MaplePrimes Questions

I have a table T with 10 numbers .How can I plot this table ?

Thanks for any explanation !

I am trying  to solve a first order differential equation.  But the maple is not able to solve. Please help me in finding the solutions...

Exact solution is not necessary. Solution in the series expansion is also be very helpful.

Here is the attached maple code..Please do check. Please scroll down to download the given maple file.


 

``

``

restart

with(Student[NumericalAnalysis])

with(PDEtools)

with(DEtools)

with(MmaTranslator)

[FromMma, FromMmaNotebook, Mma, MmaToMaple]

(1)

``

``

``

C1 := 2*M/(4*M*R^2*a-3*R^3*a)

``

D1 := -M*(8*M-9*R)*(3*ln(1+2*M/(4*M-3*R))+2*ln(1-2*M/R))/(3*R^2*(-16*M^2+26*M*R-9*R^2+(16*M^2-30*M*R+11*R^2)*ln(1+2*M/(4*M-3*R))+R^2*ln(-3*R/(4*M-3*R))))

``

A1 := R^2*(3*ln(1+2*M/(4*M-3*R))+2*ln(1-2*M/R))/(-32*M^2+52*M*R-18*R^2+(2*(16*M^2-30*M*R+11*R^2))*ln(1+2*M/(4*M-3*R))+2*R^2*ln(-3*R/(4*M-3*R)))

``

explambda := simplify((-2*C1*a*r^2+1)/(C1*a*r^2+1))

``

density := simplify(a*C1*(2*C1*a*r^2-3)/(-2*C1*a*r^2+1)^2)

``

pr := simplify(-D1+3*a*A1*C1*(2*C1*a*r^2-3)/(-2*C1*a*r^2+1)^2)

``

pt := simplify((D1*(-D1*r^2+4)-4*a^4*C1^4*r^6*(9*(1+A1)^2-(4*(1+3*A1))*D1*r^2+4*D1^2*r^4)+2*a*C1*(18*A1-(16+9*A1)*D1*r^2+4*D1^2*r^4)-3*a^2*C1^2*r^2*(9+16*A1+27*A1^2-(28*(1+A1))*D1*r^2+8*D1^2*r^4)+4*a^3*C1^3*r^4*(18+3*A1*(17+9*A1)-(10*(2+3*A1))*D1*r^2+8*D1^2*r^4))/((4*(C1*a*r^2+1))*(2*C1*a*r^2-1)^3))

``

drhodp := simplify(1/A1)

``

dptdp := (diff(pt, r))/(diff(pr, r))

``

A := simplify(-(-1-explambda)/r+4*explambda*Pi*r*(pr-density))

``

B := -(explambda^2+4*explambda+1)/r^2-64*explambda^2*Pi^2*r^2*pr^2-16*explambda*Pi*((-2+explambda)*pr-pt-density)-(-4*explambda*Pi*(pr+density)-4*explambda*Pi*drhodp*(pr+density))/dptdp

``

sys := {r*(diff(y(r), r))+y(r)^2+(A*r-1)*y(r)+r^2*B = 0}

 

[moderator edited to remove pages of output]
 

Download CALCULATION_OF_Y_v1.mw
 

I would like to use a template in Maple to create a sampled data custom component to mimic a digital controller in order to study the effects of the non-linear features of the controller.  Is it possible to do this in Maple using a template?

Hi!

Are there any plans to release a native Maple version for the Apple silicone (ARM architecture) Macs? I suppose that the current versions will work fine through Rosetta 2 emulation layer, but the Rosetta 2 will be removed from Mac OS in 2-3 years. Moreover, the native app would be much faster.

Thank you  

Good morning,

I'm new to Maple and have an informal learning relationship with calculus.

I'm exploring an expression but want the max value of a variable to be based on another equation. 

I'd be curious how to do this and then how to also graph and table the exploration. 

I'd like to evaluate, graph, and table this:

s = u*t + 1/2*a*t^2

Where the maximum value of t = (v - u)/a

s = distace

u = starting velocity

v = final velocity

a = acceleration

t = time for acceleration to reach final velocity

Thank you.

How to write the differential equation only according to the graph? Is the temperature related to newton's cooling law? 

Quite confused about this graph. 

Anyone can help me? Thank you so much! 

I cannot install the latest physics update 877 even after installing 2020.2 update. Geting an error message will try to attach screen shot. Update worked fine on physics update yesterday. Maple 2020.2 on MacBookPro OS 10.15.7

Don't know how to attach screen shot so here is text from install window;

Fetching package "Physics Updates" from MapleCloud...
ID: 5137472255164416
Version: 877
URL: https://maple.cloud

An error occurred, the package was not installed: 
Could not open workbook: /private/var/folders/bb/1n47nzcx18v_l2wy573v7z0c0000gn/T/cloudDownload5932106080613470167/Physics+Updates.maple

Tried at least 3 times before 2020.2 update and 2 times after. Similar results (diiferent download numbers each time).

Is there any useful preprocessing -- or a better data structure -- for efficient set membership testing?

I have a list X of 1.5 million hashes (30-digit compressions of arrays) and want to find an element which belongs to both this set and another set. The other set Y has 270 billion elements so I will generate just a fraction of these (a sample size of a few hundred million should be enough to give a collision). Will membership testing be faster if I first sort X? Or is the sort operation too expensive to see any visible benefit?

I have the equation x^4=4(4x^2-y^2), and I keyed in maple

>with (plots):
>eq:=x^4=4*(4*x^2-y^2);

and recieve in response x^4=4. 

I want to get eq:=x^4=4(4x^2-y^2), in order to find and graph all possible tangents in the event that y=3 and to find the point of intersection for the tangents that lie in the first quadrant. 

Thanks 

 

how this integro-differential equation can be solved?
any assumption or suggestion is appreciated. tnx in advance

EDITED: parameters are added.


 

restart

w[c]:=0.01:delta:=5:Omega:=5:w[0]:=1:gamma_0:=1:k[b]:=1:T:=100:nu[n]:=2*Pi*n*k[b]*T;

200*Pi*n

(1)

F:=2*gamma_0*w[c]^2*exp(-w[c]*tau)*sin(delta/Omega*(sin(Omega*t)-sin(Omega*(t-tau)))+w[0]*tau):

k1:=2*k[b]*T*w[c]^2*sum((w[c]*exp(-w[c]*tau)-abs(nu[n])*exp(-abs(nu[n])*tau))/(w[c]^2-nu[n]^2),n=-infinity..infinity):

G:=cos(delta/Omega*(sin(Omega*t)-sin(Omega*(t-tau)))+w[0]*tau)*k1:

eq:=diff(rho(t),t)+Int(G*rho(tau),tau=0..t)=1/2*Int(G-F,tau=0..t);

diff(rho(t), t)+Int(0.200e-1*cos(sin(5*t)-sin(5*t-5*tau)+tau)*(sum((0.1000000000e-1*exp(-0.1000000000e-1*tau)-628.3185308*abs(n)*exp(-628.3185308*abs(n)*tau))/(-394784.1762*n^2+0.1000000000e-3), n = -infinity .. infinity))*rho(tau), tau = 0 .. t) = (1/2)*(Int(0.200e-1*cos(sin(5*t)-sin(5*t-5*tau)+tau)*(sum((0.1000000000e-1*exp(-0.1000000000e-1*tau)-628.3185308*abs(n)*exp(-628.3185308*abs(n)*tau))/(-394784.1762*n^2+0.1000000000e-3), n = -infinity .. infinity))-0.2e-3*exp(-0.1e-1*tau)*sin(sin(5*t)-sin(5*t-5*tau)+tau), tau = 0 .. t))

(2)

 


 

Download integro.mw

Is it possible to draw a graph without names for the vertices? I would get something like this.

The worksheet below is a failed attempt to produce the display of a pencil of conics tangent to four lines. The worksheet contains an image of the display.

Comments within the worksheet describe the details of the attempt and the solve command which fails.

dhaar provided an answer to a similar question which I posed on November 12 (its web address is in the worksheet) and I hope s(he) will reply to this one as well.

ConicsTangent.mw

 

Hello there, 

Would you allow me to ask this question?

What would be a way to make the 'expression' as 'expression_desired' below?

In other words, what would be a way to cancel I (or j) and exp(-pi/2) each other?


 

restart;

expression := exp(-I/2*(-2*rho__m + pi))*I;

I*exp(-((1/2)*I)*(-2*rho__m+pi))

(1)

expression_desired := exp(I*(rho__m));

 

exp(I*rho__m)

(2)

 


Thank you, 

Download Q20201118.mw

I  installed Maple 2020 a week ago.   When I try to update the Maple Physics Package, the installation stalls.

Output to the command  Physics:-Version(latest):

`The "Physics Updates" version "872" is installed but is not active. The active version of Physics is within the library C:\\Program Files\\Maple 2020\\lib\\maple.mla, created 2020, March 4, 19:36 hours`

I note that there was similar complaint in June.  I am surprised that this has not yet been fixed. The reply in June seemed to be do a manual update, but I am unclear how to do that.   I can download the latest package, but I do not know how to  (or where) to install this package.  Do I just delete the version in C:\\Program Files\\Maple 2020\\lib\\maple.mla and paste the new version?

I would greatly appreciate any help since the main reason I purchased the new Maple 2020 was to use the most recent versions of the Physics package.

There is an error in the series expansion for the JacobiTheta3 and JacobiTheta4 function

> q := exp(I*((2*I)*Pi*1.20388508772313))

>series(JacobiTheta3(z, q)-JacobiTheta3(0, q), z, 2);

gives -1+O(z^2)

>series(JacobiTheta3(z, q)-JacobiTheta3(0, q), z, 2);

gives -1+O(z^2)

The issue is that 

>series(JacobiTheta3(z, q),z,2);

gives

series(Sum(2*Q^(_k1^2),_k1 = 1 .. infinity)+O(z^2),z,2)

where the term n=0 is missing.  

The same for JacobiTheta4

series(JacobiTheta4(z, Q), z, 2);

series(Sum(2*(-1)^_k1*Q^(_k1^2),_k1 = 1 .. infinity)+O(z^2),z,2)

The same issue arises when taking the limit 

limit(JacobiTheta3(z, sqrt(q))-JacobiTheta3(0, sqrt(q)), z=0); 

gives -1

same for  limit(JacobiTheta4(z, sqrt(q))-JacobiTheta4(0, sqrt(q)), z=0); gives -1

This error occurs in maple 2018 and maple 2020. 

On the other side when taking numering values approching 0 there is no problems. 

 

So it seems that series and limit uses some codes wrong formulae.

How can one patch this? 

thanks in advance

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