Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

 

with(inttrans)

eq1 := 2*(diff(y__1(t), t)) = -2*y__1(t)-3*y__2(t)+2*u__1

eq2 := diff(y__2(t), t) = 4*y__1(t)-6*y__2(t)+2*u__1+4*u__2

help("laplace")

We have two coupled differential equations relating two outputs (y__1, y__2 ) with two inputs u__1, u__2

The objective of the exercise is to obtain the four transfer functions relating the outputs to the inputs, in other words, we must find:

To save time, we will from now on write Y__1 instead of Y__1(s) , etc.

In order to find tese relations, we must solve Y__1 and Y__2 as a function of U__1 and U__2

Since our model is defined in the time-domain, the first step is to perform Laplace Transform:

Note tha y__1(0) and y__2(0)are zero because y__1 and y__2 are deviation variables, as indicated in the problem description of this exercise.

Now we have a set of two equations with two unknowns, which can be solved algebraically
(this is the advantage of the Laplace Transform). For example, from equation (3) we can
isolate Y__2:

We can substitute the expression (5) in equation (4) to obtain Y__1, as follows:

We can multiply both sides by -3 and expand the products to get:

Now we must group the factors multiplying Y__1, U__1 and U__2

Note that this relation is analogous to:

Y__1 = G__11*U__1+G__12*U__2

Since the effects of `U__1 ` and U__2 are additive, if we want to obtain the relation between one output and only one input ( for example Y__1 and "`U__1`)" we can set the other input to zero, i.e. U__2 = 0.

We still have to obtan the relation between Y__2 and the inputs. We can use equation (5) and (6):

Finally we can find the relations:

 



 

Download Transfer_function.mw

 

Hello

I have this problem:

in which I have to find the four transfer functions relating the outputs(yand y2) to the inputs (u1,u2).

The u and y are deviation variables. 

The objective is to find the four transfer functions:

So I have done it by hand but I was wondering if there are any maple commands, that could be used to solve such a question?

 

I found the transfer functions to be:

I can display an animated plot of the Normal distribution pdf and was wondering if anybody has a routine to animate the Normal cdf. If this is so - is it possible to generalise for any continuous statistical distribution?

Thanks for reading! 

I use append and cmaple to run

originally can See result in real time even if open text file

but suddenly text file become 0KB

when I copy text file and paste 

0 KB become 3 KB 

but the program can not further output to text file and no error shown

 

 

Dear Community!

I'm struggleing with a problem long since. I highly appreciate any help with this theme.

The problem is the following:

- I have a set of points, what comes from a numerical solution of a complex, but periodical function. Therefore I have a set of points (X;Y). The points are doesn't matter, but in my case, it look like this:

I want to use the Fourier-method to approximate this points with a function.

The best result I could get is this:

But it is not acceptable due to the high inaccuracy at the starting, and finishing points (there is a diagram inaccuracy %):

I'm feel like, I'm doing something wrong. Unfortunately, I had no time to look deep into the math here. Can somebody tell me, that how can I get a better result, using this method?

Thank you very much for the help in advance.

Best regards

Dávid

Could anybody give me an idea of how I would go about ignoring the Christoffel symbols with coefficients of order Omega(r)^2 in the following code? Thanks.
 

with(Physics)

[`*`, `.`, Annihilation, AntiCommutator, Antisymmetrize, Assume, Bra, Bracket, Check, Christoffel, Coefficients, Commutator, CompactDisplay, Coordinates, Creation, D_, Dagger, Decompose, Define, Dgamma, Einstein, EnergyMomentum, Expand, ExteriorDerivative, Factor, FeynmanDiagrams, Fundiff, Geodesics, GrassmannParity, Gtaylor, Intc, Inverse, Ket, KillingVectors, KroneckerDelta, LeviCivita, Library, LieBracket, LieDerivative, Normal, Parameters, PerformOnAnticommutativeSystem, Projector, Psigma, Redefine, Ricci, Riemann, Setup, Simplify, SortProducts, SpaceTimeVector, StandardModel, SubstituteTensor, SubstituteTensorIndices, SumOverRepeatedIndices, Symmetrize, TensorArray, Tetrads, ThreePlusOne, ToFieldComponents, ToSuperfields, Trace, TransformCoordinates, Vectors, Weyl, `^`, dAlembertian, d_, diff, g_, gamma_]

(1)

NULL

Setup(metric = -exp(2*alpha(r))*%d_(t)^2+exp(2*beta(r))*%d_(r)^2+r^2*%d_(theta)^2+r^2*sin(theta)^2*(%d_(phi)-Omega(r)*%d_(t))^2)

[metric = {(1, 1) = -exp(2*alpha(r))+(-r^2*cos(theta)^2+r^2)*Omega(r)^2, (1, 4) = -r^2*sin(theta)^2*Omega(r), (2, 2) = exp(2*beta(r)), (3, 3) = r^2, (4, 4) = r^2*sin(theta)^2}]

(2)

g_[]

Physics:-g_[mu, nu] = Matrix(%id = 18446746171579097566)

(3)

Christoffel[nonzero]

Physics:-Christoffel[alpha, mu, nu] = {(1, 1, 2) = -(diff(alpha(r), r))*exp(2*alpha(r))-r*Omega(r)*(cos(theta)-1)*(cos(theta)+1)*(r*(diff(Omega(r), r))+Omega(r)), (1, 1, 3) = r^2*sin(theta)*Omega(r)^2*cos(theta), (1, 2, 1) = -(diff(alpha(r), r))*exp(2*alpha(r))-r*Omega(r)*(cos(theta)-1)*(cos(theta)+1)*(r*(diff(Omega(r), r))+Omega(r)), (1, 2, 4) = -(1/2)*r*sin(theta)^2*(r*(diff(Omega(r), r))+2*Omega(r)), (1, 3, 1) = r^2*sin(theta)*Omega(r)^2*cos(theta), (1, 3, 4) = -r^2*sin(theta)*Omega(r)*cos(theta), (1, 4, 2) = -(1/2)*r*sin(theta)^2*(r*(diff(Omega(r), r))+2*Omega(r)), (1, 4, 3) = -r^2*sin(theta)*Omega(r)*cos(theta), (2, 1, 1) = (diff(alpha(r), r))*exp(2*alpha(r))+r*Omega(r)*(cos(theta)-1)*(cos(theta)+1)*(r*(diff(Omega(r), r))+Omega(r)), (2, 1, 4) = (1/2)*r*sin(theta)^2*(r*(diff(Omega(r), r))+2*Omega(r)), (2, 2, 2) = (diff(beta(r), r))*exp(2*beta(r)), (2, 3, 3) = -r, (2, 4, 1) = (1/2)*r*sin(theta)^2*(r*(diff(Omega(r), r))+2*Omega(r)), (2, 4, 4) = -r*sin(theta)^2, (3, 1, 1) = -r^2*sin(theta)*Omega(r)^2*cos(theta), (3, 1, 4) = r^2*sin(theta)*Omega(r)*cos(theta), (3, 2, 3) = r, (3, 3, 2) = r, (3, 4, 1) = r^2*sin(theta)*Omega(r)*cos(theta), (3, 4, 4) = -r^2*sin(theta)*cos(theta), (4, 1, 2) = -(1/2)*r*sin(theta)^2*(r*(diff(Omega(r), r))+2*Omega(r)), (4, 1, 3) = -r^2*sin(theta)*Omega(r)*cos(theta), (4, 2, 1) = -(1/2)*r*sin(theta)^2*(r*(diff(Omega(r), r))+2*Omega(r)), (4, 2, 4) = r*sin(theta)^2, (4, 3, 1) = -r^2*sin(theta)*Omega(r)*cos(theta), (4, 3, 4) = r^2*sin(theta)*cos(theta), (4, 4, 2) = r*sin(theta)^2, (4, 4, 3) = r^2*sin(theta)*cos(theta)}

(4)

``


 

Download Christoffel.mw

Hi guys,

I'm trying to apply boundary condition on the seris i generated using Adomian decomposition. Could some one please check it for me?
 

NULL

u[0] := a1+a2*y:

NULL

NULL

w[0] := a3+a4*y:

theta[0] := a6*y+a5

phi[0] := a8*y+a7

NULL

NULL

``

``

``

``

``

A[1] := R*(diff(u[0], y))+A-Gr*(B*phi[0]+theta[0])/Ree+Ha^2*(alpha*u[0]+beta*w[0])/(alpha^2+beta^2)

R*a2+A-Gr*(a5+a6*y+B*(a7+a8*y))/Ree+Ha^2*(alpha*(a1+a2*y)+beta*(a3+a4*y))/(alpha^2+beta^2)

(1)

u[1] := int(A[1], y = 0 .. y)

(1/2)*(-Gr*(a6+B*a8)/Ree+Ha^2*(alpha*a2+beta*a4)/(alpha^2+beta^2))*y^2+R*a2*y+A*y-Gr*(a5+B*a7)*y/Ree+Ha^2*(alpha*a1+beta*a3)*y/(alpha^2+beta^2)

(2)

u[11] := int(u[1], y = 0 .. y)

(1/3)*(-(1/2)*Gr*(a6+B*a8)/Ree+(1/2)*Ha^2*(alpha*a2+beta*a4)/(alpha^2+beta^2))*y^3+(1/2)*(R*a2+A-Gr*(a5+B*a7)/Ree+Ha^2*(alpha*a1+beta*a3)/(alpha^2+beta^2))*y^2

(3)

u = u[0]+u[11]

u = a1+a2*y+(1/3)*(-(1/2)*Gr*(a6+B*a8)/Ree+(1/2)*Ha^2*(alpha*a2+beta*a4)/(alpha^2+beta^2))*y^3+(1/2)*(R*a2+A-Gr*(a5+B*a7)/Ree+Ha^2*(alpha*a1+beta*a3)/(alpha^2+beta^2))*y^2

(4)

A[2] := R*(diff(w[0], y))-Ha^2*(beta*u[0]-alpha*w[0])/(alpha^2+beta^2)

R*a4-Ha^2*(beta*(a1+a2*y)-alpha*(a3+a4*y))/(alpha^2+beta^2)

(5)

w[1] := int(A[2], y = 0 .. y)

-(1/2)*Ha^2*(beta*a2-alpha*a4)*y^2/(alpha^2+beta^2)+R*a4*y-Ha^2*(beta*a1-alpha*a3)*y/(alpha^2+beta^2)

(6)

w[11] := int(w[1], y = 0 .. y)

-(1/6)*Ha^2*(beta*a2-alpha*a4)*y^3/(alpha^2+beta^2)+(1/2)*(R*a4-Ha^2*(beta*a1-alpha*a3)/(alpha^2+beta^2))*y^2

(7)

``

w = w[0]+w[11]

w = a3+a4*y-(1/6)*Ha^2*(beta*a2-alpha*a4)*y^3/(alpha^2+beta^2)+(1/2)*(R*a4-Ha^2*(beta*a1-alpha*a3)/(alpha^2+beta^2))*y^2

(8)

A[3] := R*Pr*(diff(theta[0], y))-2*Br*((diff(u[0], y))^2+(diff(w[0], y))^2+M^2*C*(u[0]^2+w[0]^2))-gamma*R*Pr*theta[0]

R*Pr*a6-2*Br*(a2^2+a4^2+M^2*C*((a1+a2*y)^2+(a3+a4*y)^2))-gamma*R*Pr*(a5+a6*y)

(9)

theta[1] := int(A[3], y = 0 .. y)

-(2/3)*Br*M^2*C*(a2^2+a4^2)*y^3+(1/2)*(-2*Br*M^2*C*(2*a1*a2+2*a3*a4)-gamma*R*Pr*a6)*y^2+R*Pr*a6*y-2*Br*(a2^2+a4^2+M^2*C*(a1^2+a3^2))*y-gamma*R*Pr*a5*y

(10)

theta[11] := int(theta[1], y = 0 .. y)

-(1/6)*Br*M^2*C*(a2^2+a4^2)*y^4+(1/3)*(-Br*M^2*C*(2*a1*a2+2*a3*a4)-(1/2)*gamma*R*Pr*a6)*y^3+(1/2)*(R*Pr*a6-2*Br*(a2^2+a4^2+M^2*C*(a1^2+a3^2))-gamma*R*Pr*a5)*y^2

(11)

theta = theta[0]+theta[11]

theta = a5+a6*y-(1/6)*Br*M^2*C*(a2^2+a4^2)*y^4+(1/3)*(-Br*M^2*C*(2*a1*a2+2*a3*a4)-(1/2)*gamma*R*Pr*a6)*y^3+(1/2)*(R*Pr*a6-2*Br*(a2^2+a4^2+M^2*C*(a1^2+a3^2))-gamma*R*Pr*a5)*y^2

(12)

``

 

NULL

A[4] := R*Sc*(diff(phi[0], y))-K*Sc*phi[0]

R*Sc*a8-K*Sc*(a7+a8*y)

(13)

phi[1] := int(A[4], y = 0 .. y)

-(1/2)*K*Sc*a8*y^2+R*Sc*a8*y-K*Sc*a7*y

(14)

phi[11] := int(phi[1], y = 0 .. y)

-(1/6)*K*Sc*a8*y^3+(1/2)*(R*Sc*a8-K*Sc*a7)*y^2

(15)

phi = phi[0]+phi[11]

phi = a7+a8*y-(1/6)*K*Sc*a8*y^3+(1/2)*(R*Sc*a8-K*Sc*a7)*y^2

(16)

``


 

Download second_problem.mw

Hi everyone,

Please, I really need your expertise advice(s) on what i am not doing right in the code attached below. I was actually writing the code on Multi-step DTM, but, instead of continuing from the last point, it starting all over again. Please, your expertise will save a soul here. Regard

Thanks

MsDTM3.mw

I'm pretty annoyed with maple because when I try to create proc's it dooes not use tabbing or smart tabbing. This makes writing readable code a chore. Basically it's always screwing up alignment. (it wants to left justify things a lot)...

 

What's worse is that using the tab key takes one outside the proc rather than adding a tab, making one having to use spaces.

Any way to fix this?

Hello, I try this integral, but Maple not solutions, the answer is the same integral.

int(N*exp((2*(-(1/2)*x^2-2*a^2*ln(x)*x/(-2*x^2+2)))/sigma^2)/(-2*x^2+2), x = -1 .. 1)

N,a, sigma are constants.

Regards

I'm having trouble connecting from Maple on Windows 10 to MSQL Server. I tried Microsoft recommended drivers such as sqljdbc_6.4.0.0, did (as I thought) all required steps. The only invariable result I get is "Cannot load driver". I was wandering if anyone had implemented such a construction. Driver name & version , connection string and Java version would be greatly appreciated. Another option is to have any driver, which connects to any of standard databases (Oracle, MySQL).  The only limitation is- it must be from Windows 7 or 10.
          Thanks.
           A.B.

I remember there was a command that used to start an independent java session each time. I thought it's "xmaple -singlemode" but it's not. So could anybody please remind me what was the command. I just killed a second java session after losing kernel connection and java running wild. I'd be very happy to do my calculation in another java session so that if anything goes bad II won't have to open all my 5 tabs again.

Integrating a positive definite function (normal distribution) and a >= 0 function (Heaviside) should not return a negative value.

 

 

with(Statistics);
X := RandomVariable(Normal(1, sqrt(2.25)));
int(PDF(X, x)*Heaviside(x^7-5*x^4-3*x+1), x = -infinity .. infinity);
                         -0.08507120131

 

 

Bug.mw

I'm using dsolve command to solve a differential equation. Using infolevel to 3 will tell me the classification of said DE. However, how can I see the step by step solution? I'm using Maple as a study tool so I do solve manually a DE then I'd like to compare my answer with Maple's. How can I acomplish this? Thanks in advance. 

Please may I know if you can offer ma student's discount ob the seleted version.

Thank you.

Fred.

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