Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hi everybody;

I have a problem with Physics[diff] command. When I run the following code, error messages appear where the Physics[diff] command exist. What is the source of error? How can I fix it?

Thanks in advance

Q1.mw

Hello.

I am taking an intermediate mathematics course. Now we are heading towards the finals and I have started to review all the topics we have been visiting during this semester.

Now I came across an excercise I cannot solve, taking into consideration what our lectures looks like and topics on the list my best bet is using lagrange multiplie method to optimize a multivariable function with constraints.

The task gives a shape that is drawn within the circle given by the equation: x^2+y^2=2.

The shape is a hexagon with 2 vertecies on the y-axsis +- the radius 2, the other 4 vertecies are the following [+-x,+-y].

I´m told that this hexagon is spinned around the y-axis to form a solid sylinder with 2 cones. The problem is to choose both radius and hight of the cylinder in order to maximize the volume.

The first problem that I dont know how i can plot this in maple, I would like to plot both the 2d hexagon and the solid spinned around the y-axsis

Also I´m not to confident what the constraint should look like.

I know how to use the lagrange multiplier by hand and can apply that inside maple, however I would like to use this opportunity to get to know the power of maple functionality more in detail.

https://i.gyazo.com/9d9585ddb8eb719d2a5bd24a1ba1671b.png

The link provoided is an image of the hexagon, i didnt find out how to use image tags.

how to configure maple to show every steps it run when solve a equation or system?

if so,

can i run the steps again and return the same result as a solve function do?

solve Derivative in maple

see in photo

 

Hello! 

I want to generate a table in maple, but with generic content. For example, in Mathematica you can do this using 

table=Table[0,{n=10},{m=2}];
 

and this generates a table with 2 columns and 10 rows with zeros in all its elements. I want to do this exactly but in maple. 

Thanks for your time! 

O(t) = 9.2-[(8.93*35.3)/(11.17-8.93)]*(exp(-8.93*t)-exp(-11.17*t))-8.3*exp(-11.17*t)

t betwen 0 and 1

I'd like to bring up all the Maple 2016 applications from the application center.

How do I do that?

Dear all,

I would like to ask you to help me with the following problem that I got error.

Thanks in advance

 

restart; Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot);
with(plots);
N1 := 1; N3 := .5; N2 := 5; Bt := 6; AA := N1*Bt; gamma1 := .2; blt1 := 1;
FNS := {f(eta), fp(eta), fpp(eta), g(eta), gp(eta), h(eta), hp(eta), i(eta), ip(eta), fppp(eta)};
ODE := {diff(f(eta), eta) = fp(eta), diff(fp(eta), eta) = fpp(eta), diff(fpp(eta), eta) = fppp(eta), diff(g(eta), eta) = gp(eta), diff(gp(eta), eta) = N1*(2*g(eta)+eta*gp(eta)+2*g(eta)*fp(eta)-2*f(eta)*gp(eta)+2*N2*N3*(h(eta)*ip(eta)-i(eta)*hp(eta))), diff(h(eta), eta) = hp(eta), diff(hp(eta), eta) = AA*(h(eta)+eta*hp(eta)-2*f(eta)*hp(eta)+2*h(eta)*fp(eta)), diff(i(eta), eta) = ip(eta), diff(ip(eta), eta) = AA*(2*i(eta)+eta*ip(eta)-2*f(eta)*ip(eta)+2*N2*h(eta)*gp(eta)/N3), diff(fppp(eta), eta) = N1*(3*fpp(eta)+(eta-2*f(eta))*fppp(eta)-(2*N2*N2)*(diff(hp(eta), eta)))};
IC := {f(0) = 0, fp(0) = gamma1*fpp(0), g(0) = 1+gamma1*gp(0), gp(0) = beta, h(0) = 0, hp(0) = beta1, i(0) = 0, ip(0) = beta2, fppp(0) = alpha};
BC1 := {f(blt1) = .5, fp(blt1) = gamma1*fpp(blt1), g(blt1) = gamma1*gp(blt1), h(blt1) = 1, i(blt1) = 1};
infolevel[shoot] := 1;
S := shoot(ODE, IC, BC1, FNS, [alpha = .1, beta = .2, beta1 = .3, beta2 = .4], maxfun = 50000);
 

hi

please help me for fsolve algebric equations...

thanks

AGM.mw
 

restart:

F(eta):=sum(a[i]*eta^i,i=0..5):

theta(eta):=sum(b[i]*eta^i,i=0..5):K(eta):=sum(c[i]*eta^i,i=0..5):Omega(eta):=sum(d[i]*eta^i,i=0..5):

``

U1:=diff(theta(eta), eta, eta)-3*Omega(eta)*(F(eta)*(diff(theta(eta), eta))-theta(eta)*(diff(F(eta), eta)))/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(theta(eta), eta)) = 0:U2:= diff(F(eta), eta, eta, eta)+Omega(eta)*(3*F(eta)*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2)/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(F(eta), eta, eta))+Omega(eta)/K(eta) = 0:U3:= diff(K(eta), eta, eta)+Omega(eta)*(1.5*F(eta)*(diff(K(eta), eta))-K(eta)*(diff(F(eta), eta)))/K(eta)+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(K(eta), eta))+(diff(F(eta), eta, eta))^2-Omega(eta)^2 = 0:U4:= diff(Omega(eta), eta, eta)+Omega(eta)*(3*F(eta)*(diff(Omega(eta), eta))+Omega(eta)*(diff(F(eta), eta)))/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(Omega(eta), eta))+Omega(eta)*(diff(F(eta), eta, eta))^2/K(eta)-Omega(eta)^3/K(eta) = 0:

F(eta):=unapply(F(eta),eta):

theta(eta):=unapply(theta(eta),eta):K(eta):=unapply(K(eta),eta):Omega(eta):=unapply(Omega(eta),eta):

U1:=unapply(U1,eta):U2:=unapply(U2,eta):U3:=unapply(U3,eta):U4:=unapply(U4,eta):

 

s1:=F(eta)(0) = 0:

s2:=K(eta)(0) = 0:s3:=Omega(eta)(0) = 0:s4:=theta(eta)(0) = 1:s5:=theta(eta)(1) = 0:s6:=(D(F(eta)))(0) = 0:s7:=(D(K(eta)))(1) = 0:s8:=(D(Omega(eta)))(1) = 0:s9:=((D@@2)(F(eta)))(1) = 0

20*a[5]+12*a[4]+6*a[3]+2*a[2] = 0

(1)

s10:=U1(0):s11:=U2(0):s12:=U3(0):s13:=U4(0):        s14:=U1(1):s15:=U2(1):s16:=U3(1):s17:=U4(1):    s18:=D(U1)(0):s19:=D(U2)(0):s20:=D(U3)(0):s21:=D(U4)(0):     s22:=D(U1)(1):s23:=D(U2)(1):s24:=D(U3)(1):

 

 

Q:=fsolve([s1,s2,s3,s4,s5,s6,s7,s8,s9,s10,s11,s12,s13,s14,s15,s16,s17,s18,s19,s20,s21,s22,s23,s24],{a[0],a[1],a[2],a[3],a[4],a[5],b[0],b[1],b[2],b[3],b[4],b[5],c[0],c[1],c[2],c[3],c[4],c[5],d[0],d[1],d[2],d[3],d[4],d[5]}):

F(eta):=eval(sum(a[i]*eta^i,i=0..5),Q):

Error, invalid input: eval received S, which is not valid for its 2nd argument, eqns

 

theta(eta):=eval(sum(b[i]*eta^i,i=0..5),Q):K(eta):=eval(sum(c[i]*eta^i,i=0..5),Q):Omega(eta):=eval(sum(d[i]*eta^i,i=0..5),Q):

Error, invalid input: eval received S, which is not valid for its 2nd argument, eqns

 

plot(g(x),x=0..1,axes=boxed,color=green,thickness=2,labels=[x,g]):

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

plot(f(x),x=0..1,axes=boxed,color=blue,thickness=2,labels=[x,f]):

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

 


 

Download AGM.mw

 

I consider  100 .100 real matrices A,B=Matrix(100,100,(i,j)->rand()) (with 12 significant digits).  In general, ConditionNumber(A) is <10^5; also I choose Digits:=17.Theoretically, the complexity of the calculations of Determinant(A), CharacteristicPolynomial(A,x), A.B and MatrixInverse(A) are similar (~n^3). Yet, the times of these calculations are respectively: 0"13, 0"67, 0"60 and, what surprises me, 75" (moreover, I don't display any result).

My question: concerning the calculation of the inverse, where does this factor 100 come from ? Would Matlab  be 100 times faster ? I do not see why this would be the case; in particular, the standard methods for the calculation of the inverse are  easily programmable.

Thanks in advance.

 


 

T := proc (t) options operator, arrow; 80+(-1)*1.4375*53*(1-exp((-1)*0.13775e-1*2.875*k*h__1*h__2*t/(1.4375^2*4190*(k*(h__1+h__2)+0.1e-2*h__1*h__2))))/2.875 end proc

proc (t) options operator, arrow; 80+(-1)*1.4375*53*(1-exp((-1)*0.13775e-1*2.875*k*h__1*h__2*t/((1.4375^2*4190*(k*(h__1+h__2)+0.1e-2*h__1*h__2)))))/2.875 end proc

(1)

T(204.39)

53.50000000+26.50000000*exp(-8.094482719*k*h__1*h__2/(8658.242188*k*(h__1+h__2)+8.658242188*h__1*h__2))

(2)

T(429.63)

53.50000000+26.50000000*exp(-17.01469059*k*h__1*h__2/(8658.242188*k*(h__1+h__2)+8.658242188*h__1*h__2))

(3)

T(872.5)

53.50000000+26.50000000*exp(-34.55372656*k*h__1*h__2/(8658.242188*k*(h__1+h__2)+8.658242188*h__1*h__2))

(4)

fsolve({53.50000000+26.50000000*exp(-34.55372656*k*h__1*h__2/(8658.242188*k*(h__1+h__2)+8.658242188*h__1*h__2)) = 56.15, 53.50000000+26.50000000*exp(-17.01469059*k*h__1*h__2/(8658.242188*k*(h__1+h__2)+8.658242188*h__1*h__2)) = 64.1, 53.50000000+26.50000000*exp(-8.094482719*k*h__1*h__2/(8658.242188*k*(h__1+h__2)+8.658242188*h__1*h__2)) = 72.05}, {h__1 = 0 .. 1000, h__2 = 0 .. 1000, k = 0 .. 1000})

fsolve({53.50000000+26.50000000*exp(-34.55372656*k*h__1*h__2/(8658.242188*k*(h__1+h__2)+8.658242188*h__1*h__2)) = 56.15, 53.50000000+26.50000000*exp(-17.01469059*k*h__1*h__2/(8658.242188*k*(h__1+h__2)+8.658242188*h__1*h__2)) = 64.1, 53.50000000+26.50000000*exp(-8.094482719*k*h__1*h__2/(8658.242188*k*(h__1+h__2)+8.658242188*h__1*h__2)) = 72.05}, {h__1, h__2, k}, {h__1 = 0 .. 1000, h__2 = 0 .. 1000, k = 0 .. 1000})

(5)

``

it would be great if you could explain me why maple cant numerically solve this set of 3 ecuatios for h1, h2, k being my unknows terms, it works with an exponential function. there is a way to solve it?

thanks..
 

Download heat_ecuation.mw

I have code 
with(plots);

implicitplot3d((r*sin(theta)*cos(phi))^2+(r*sin(theta)*sin(phi))^2+(r*cos(theta))^2=36,r=-3..3, phi=0..2*Pi,theta=0..Pi,coords=spherical);

How can I fix the code to display the picture

How to plot f(x)=x in the interval -2<x<2 with a period 4?

The plot should look like this

Hello,
How do i generate 4d plot of f(x,y,z)=1 is it possible made it in 3d?

So I am trying to find the structure of a material from x-ray diffraction data. To accomplish this I have to solve a system of nonlinear equations. Since there is some unaccuracy in the measurements I wanted to use a numerical tool, so I am trying to solve using fsolve. To check that I am doing this correctly I am trying to solve a set of similar equations where I know the solution. My code is shown below.

eqs := {(2^2/a^2+2^2/c^2-2*(2*2)*cos(x)/(a*c))/sin(x)^2 = 1/2.2393^2, (2^2/a^2+4^2/c^2+4*(2*2)*cos(x)/(a*c))/sin(x)^2 = 1/1.5968^2, (1^2/a^2+sin(x)^2/b^2+2^2/c^2+(2*2)*cos(x)/(a*c))/sin(x)^2 = 1/2.7896^2, 1/sin(x)^2*(2^2*sin(x)^2/b^2) = 1/2.8650^2}

fsolve(eqs)

For this system I know that a = 5.44 b = 5.73 c = 7.89 x=pi/2, but fsolve only returns the input.

Am I doing something wrong or should I use a different function? I am quite new to Maple, so have some patience with me.

Thanks in advance.

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