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Hi, 

     I'm computing a simple covariant derivative of a tensor field W[a,b] in 3 spacetime dimensions. Unfortuntly, my result in Maple 2015 is disagreeing with those obtained in GRTensorII. I think this could be a bug in D_.

Looking at the first result, W[r t ; t] = mu/r in GRTensor II  but D_[t] W[r t] = -mu/r*(cos(theta)^2 - 2). Some ones are correct (diagonals), and some are off by a factor of 2. Some are completely off though.

ErrorsInD.mw


Thanks,

Hi,

I would like to plot E2(t) , but It gives errors. How can I avoid the singularity and solve this problem?


restart: with(plots):
with(Student[NumericalAnalysis]):
g1:=(x,t)->(-sqrt(t)/(2*sqrt(Pi*r^3)))*(sin((r*(x-1)^(2)/(4*t))+(Pi/4))-sin((r*(x+1)^(2)/(4*t))+(Pi/4))):

g2:=(x,t)->int(g1(x,t),r=1..infinity);

g3:=(x,t) -> (diff(g2(x,t),t)):


g4:=(x,t) -> (diff(g2(x,t),x,x)):


g5:=(x,t) -> ((1/2)*(g3(x,t)^2+g4(x,t)^2)):


E2:=t->(int(g5(x,t),x=0..100)):

evalf(E2(0));
Error, (in g1) numeric exception: division by zero
evalf(E2(1));
Error, (in g3) invalid input: diff received 1, which is not valid for its 2nd argument
plot(E2(t),t=0..20);

Best regards,

 

I wish to evaluate the expression

knowing that

where a is a constant.  It is not hard to see, assuming enough differentiability,  that the expression evaluates to

I know how to do this when all the derivatives are expressed in terms of the diff() operator.  Here it is:

eq := diff(u(x,t),t) = a^2*diff(u(x,t),x,x);
expr := diff(u(x,t),t,t);
eval['recurse'](expr,[eq]);

However, I would prefer to do the computations when all derivatives are expressed in terms of the D operator but cannot get that to work.  What is the trick?

I googled everywhere for this and most results just tell me what diff and D does...

 

Basically I have a function, let's say

 

f:= x -> x^2

How do I turn the derivative of f into a function?

 

I tried

 

fprime := x -> diff(x^2,x)

 

But tihs just shows me diff(x^2,x), instead of x -> 2x

How to find the determining equation for a system of fractional differential equation using Maple 15?

I input:

solve({My(x, -(1/2)*b) = 0, My(x, (1/2)*b) = 0, w(x, -(1/2)*b) = 0, w(x, (1/2)*b) = 0}, {Am, Bm, Cm, Dm});

and recieved: 

Error, (in My) invalid input: diff received -1, which is not valid for its 2nd argument

 

My is 

My := proc (x, y) options operator, arrow; -((1/2)*I)*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^2*a^2)+I*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*(exp(Pi*(I*x-y)/a))^2/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^3*a^2)+I*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*(exp(Pi*(I*x+y)/a))^2/((exp(Pi*(I*x+y)/a)-1)^3*(-1+exp(Pi*(I*x-y)/a))*a^2)-I*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x+y)/a)*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))^2*a^2)+I*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*(exp(Pi*(I*x+y)/a))^2/((exp(Pi*(I*x+y)/a)-1)^3*(-1+exp(Pi*(I*x-y)/a))*a^2)-I*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x+y)/a)*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))^2*a^2)-((1/2)*I)*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x+y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))*a^2)-((1/2)*I)*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x+y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))*a^2)-I*Dm*(exp((2*I)*Pi*x/a)-1)*Pi*exp(Pi*(I*x+y)/a)/((exp(Pi*(I*x+y)/a)-1)^2*(-1+exp(Pi*(I*x-y)/a))*a)+I*Bm*(exp((2*I)*Pi*x/a)-1)*Pi^2*(exp(Pi*(I*x-y)/a))^2/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^3*a^2)+I*Dm*(exp((2*I)*Pi*x/a)-1)*Pi*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^2*a)-((1/2)*I)*Dm*y*(exp((2*I)*Pi*x/a)-1)*Pi^2*exp(Pi*(I*x-y)/a)/((exp(Pi*(I*x+y)/a)-1)*(-1+exp(Pi*(I*x-y)/a))^2*a^2)+sum(-4*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(diff(d(y), y), y))/(Pi(y)^7*m(y)^7*d(y)^2)+32*(diff(po(y), y))*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))/(Pi(y)^7*m(y)^7*d(y))-56*(diff(po(y), y))*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(Pi(y), y))/(Pi(y)^8*m(y)^7*d(y))-56*(diff(po(y), y))*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(m(y), y))/(Pi(y)^7*m(y)^8*d(y))-8*(diff(po(y), y))*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(d(y), y))/(Pi(y)^7*m(y)^7*d(y)^2)+32*po(y)*a(y)^3*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)*(diff(a(y), y))/(Pi(y)^7*m(y)^7*d(y))+16*po(y)*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(diff(a(y), y), y))/(Pi(y)^7*m(y)^7*d(y))-56*po(y)*a(y)^4*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)*(diff(Pi(y), y))/(Pi(y)^8*m(y)^7*d(y))-56*po(y)*a(y)^4*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)*(diff(m(y), y))/(Pi(y)^7*m(y)^8*d(y))-8*po(y)*a(y)^4*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)*(diff(d(y), y))/(Pi(y)^7*m(y)^7*d(y)^2)-224*po(y)*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))*(diff(Pi(y), y))/(Pi(y)^8*m(y)^7*d(y))-224*po(y)*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))*(diff(m(y), y))/(Pi(y)^7*m(y)^8*d(y))-32*po(y)*a(y)^3*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))*(diff(d(y), y))/(Pi(y)^7*m(y)^7*d(y)^2)+392*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(Pi(y), y))*(diff(m(y), y))/(Pi(y)^8*m(y)^8*d(y))+56*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(Pi(y), y))*(diff(d(y), y))/(Pi(y)^8*m(y)^7*d(y)^2)+56*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(m(y), y))*(diff(d(y), y))/(Pi(y)^7*m(y)^8*d(y)^2)+4*(diff(diff(po(y), y), y))*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)/(Pi(y)^7*m(y)^7*d(y))+8*(diff(po(y), y))*a(y)^4*(2*Pi(y)*m(y)^2*y(y)^2*(diff(Pi(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(m(y), y))+2*Pi(y)^2*m(y)^2*y(y)*(diff(y(y), y))+8*a(y)*(diff(a(y), y)))*sin(m*Pi*x/a)/(Pi(y)^7*m(y)^7*d(y))+4*po(y)*a(y)^4*(2*(diff(Pi(y), y))^2*m(y)^2*y(y)^2+8*Pi(y)*m(y)*y(y)^2*(diff(Pi(y), y))*(diff(m(y), y))+8*Pi(y)*m(y)^2*y(y)*(diff(Pi(y), y))*(diff(y(y), y))+2*Pi(y)*m(y)^2*y(y)^2*(diff(diff(Pi(y), y), y))+2*Pi(y)^2*(diff(m(y), y))^2*y(y)^2+8*Pi(y)^2*m(y)*y(y)*(diff(m(y), y))*(diff(y(y), y))+2*Pi(y)^2*m(y)*y(y)^2*(diff(diff(m(y), y), y))+2*Pi(y)^2*m(y)^2*(diff(y(y), y))^2+2*Pi(y)^2*m(y)^2*y(y)*(diff(diff(y(y), y), y))+8*(diff(a(y), y))^2+8*a(y)*(diff(diff(a(y), y), y)))*sin(m*Pi*x/a)/(Pi(y)^7*m(y)^7*d(y))-28*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(diff(m(y), y), y))/(Pi(y)^7*m(y)^8*d(y))+48*po(y)*a(y)^2*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(a(y), y))^2/(Pi(y)^7*m(y)^7*d(y))+224*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(Pi(y), y))^2/(Pi(y)^9*m(y)^7*d(y))+224*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(m(y), y))^2/(Pi(y)^7*m(y)^9*d(y))+8*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(d(y), y))^2/(Pi(y)^7*m(y)^7*d(y)^3)-28*po(y)*a(y)^4*(Pi(y)^2*m(y)^2*y(y)^2+4*a(y)^2)*sin(m*Pi*x/a)*(diff(diff(Pi(y), y), y))/(Pi(y)^8*m(y)^7*d(y)), m = 1 .. infinity) end proc;

[Lengthy, poorly formatted, and very-difficult-to-read plaintext prettyprint of the above procedure removed by a moderator.--Carl Love]

Hi, 


     I've been playing around with the Physics package, and I'm confused on evaluaing derivatives of explicit funcitons of the coordinates. This code below doesnt behave as I would think. I'm trying to define z as a function of X[mu]*X[mu], and take diff(z, X[mu]). You can see that each method d_, diff,  disagree and none are satisfactory ansers. (Maple 2015, Windows 8.1 64-bit, Intel i5 Haswell) 

# Declare coordinates for 2 dimensions, flat space

restart:
with(Physics):
Setup(mathematicalnotation = true, dimension = 2):
Coordinates(X):

# Method 1: Using Define and various differential operators
Define(z):
z :=sqrt(R^2-X[mu]*X[mu]);
d_[mu](z(X));
d_[1](z(X));
diff(z, x1);  #This one is correct
diff(z, X[mu]); # off by 2

# Method #2: Using functions
# Off by a factor of 2
z2 := mu -> sqrt(R^2-X[mu]*X[mu]);
diff(z2(mu), X[mu]); # off by 2

 PhysicsDiffBug.mw

In the following, the diff operator calcuates the derivative correctly, but the D operator doesn't.  A bug?

restart;

f := x -> a[1][2]*x;    # the double index on a[][] is intended

proc (x) options operator, arrow; a[1][2]*x end proc

 

diff(f(x), x);

a[1][2]

 

D(f)(x);

(D(f))(x)

 


Here is a worksheet containing the commands above in case you want to try it yourself: mw.mw

Hi all,

 

It's been a while since I have used Maple. To be honest I haven't used it for over six years.

 

I am trying to solve simple differential equations, however I have many issues.

 

I am trying to simulate what author of this paper did 06421188.pdf

 

My file looks like this (Pendulum.mw)

 

Can someone help me to simulate this system? I simply can't remember how to do it.

 

Cheers,

Bart

I have the following :

with(powseries):
difeq:=diff(y(x),x,x)+x*y=0;
icval:=y(0)=1,D(y)(0)=0;
pow_soln:=powsolve({difeq,icval});
tpsform(pow_soln,x,30);
pow_soln(_k);

for which the  transformed power series

is : 1 -(1/6)y*(x^3)

and pow_soln(_k) returns 0. What does this mean?

 

 

****** My question *****

for k from 0 to n do    # n is any integer.

func := f(x):             # func is any funciton of x.

D := diff(func, x$k);   # The maple don't allow to uses k but I want to diff k-th order in each k-loop.

end do;                    # How to diff func for k-th times in each k-loop.

I have a nice family of functions of the form:

W:=(p,n,mu,w)->sum(w[k] * (n-k)* mu(n-k),k=1..n)

which can be evaluated for different p's using the operator mu*diff(...,mu)

The recursion begins with p=0 and proceeds using mu*diff(W(p,n,mu,w),mu) = W(p+1,n,mu,w).

Can anybody implement this procedure in Maple

Thank you 

I've got the following piecewise function :

(x^2+y^2)^(alpha).arcsin(y/x) if (x,y) are in [-pi/2,pi/2]

0, (x,y)=(0,0)

1. How do I plot this function taking the alpha variable and the piecewise construct into account?

2. How can I check for points of discontinuity, indifferentiability from the plot/function itself?

 

 

I've got a function y(x) that is initially defined as x^3+y^3=1 and need to plot it, and find y',y''.

At present, I've used implicitplot(x^3+y^3=1,x=0..5,y=0..5) to plot it, but that doesnt seem to work. Also, to find y'

I've used the statement

implicitdiff(g(x,y),y(x),x) where g:=(x,y)->x^3+y^3=1 but this gives me an error that my input is invalid; y(x) is expected to be of the form {(name, set(name), set(function(name))}.

I don't quite understand..

I am new to Maple. I am working though the manual and in chapter two I tried to get the derivative of ln(x^2+1). I am getting something completely different that the actual derivative. I tried a simple derivatie (the derivative of 2x and get 0). I do not know what I am doing wrong. Any help will be appreciated.

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