MaplePrimes Questions

@tomleslie 

Dear Tom,

I need your help. I have a delay differential equation to solve and extract the value of the solution y(t) at a selected point of the independent variable t.  I am uploading a small sample code. 

Thanks.
 

dsys := {diff(y(t), t) = -y(t-1), y(0) = 2}; dsn := dsolve(dsys, numeric)

{diff(y(t), t) = -y(t-1), y(0) = 2}

(1)

 

 

``


 

Download delay-differential-equation.mw
 

dsys := {diff(y(t), t) = -y(t-1), y(0) = 2}; dsn := dsolve(dsys, numeric)

{diff(y(t), t) = -y(t-1), y(0) = 2}

(1)

 

 

``


 

Download delay-differential-equation.mw

 

Hi everyone: 

I want to obtain r1(t), V(t) , q(t) in terms of U0 and plot V(t) in terms of U0, how? 

eq1:= diff(r[1](t), t, t)+(.3293064114+209.6419478*U[0])*(diff(r[1](t), t))+569.4324330*r[1](t)-0.3123434112e-2*V(t) = -1.547206836*U[0]^2*q(t)
eq2:= 2.03*10^(-8)*(diff(V(t), t))+4.065040650*10^(-11)*V(t)+0.3123434112e-2*(diff(r[1](t), t)) = 0
eq3 := diff(q(t), t, t)+1047.197552*U[0]*(q(t)^2-1)*(diff(q(t), t))+1.096622713*10^6*U[0]^2*q(t) = -2822.855019*(diff(r[1](t), t, t))
ics:=r1(0)=0,D(r1)(0)=0,V(0)=0,q(0)=0,D(q)(0)=0;

Tnx...

Hi, everytimes I enter anythings, it turn out with Typesetting:-mparsed( bla1bla2, bla1bla2;"_noterminate")

example:

For an Array A, say, and some positive integer n, say, Maple interpretes A^n as raising each entry separately to the same power n. Without the Physics package loaded, A^n can also be written as A . A . ... . A (n times). But with the Physics package loaded, this equality is broken (at least in Maple 2017): If A is a 2D square Array, A . A all of a sudden is no longer equal to A^2, but rather to convert(A,Matrix)^2, i.e., to the square of the Array considered as a Matrix. The presence of the dot operator seems to make the Physics enviroment convert A to a Matrix. This seems to me to be a bug.

In the C programming language the following code makes i = 1

real r;      integer i;      r = 1.9;         i = r;

How do I do the same in Maple?

During running my ws I faced with memory error as below, where as my system have enough memory (120GB)

Warning, Run: unable to set assignto result due to error:  Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc

Maple's help suggests :Software limits are imposed by the -T command-line argument, the datalimit argument to kernelopts and system imposed user limits (for example shell limits).
  But I could not understand how to increase software limit.

 

how to fix that?

find the fourier cosine and sine transform. Use your identites and integrals to eliminate all exponents.

piecewise function is {cosh(t) for 0 less or equal to t, t is less than 1,

                                   0 for 1is less than or equal to t.}

alpha+{6*RK[1]*alpha+2+(96/5)*R^2*K^2*alpha^2-(1/6)*R*alpha+64*R^3*K^3*alpha^3}*beta+{(24/5)*RK+44*R^2*K^2*alpha^3}*beta^2=0

i am currently using Maple 18, i have a problem on inserting 12 row by 12 column matrix and above is seem to be impossible. please can help or direct me on how to insert 12 row by 12 column matrix in maple. because my maple 18 seem to stop in 10 row by 10 column matrix.  thanks

Hi everybody.....

I want to obtain the roots of below equation, How? 

eq:=1+cos(beta)*cosh(beta)+.5720823799*beta*(cos(beta)*sinh(beta)-cosh(beta)*sin(beta))-0.1285578382e-1*beta^2*sin(beta)*sinh(beta)-0.9629800618e-4*beta^3*(cos(beta)*sinh(beta)+cosh(beta)*sin(beta))+0.1377259814e-4*beta^4*(1-cos(beta)*cosh(beta)) = 0

Tnx...

Dear users,

I have an issue with finding real part of a complex variable function. In calculating the real part I see two arguments and the plot is not smooth. How to get real part correct. The worksheet is attached.
 

``

 

 

##Toya complex variable method

``

restart;

stress_c:=-(1+1/nu_c)*k*p2*zeta_c/2;

-(1/2)*(1+1/nu_c)*k*p2*zeta_c

(1.1)

p2:=(c0_c-d_1c/k)*(z-a*(cos(alpha)+2*lambda*sin(alpha)))+(1-k)/k*a*(N_infty-T_infty)*exp(2*I*phi_c+2*lambda*(alpha-Pi))*((a*(cos(alpha)-2*lambda*sin(alpha)))/z-a^2/z^2)

(c0_c-d_1c/k)*(z-a*(cos(alpha)+2*lambda*sin(alpha)))+(1-k)*a*(N_infty-T_infty)*exp((2*I)*phi_c+2*lambda*(alpha-Pi))*(a*(cos(alpha)-2*lambda*sin(alpha))/z-a^2/z^2)/k

(1.2)

``

z := exp(I*theta)

exp(I*theta)

(1.3)

``

k := beta_c/(1+nu_c)

beta_c/(1+nu_c)

(1.4)

nu_c := (kappa2*mu+mu2)/(kappa*mu2+mu)

(kappa2*mu+mu2)/(kappa*mu2+mu)

(1.5)

d_1c := (N_infty+T_infty)*(1/2)

(1/2)*N_infty+(1/2)*T_infty

(1.6)

lambda := -evalf(ln(nu_c)/(2*Pi))

-.1591549430*ln((kappa2*mu+mu2)/(kappa*mu2+mu))

(1.7)

``

beta_c := mu*(1+kappa2)/(kappa*mu2+mu)

mu*(1+kappa2)/(kappa*mu2+mu)

(1.8)

zeta_c := ((z-a*exp(I*alpha))/(z-a*exp(-I*alpha)))^(I*lambda)/((z-a*exp(I*alpha))^.5*(z-a*exp(-I*alpha))^.5)

((exp(I*theta)-a*exp(I*alpha))/(exp(I*theta)-a*exp(-I*alpha)))^(-(.1591549430*I)*ln((kappa2*mu+mu2)/(kappa*mu2+mu)))/((exp(I*theta)-a*exp(I*alpha))^.5*(exp(I*theta)-a*exp(-I*alpha))^.5)

(1.9)

``

c0_c := G_c+I*H_c

G_c+I*H_c

(1.10)

G_c:=(0.5*(T_infty+N_infty)*(1-(cos(alpha)+2*lambda*sin(alpha))*exp(2*lambda*(evalf(Pi)-alpha)))-0.5*(1-k)*(1+4*lambda^2)*(N_infty-T_infty)*(sin(alpha))^2*cos(2*phi_c))/(2-k-k*(cos(alpha)+2*lambda*sin(alpha))*exp(evalf(2*lambda*(Pi-alpha))));

(.5*(N_infty+T_infty)*(1-(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-alpha)))-.5*(1-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))*(.1013211835*ln((kappa2*mu+mu2)/(kappa*mu2+mu))^2+1)*(N_infty-T_infty)*sin(alpha)^2*cos(2*phi_c))/(2-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu)))-mu*(1+kappa2)*(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-1.*alpha))/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))

(1.11)

H_c:=0.5*(1-k)*(1+4*lambda^2)*(-T_infty+N_infty)*(sin(alpha))^2*sin(2*phi_c)/(k*(1+(cos(alpha)+2*lambda*sin(alpha))*exp(2*lambda*(evalf(Pi)-alpha))));

.5*(1-mu*(1+kappa2)/((kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))))*(.1013211835*ln((kappa2*mu+mu2)/(kappa*mu2+mu))^2+1)*(N_infty-T_infty)*sin(alpha)^2*sin(2*phi_c)*(kappa*mu2+mu)*(1+(kappa2*mu+mu2)/(kappa*mu2+mu))/(mu*(1+kappa2)*(1+(cos(alpha)-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*sin(alpha))*exp(-.3183098860*ln((kappa2*mu+mu2)/(kappa*mu2+mu))*(3.141592654-alpha))))

(1.12)

##Input

alpha:=evalf(Pi/6)

.5235987758

(1.13)

phi_c:=alpha;

.5235987758

(1.14)

N_infty:=0;

0

(1.15)

T_infty:=1;

1

(1.16)

a:=1;nu2:=22/100;kappa2:=3-4*nu2;nu:=35/100;kappa:=3-4*nu;mu:=239/100;mu2:=442/10;

1

 

11/50

 

53/25

 

7/20

 

8/5

 

239/100

 

221/5

(1.17)

``

stress_c

-(9321/123167)*(((.5586916801-.5*(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775))+0.5946710490e-2*ln(123167/182775)^2)/(22817/11767-(717/11767)*(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775)))-(1.668336947*I)*(.1013211835*ln(123167/182775)^2+1)/(1+(.8660254037-.1591549431*ln(123167/182775))*exp(-.8333333329*ln(123167/182775)))-11767/1434)*(exp(I*theta)-.8660254037+.1591549431*ln(123167/182775))-(11050/717)*exp(1.047197552*I+.8333333328*ln(123167/182775))*((.8660254037+.1591549431*ln(123167/182775))/exp(I*theta)-1/(exp(I*theta))^2))*((exp(I*theta)+(-.8660254037-.5000000002*I))/(exp(I*theta)+(-.8660254037+.5000000002*I)))^(-(.1591549430*I)*ln(123167/182775))/((exp(I*theta)+(-.8660254037-.5000000002*I))^.5*(exp(I*theta)+(-.8660254037+.5000000002*I))^.5)

(1.18)

assume((1/6)*Pi < theta, theta < 2*Pi-(1/6)*Pi)

simplify(evalc(Re(stress_c)))

-0.8815855810e-10*((((1.000000000*cos(theta)^7+(0.5294827753e-2+.5671599115*sin(theta))*cos(theta)^6-4.533186669*cos(theta)^5+(-11.80630620+4.886343937*sin(theta))*cos(theta)^4+3.402782742*cos(theta)^3+(9213180122.+0.9866808100e-1*sin(theta))*cos(theta)^2+(-0.1055437876e11+0.1595769608e11*sin(theta))*cos(theta)-5794103792.*sin(theta)+1760041721.)*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-.5600908440*cos(theta)^7+(0.6523625301e-2+1.134319823*sin(theta))*cos(theta)^6+4.644568297*cos(theta)^5+(-0.2905669688e-1+10.20004207*sin(theta))*cos(theta)^4-0.1774243515e-1*cos(theta)^3+(0.1595769609e11-9.082306669*sin(theta))*cos(theta)^2+(-7023191163.-9213180109.*sin(theta))*cos(theta)-3154310102.*sin(theta)-7408031461.)*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037)))*cos(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))+(-.5600908440*cos(theta)^7+(1.134319823*sin(theta)+0.4756356038e-2)*cos(theta)^6+4.644568284*cos(theta)^5+(11.37920491*sin(theta)-0.2640575516e-1)*cos(theta)^4-0.1774243890e-1*cos(theta)^3+(-11.39571957*sin(theta)+0.1595769607e11)*cos(theta)^2+(-9213180108.*sin(theta)-7023191160.)*cos(theta)-7408031458.-3154310086.*sin(theta))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-1.000000000*cos(theta)^7+(-.5671599115*sin(theta)-0.5294826902e-2)*cos(theta)^6+4.531921682*cos(theta)^5+(-4.886343941*sin(theta)+11.76153292)*cos(theta)^4-3.358186195*cos(theta)^3+(-0.9866807692e-1*sin(theta)-9213180122.)*cos(theta)^2+(-0.1595769609e11*sin(theta)+0.1055437877e11)*cos(theta)-1760041726.+5794103798.*sin(theta))*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037)))*cos(0.314104002e-1*ln(1492820323.-1292820323.*cos(theta)+746410161.*sin(theta))-0.314104002e-1*ln(-1292820322.*cos(theta)-746410161.4*sin(theta)+1492820322.))+(((-.5600908440*cos(theta)^7+(1.134319823*sin(theta)+0.4756356038e-2)*cos(theta)^6+4.626658979*cos(theta)^5+(-0.2905667760e-1+10.24488508*sin(theta))*cos(theta)^4-.1341529536*cos(theta)^3+(0.1595769608e11-9.127079936*sin(theta))*cos(theta)^2+(-7023191161.-9213180109.*sin(theta))*cos(theta)-3154310089.*sin(theta)-7408031435.)*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(-1.134319823*cos(theta)^7-.5671599115*sin(theta)*cos(theta)^6+4.531921682*cos(theta)^5+(11.80860365-4.107288978*sin(theta))*cos(theta)^4-3.402959469*cos(theta)^3+(-9213180123.+0.1774243833e-1*sin(theta))*cos(theta)^2+(0.1055437876e11-0.1595769608e11*sin(theta))*cos(theta)+5794103807.*sin(theta)-1760041748.)*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037)))*cos(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))+(-1.000000000*cos(theta)^7-.5671599115*sin(theta)*cos(theta)^6+4.537223485*cos(theta)^5+(-4.886343950*sin(theta)+11.80860366)*cos(theta)^4-3.358186195*cos(theta)^3+(-0.9866807250e-1*sin(theta)-9213180123.)*cos(theta)^2+(0.1055437876e11-0.1595769608e11*sin(theta))*cos(theta)-1760041739.+5794103821.*sin(theta))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037))*cos(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))+(.5600908440*cos(theta)^7+(-1.134319823*sin(theta)-0.4756356038e-2)*cos(theta)^6-4.644554360*cos(theta)^5+(-10.21771474*sin(theta)+0.2905668928e-1)*cos(theta)^4+0.1774243685e-1*cos(theta)^3+(9.082306650*sin(theta)-0.1595769608e11)*cos(theta)^2+(9213180109.*sin(theta)+7023191165.)*cos(theta)+7408031453.+3154310085.*sin(theta))*sin(.5*arctan(sin(theta)+.5000000002, cos(theta)-.8660254037))*sin(.5*arctan(sin(theta)-.5000000002, cos(theta)-.8660254037)))*sin(0.314104002e-1*ln(1492820323.-1292820323.*cos(theta)+746410161.*sin(theta))-0.314104002e-1*ln(-1292820322.*cos(theta)-746410161.4*sin(theta)+1492820322.)))/((-sin(theta)+2.-1.732050807*cos(theta))^(1/4)*(sin(theta)+2.-1.732050807*cos(theta))^(1/4))

(1.19)

plot(%, theta = (1/6)*Pi .. 2*Pi-(1/6)*Pi)

 


 

Download Toya_complexPlot2.mw

Hi all, how to get name file  in directory?

Example. I have  and I want call then return

["equals", "function", "polynomial", "viete"]

or

["equals.txt", "function.txt", "polynomial.txt", "viete.txt"]

Thank you very much.

Dear authors,
How to solve this ode problem.

Download link ode.mw

In this problem the boundary condition is

Note: F=g in our problem.

eta approaches N.

Thank you.

 

If I let Maple computer the integral of tan(x), it gets

Int(tan(x), x)=int(tan(x),x), which is the same result as many other softwares get.

However, if I do integral of tan(2*x), it becomes

Int(tan(2*x), x)=(1/4)*ln(1+tan(2*x)^2), instead of -(1/2)*ln(cos(2*x)). The latter form should make more sense considering what Maple gives for tan(x).

In fact, Maple alwys gives the anwer ln(1+tan(n*x)^2)/(2*n) (1) as the integral for tan(n*x) when n>=2. While this is also an indefinite integral of tan(n*x), it is not exactly the equivalent of -(1/n)*ln(cos(n*x)) (2), which is the form Maple gives for integral of tan(x). Expression (2) sometimes evaluates to complex values while (1) only evaluates to real values. It seems that for integral of tan(2x) Maple tries to find the antiderivative that always evaluates to real values, but for tan(x) Maple is happy with -ln(cos(x)), whose value may be complex.

Is there a reason why Maple does this? And is there any way to change the way Maple computes indefinite integrals?

I am trying to put a number of related 2-d plots into a 3-d frame so I can see them stacked up in the third dimension (which follows a parameter) and rotate things around.

The way I once did this successfully was to create the 2-d plots and then use plottools:-transform to move the individual plots in the third dimension, like so:

plt:=plot(something);

tr:=plottools:-transform((x,y) -> [x,2,y]); # the "2" gets changed for the other plots (not shown here).

plots:-display(tr(plt));

The only effect I can get is that the GUI gets confused and I have to close and reload the sheet to get it back again. I have a (complicated) sheet where this actually works, but I am not able to make it work even in the small example I am posting below.

Any hint of where I am going off trail is appreciated. Incidentally, this problem is what led to the corrupted sheet I had maybe a week ago.

Thanks,

Mac Dude.

display3d.mw

 

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