teta)))*(1-cos(si))-`.`(cos(phi), cos(teta), sin(si)), (1, 3) = (`.`(sin(phi), cos(phi), cos(teta)))*(1-cos(si))-sin(teta)*cos(phi).sin(si), (2, 1) = -2*(sin(phi).cos(phi).sin(teta).cos(teta))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2), (2, 2) = 2*(cos(phi)^2.(sin(teta)^2).cos(teta))*(1-cos(si))+cos(teta).cos(si)-`.`(sin(teta), sin(phi), sin(si)), (2, 3) = -2*(cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-`.`(sin(phi), cos(teta), sin(si))-sin(teta).cos(si), (3, 1) = (sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*(cos(phi).cos(teta).sin(teta).sin(si)), (3, 2) = (cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+`.`(sin(phi), cos(teta), sin(si)), (3, 3) = (cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-`.`(sin(phi), sin(teta), sin(si))+cos(teta).cos(si)})

(3)

NULL

R_arm_F2 := RT.R_I_F2

R_arm_F2 := Matrix(3, 3, {(1, 1) = cos(phi)*cos(si)*(sin(phi)^2.(1-cos(si))+cos(si))+(sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si))*(-2*(`.`(sin(phi), cos(phi), sin(teta), cos(teta)))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2))+(-cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si))*((sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*(`.`(cos(phi), cos(teta), sin(teta), sin(si)))), (1, 2) = cos(phi)*cos(si)*(-(`.`(sin(phi), cos(phi), sin(teta)))*(1-cos(si))-`.`(cos(phi), cos(teta), sin(si)))+(sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si))*(2*(`.`(cos(phi)^2, sin(teta)^2, cos(teta)))*(1-cos(si))+cos(teta).cos(si)-`.`(sin(teta), sin(phi), sin(si)))+(-cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si))*((cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+`.`(sin(phi), cos(teta), sin(si))), (1, 3) = cos(phi)*cos(si)*((`.`(sin(phi), cos(phi), cos(teta)))*(1-cos(si))-sin(teta)*cos(phi).sin(si))+(sin(teta)*sin(phi)*cos(si)+cos(teta)*sin(si))*(-2*(cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-`.`(sin(phi), cos(teta), sin(si))-sin(teta).cos(si))+(-cos(teta)*sin(phi)*cos(si)+sin(teta)*sin(si))*((cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-`.`(sin(phi), sin(teta), sin(si))+cos(teta).cos(si)), (2, 1) = -cos(phi)*sin(si)*(sin(phi)^2.(1-cos(si))+cos(si))+(-sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si))*(-2*(`.`(sin(phi), cos(phi), sin(teta), cos(teta)))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2))+(cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si))*((sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*(`.`(cos(phi), cos(teta), sin(teta), sin(si)))), (2, 2) = -cos(phi)*sin(si)*(-(`.`(sin(phi), cos(phi), sin(teta)))*(1-cos(si))-`.`(cos(phi), cos(teta), sin(si)))+(-sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si))*(2*(`.`(cos(phi)^2, sin(teta)^2, cos(teta)))*(1-cos(si))+cos(teta).cos(si)-`.`(sin(teta), sin(phi), sin(si)))+(cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si))*((cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+`.`(sin(phi), cos(teta), sin(si))), (2, 3) = -cos(phi)*sin(si)*((`.`(sin(phi), cos(phi), cos(teta)))*(1-cos(si))-sin(teta)*cos(phi).sin(si))+(-sin(teta)*sin(phi)*sin(si)+cos(teta)*cos(si))*(-2*(cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-`.`(sin(phi), cos(teta), sin(si))-sin(teta).cos(si))+(cos(teta)*sin(phi)*sin(si)+sin(teta)*cos(si))*((cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-`.`(sin(phi), sin(teta), sin(si))+cos(teta).cos(si)), (3, 1) = sin(phi)*(sin(phi)^2.(1-cos(si))+cos(si))-sin(teta)*cos(phi)*(-2*(`.`(sin(phi), cos(phi), sin(teta), cos(teta)))*(1-cos(si))+(cos(phi).sin(si))*(cos(teta)^2-sin(teta)^2))+cos(teta)*cos(phi)*((sin(phi).cos(phi))*(1-cos(si))*(cos(teta)^2-sin(teta)^2)+2*(`.`(cos(phi), cos(teta), sin(teta), sin(si)))), (3, 2) = sin(phi)*(-(`.`(sin(phi), cos(phi), sin(teta)))*(1-cos(si))-`.`(cos(phi), cos(teta), sin(si)))-sin(teta)*cos(phi)*(2*(`.`(cos(phi)^2, sin(teta)^2, cos(teta)))*(1-cos(si))+cos(teta).cos(si)-`.`(sin(teta), sin(phi), sin(si)))+cos(teta)*cos(phi)*((cos(phi)^2.sin(teta))*(sin(teta)^2-cos(teta)^2)*(1-cos(si))+cos(si).sin(teta)+`.`(sin(phi), cos(teta), sin(si))), (3, 3) = sin(phi)*((`.`(sin(phi), cos(phi), cos(teta)))*(1-cos(si))-sin(teta)*cos(phi).sin(si))-sin(teta)*cos(phi)*(-2*(cos(phi)^2.sin(teta))*cos(teta)^2*(1-cos(si))-`.`(sin(phi), cos(teta), sin(si))-sin(teta).cos(si))+cos(teta)*cos(phi)*((cos(phi)^2.cos(teta))*(cos(teta)^2-sin(teta)^2)*(1-cos(si))-`.`(sin(phi), sin(teta), sin(si))+cos(teta).cos(si))})

(4)

Twflex := Typesetting:-delayDotProduct(Ixflex, (Typesetting:-delayDotProduct(tetadot, Typesetting:-delayDotProduct(sin(phi)^2, 1-cos(si))+cos(si))+Typesetting:-delayDotProduct(sidot, sin(phi)^3+Typesetting:-delayDotProduct(cos(phi)^2, Typesetting:-delayDotProduct(sin(phi), cos(si)+Typesetting:-delayDotProduct(cos(teta), 1-cos(si)))+Typesetting:-delayDotProduct(sin(teta), sin(si)))))^2)

Ixflex.((tetadot.(sin(phi)^2.(1-cos(si))+cos(si))+sidot.(sin(phi)^3+cos(phi)^2.(sin(phi).(cos(si)+cos(teta).(1-cos(si)))+sin(teta).sin(si))))^2)

(5)

simplify(Twflex)

Ixflex.((tetadot.(sin(phi)^2.(1-cos(si))+cos(si))+sidot.(-sin(phi)*cos(phi)^2+sin(phi)+cos(phi)^2.(sin(phi).(cos(si)+cos(teta).(1-cos(si)))+sin(teta).sin(si))))^2)

(6)

expand(Twflex)

Ixflex.((tetadot.(sin(phi)^2.(1-cos(si))+cos(si))+sidot.(sin(phi)^3+cos(phi)^2.(sin(phi).(cos(si)+cos(teta).(1-cos(si)))+sin(teta).sin(si))))^2)

(7)

``

NULL


Download matrix_f.mw

hi every one ! i want to use Assume option to simplify some expression ! but it is not working ! what should i do !?

i have assume that ( a+b+c=0) and i want maple returns me exp(a+b+c) =1 ! but it does not ! what should i do !?


restart:with(Physics):

Assume(a+b+c=0):

about(a+b+c)

a+b+c:

  is assumed to be: 0

 

simplify(exp(a)*exp(b)*exp(c))

exp(a+b+c)

(1)

simplify(exp(a+b+c))

exp(a+b+c)

(2)

 


Download assume.mw

updated:

with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4]], x);
f2 := solve(f=y,x);
area1 := int(f, x=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);
with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3]], x);
f2 := solve(f=y,x);
area1 := int(f, x=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);

 

i use 5 points trapezoid got RootOf  in result,

only 4 points is acceptable

 

when i try 5 points, there is no problem, but when more points such as

30 points, got RootOf for c sharp code

 

moreover, i got a problem when i copy the area1 result into 

visual studio c# code, it has error Integral Constant is too large

 

with(CurveFitting);
f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4],[5, x5],[6, x6],[7, x7],[8, x8],[9, x9],[10, x10],[11, x11],[12, x12],[13, x13],[14, x14],[15, x15],[16, x16],[17, x17],[18, x18],[19, x19],[20, x20],[21, x21],[22, x22],[23, x23],[24, x24],[25, x25],[26, x26],[27, x27],[28, x28],[29, x29]], x);
f2 := solve(f=y,x);
area1 := int(f, y=0..1);
with(student):
area2 := trapezoid(f2[1], x = 0..1);
with(CodeGeneration):
CSharp(area1, resultname = "area1");
CSharp(area2, resultname = "area2");

i find area2 has

Warning, the function names {RootOf, Sum} are not recognized in the target language
Warning, precedence for Range unspecified
Warning, cannot translate range
area2 = RootOf((System.Double) (19276689540529530246975515949293568 * x3 - 2626509155780373903082144116707328 * x2 + 239680950855919251544490932629504 * x1 -

Hi,

I am trying to solve a set of homogeneous equations for the non-trivial solutions. Mathematically it is possible to get it. But is there any way to get it in Maple. Please find the attached maple sheet for the question. Please help me regarding this.

Regards

Sunit

restart

with(plots):

with(LinearAlgebra):

eq[1] := diff(x[1](t), t)-x[2](t)

diff(x[1](t), t)-x[2](t)

(1)

eq[2] := diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(x[2](t), t)+2*zeta*beta*x[2](t)+beta^2*x[1](t)+n*psi*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(2)

eq[3] := diff(phi[1](t), t)-phi[2](t)

diff(phi[1](t), t)-phi[2](t)

(3)

eq[4] := diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

diff(phi[2](t), t)+2*kappa*phi[2](t)+phi[1](t)+n*(-v*(phi[1](t)-phi[1](t-2*Pi/(n*omega0)))+x[1](t)-x[1](t-2*Pi/(n*omega0)))

(4)

for k to 4 do eqn[k] := simplify(coeff(map(expand, eval(eq[k], [x[1] = (proc (t) options operator, arrow; x[1]*exp(lambda*t) end proc), x[2] = (proc (t) options operator, arrow; x[2]*exp(lambda*t) end proc), phi[1] = (proc (t) options operator, arrow; phi[1]*exp(lambda*t) end proc), phi[2] = (proc (t) options operator, arrow; phi[2]*exp(lambda*t) end proc)])), exp(lambda*t))) end do

x[1]*lambda-x[2]

 

x[2]*lambda+2*zeta*beta*x[2]+beta^2*x[1]-n*psi*v*phi[1]+n*psi*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*psi*x[1]-n*psi*x[1]*exp(-2*lambda*Pi/(n*omega0))

 

phi[1]*lambda-phi[2]

 

phi[2]*lambda+2*kappa*phi[2]+phi[1]-n*v*phi[1]+n*v*phi[1]*exp(-2*lambda*Pi/(n*omega0))+n*x[1]-n*x[1]*exp(-2*lambda*Pi/(n*omega0))

(5)

A, b := GenerateMatrix([seq(eqn[k], k = 1 .. 4)], [x[1], x[2], phi[1], phi[2]])

A, b := Matrix(4, 4, {(1, 1) = lambda, (1, 2) = -1, (1, 3) = 0, (1, 4) = 0, (2, 1) = beta^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)), (2, 2) = 2*Zeta*beta+lambda, (2, 3) = n*psi*v*exp(-2*lambda*Pi/(n*omega0))-n*psi*v, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = lambda, (3, 4) = -1, (4, 1) = n-n*exp(-2*lambda*Pi/(n*omega0)), (4, 2) = 0, (4, 3) = -n*v+1+n*v*exp(-2*lambda*Pi/(n*omega0)), (4, 4) = 2*kappa+lambda}), Vector(4, {(1) = 0, (2) = 0, (3) = 0, (4) = 0})

(6)

right_vector := Matrix(4, 1, [r[1], r[2], r[3], r[4]])

right_vector := Matrix(4, 1, {(1, 1) = r[1], (2, 1) = r[2], (3, 1) = r[3], (4, 1) = r[4]})

(7)

junk := MatrixVectorMultiply(subs(lambda = I*omega, A), right_vector)

junk := Matrix(4, 1, {(1, 1) = I*omega*r[1]-r[2], (2, 1) = (beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*Zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3], (3, 1) = I*omega*r[3]-r[4], (4, 1) = (n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(-n*v+1+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]})

(8)

junk(1)

I*omega*r[1]-r[2]

(9)

for k to 4 do eqnn[k] := junk(k) end do

I*omega*r[1]-r[2]

 

(beta^2+n*psi-n*psi*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(2*zeta*beta+I*omega)*r[2]+(n*psi*v*exp(-(2*I)*omega*Pi/(n*omega0))-n*psi*v)*r[3]

 

I*omega*r[3]-r[4]

 

(n-n*exp(-(2*I)*omega*Pi/(n*omega0)))*r[1]+(1-n*v+n*v*exp(-(2*I)*omega*Pi/(n*omega0)))*r[3]+(2*kappa+I*omega)*r[4]

(10)

solve({seq(eqnn[k], k = 1 .. 4)}, {seq(r[k], k = 1 .. 4)})

{r[1] = 0, r[2] = 0, r[3] = 0, r[4] = 0}

(11)

``

``

``

 

Download question4.mw

Hello all..

Im sharena and i am solving ODE BVP by using maple. i used this command to solved the equation..

 

However, i dont know which method this programm solved my ODE. Is it RK45 method??

Hello Everyone,

May I ask you about this  "Error,   (in pdsolve/numeric/process_PDEs)  number of dependent variables and number of PDE must be the same". Does anyone have idea about solving linear instability equation (flow inside pipe, oscillating flow) ?

Thank you,

 

 

 

Hello, I need help in add/sum, there are two problems:

 

1. How we write triple summation (sigma) in Maple? (See pic)

Pic 1 (Triple Sigma)

I try sum(sum(sum or add(add(add but it isn't working.

 

 

2. How we write summation like in this pic?

Pic 2

I already try these syntax:

for e from 1 to 9 do

for k from 1 to 17 do

if i=(2*e-1) then next else

constraint12[2*e-1,k]:=add(x[2*e-1,i,k],i from i in T)=1

end if

end do

end do

 

For example, the expected result for e=2 and k=1 is like following equation:

x[2,1,1]+x[2,3,1]+x[2,4,1]+x[2,5,1]+...+x[2,17,1]+x[2,18,1]=1

But the result I get:

x[2,1,1]+x[2,2,1]+x[2,3,1]+...+x[2,18,1]=1

 

How to omit the x[2,2,1]?

 

Thank you.

pls help review this code, its doesnt return a solution

 

 

restart;
Digits := 16;
M := .5; lambda := .5; Pr := .72; beta := 1; L[w] := 0; m := 1; R := 1; Ec := 1;
N := 7;
for j from 0 to N do J[j] := sum(f[k](t)*(diff(f[j-k](t), `$`(t, 2))), k = 0 .. j) end do;
for i from 0 to N do K[i] := sum((diff(f[k](t), t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
for j from 0 to N do G[j] := sum(f[k](t)*(diff(theta[j-k](t), t)), k = 0 .. j) end do;
for j from 0 to N do H[j] := sum((diff(f[k](t), t))*theta[j-k](t), k = 0 .. j) end do;
for i from 0 to N do P[i] := sum((diff(f[k](t), t, t))*(diff(f[i-k](t), t)), k = 0 .. i) end do;
epsilon := 1; delta := 0;
f[0] := proc (t) options operator, arrow; L[w]+epsilon+delta*A*t+(1/2)*A*t^2 end proc;
1 2
t -> L[w] + epsilon + delta A t + - A t
2
theta[0] := proc (t) options operator, arrow; 1+B*t end proc;
t -> 1 + B t
NULL;
;
NULL;
NULL;
NULL;
NULL;
for i to N do f[i] := simplify(-((m+1)*(1/2))*(int(int(int(J[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))+m*(int(int(int(1-K[i-1], t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-M*(int(int(int(diff(f[i-1](t), t)-1, t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))-lambda*(int(int(int(theta[i-1](t), t = 0 .. eta), t = 0 .. eta), t = 0 .. eta))); f[i] := unapply(f[i], eta); theta[i] := simplify(-3*Pr*R*(((m+1)*(1/2))*(int(int(G[i-1], t = 0 .. eta), t = 0 .. eta))-(2*m-1)*(int(int(H[i-1], t = 0 .. eta), t = 0 .. eta))+Ec*(int(int(P[i-1], t = 0 .. eta), t = 0 .. eta)))/(4+3*R)); theta[i] := unapply(theta[i], eta) end do;
NULL;
F(eta):=collect((∑)f[z](eta),eta):
Theta(eta):=collect((∑)theta[z](eta),eta):
with(numapprox);
for k from 2 to 5 do W[k] := pade(diff(F(eta), eta), eta, [k, k]); Q[k] := pade(Theta(eta), eta, [k, k]); SOLL1[k] := expand(coeff(numer(W[k]), eta^k)) = 1; SOLL2[k] := expand(coeff(numer(Q[k]), eta^k)) = 0; SOL[k] := solve({SOLL1[k], SOLL2[k]}, {A, B}); print([k] = SOL[k]) end do;
Warning, computation interrupted

 

 

 

 

 

 

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