Hey there!

this is the formula:

diff(ca(t), t) = -3.600000000*10^20*exp(-15098.13790/(340-20*ca(t)))*ca(t), ca(0) = 2

I can easily plot it by solving DE numerically, however I can't seem to find a way to determine what 't' is at ca(t)=0.2

thank you so much in advance!

Kind regards, 

Gerard 

Download 2222222222222222222.mw

> restart; 
> A[0] := 10^(-3); a := 10^5;
> sys := diff(R(theta), theta) = A[0]*exp(2*mu(theta))*sin(theta)/(2*a), R(theta) = 2*exp(-2*mu(theta))*(1-(diff(mu(theta), `$`(theta, 2)))-cot(theta)*(diff(mu(theta), theta)));
> cond := R(0) = 10^(-5), mu(0) = 118.92, (D(mu))(0) = 0;
> F := dsolve({cond, sys}, [R(theta), mu(theta)], numeric);
> with(plots);
> odeplot(F, [theta, R(theta)], 0 .. 3.14, color = black, thickness = 3, linestyle = 4)
> odeplot(F, [theta, mu(theta)], 0 .. 3.14, color = blue, thickness = 3, linestyle = 1)

After last two lines maple writes:

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

And gives me empty plots. I can't figure out where an error can be. Some things I noticed:

Maple doesn't calculate the system before and after zero. If I change the range from 0..3.14 to -10..10 or to 0.00001..0.00001, it gives me 2 errors for 1 plot.

Also if I change the condition mu(0) = 118.92 to mu(0) = 1 or mu(0) = 50 or mu(0) = 80, it works. After ~80 it gives an error. I can't imagine where could appear a division by 0 or some other mistake.

Hello People in mapleprimes,

I have a question about collecting part of expression.
Please teach me an answer to this.

I want to modify a1 to b1.


e3.mw

Thanks in advance.

Dears,

I have a question and I hope someone will be able to answer it.

I would like to create a matrix of functions depending on the number of the line or the arrow. I think the best is to show with a very basic example:

I have the following program

n:=4:

R:=Matrix(1,n):

for i from 1 to n do: R(1,i):=x->i*x:end do:

So, I have a matrix, one row, n columns. At the ith column, I want to have the function f(x)=i*x.

Unfortutanely, with my program, I obtain for example for the first column the function f(x)=11*x. At the second column, I get the same result. It seems that I can define matrices of functions but it is impossible in the definition of the function to use the number of the column. Do you have any idea about how to write a program?

Any help would be very appreciated. 

For a 2D parametric plot with only one parameter, in Maple we use plot([x,y,range]) but what about the case x and y are expressed by more than one parameter? How should I assign the range? For example I tried the following one

h := k[1]*k[3]+k[1]*k[4]+k[2]*k[4]:
x := k[2]/h:
y := (k[3]+k[4])/h:
A := seq(k[i] = 1 .. 2, i = 1 .. 4):
plot([x, y, A]);

But then I encountered the following error:
Error, (in plot) incorrect first argument [k[2]/(k[1]*k[3]+k[1]*k[4]+k[2]*k[4]), (k[3]+k[4])/(k[1]*k[3]+k[1]*k[4]+k[2]*k[4]), k[1] = 0.1e-2 .. 1000, k[2] = 0.1e-2 .. 1000, k[3] = 0.1e-2 .. 1000, k[4] = 0.1e-2 .. 1000]

For one parameter the above method doesn't make an error like the following:

x := t+1:
y := t^2:
A := t = 1 .. 2:
plot([x, y, A]);

So for more than one parameter, there should be another way to ask the plot. Does anyone know how to do that?

I want to plot a simple power function in diferent pieces by using diferent range and  for different values of parameter a[i] at i=0,1,2 define in the attached sheet.

plot_at_different_intervals.mw

Given a list L of n^2 integers, I can fill an nxn matrix through Matrix(n,n,L).  for instance:
n := 4:
L := [$1..n^2]:
A := Matrix(n,n, L);

I don't know how to do this with a 0-based Array.  I wished that as in the case of the Matrix, the command
B := Array(0..n-1, 0..n-1, L);
would assign B[0,0]=1, B[0,1]=2, ..., B[3,3]=16, but it doesn't.

I know how to fill B's entries through doubly nested for-loops but I suspect that there might be a clever way of doing that. If so, then please show me how.

I wonder if there is a way to represent each piece of a piecewise function in Maple.

For example, for a piecewise function: f:=x->piecewise(1<=x<=2,c[1]*x+c[2],2<=x<=3,c[3]*x+c[4],3<=x<=4,c[5]*x+c[6]);

I want to have a way to retrieve each piece, e.g.: c[3]*x+c[4], but f(x)[2] doesn't work.

Is it archievable?

On Y axis: (Each set represents a car and each set has 10 values for different position of same car)

[[761, 768, 776, 784, 793, 803, 813, 823, 833, 842], [723, 725, 728, 731, 734, 738, 743, 749, 756, 764], [516, 516, 516, 517, 519, 522, 526, 531, 536, 541], [382, 384, 386, 389, 393, 398, 404, 411, 419, 427], [78, 86, 95, 105, 115, 125, 135, 144, 154, 164], [751, 760, 770, 780, 790, 799, 809, 819, 829, 839], [773, 783, 793, 803, 812, 822, 831, 840, 850, 859], [160, 170, 180, 189, 199, 209, 219, 229, 239, 249],.....]

On X axis: (time for 1 to 10)

[1,2,3,4,5,6,7,8,9,10] for each of above sets. 

In each set for example, 1 corresponds to 761, 2 to 768 and so on until 10 to 842, then onto next set. The number of sets I will generate can be between 50-500. And I need to have all of the same graph. This data will tell me under the conditions I set how one car's position effects other cars. 

I also have relative velocity values in same format:

[[7, 7, 8, 8, 9, 10, 10, 10, 10, 9], [1, 2, 3, 3, 3, 4, 5, 6, 7, 8], [0, 0, 0, 1, 2, 3, 4, 5, 5, 5], [1, 2, 2, 3, 4, 5, 6, 7, 8, 8], [8, 8, 9, 10, 10, 10, 10, 9, 10, 10], [8, 9, 10, 10, 10, 9, 10, 10, 10, 10], [10, 10, 10, 10, 9, 10, 9, 9, 10, 9], [9, 10, 10, 9, 10, 10, 10, 10, 10, 10], [8, 8, 9, 9, 9, 10, 9, 9, 9, 9], [8, 9, 10, 9, 10, 9, 10, 9, 10, 9], [9, 10, 9, 9, 10, 10, 10, 10, 10, 10], [7, 7, 8, 9, 10, 10, 9, 9, 10, 10], [10, 10, 10, 9, 9, 10, 9, 10, 10, 10],...]

I will also need to graph this. 

Please Help!
 

Hello people in mapleprimes,

Please help me with simplifying the next expression.
This e1 has the expression of ((epsilon-1)*k/epsilon)^epsilon in the numerator and the denominator. How can I collect each of them with that expression?

e1.mw

Thanks in advance.

Taro

Hello,

To check my arguments in a procedure I need something like

myproc := proc(M :: Matrix(square, rational)

                       , N :: Matrix(shape=triangular[lower, unit], datatype = rational
                       , O :: Matrix(shape = square, dimension = 5

               )

end proc;

How does that work in Maple? What is the correct Syntax? I tried many different things that doesn't fit.

Let us consider 

sol := pdsolve({diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) = (1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t}, {u(0, t) = 0, u(x, 0) = 0, v(0, t) = 0, v(x, 0) = 0}, time = t, numeric, timestep = 0.1e-1, spacestep = 0.1e-1, range = 0 .. 1); 
sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 .. 1);

A nice plot similar to the one produced by Mma (see the  attached pdf file pdesystem.pdf) is expected. 
The exact solutions u(x,t)=x*t,v(x,t)=x*t^2 are known

pdetest({u(x, t) = x*t, v(x, t) = x*t^2}, {diff(u(x, t), t)-(diff(v(x, t), x))+u(x, t)+v(x, t) =
(1+t)*x+(x-1)*t^2, diff(v(x, t), t)-(diff(u(x, t), x))+u(x, t)+v(x, t) = (1+t)*x*t+(2*x-1)*t});
                              {0}

But the wrong result

               module() ... end module         
Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.26000000000000006):
solution becomes undefined, problem may be ill posed or method may be ill suited to solution

is obtained. Also 

sol:-plot3d(v(x, t), x = 0 .. 1, t = 0 ..0.1);

The plot 

sol:-plot3d(v(x, t), x = 0 .. .5, t = 0 .. .1);

is not better.

If I calculate the integral:

z:=exp(I*t)

evalf(Int(z^(1/2)*(diff(z, t)), t = 0 .. 2*Pi))

I get -1.33333333*I

If I calculate

int(z^(1/2)*(diff(z, t)), t = 0 .. 2*Pi)

I get -4/3

so where is the I coming from? Am I doing sth  something   wrong?

I might add: if I calculate the same for z:=0.5+exp(I*t) I get 0 and -I*0.4714....

so what is going different here?

Try this command.

display(semitorus([0, 0, 0], 0 .. Pi, 1, 2), lightmodel = light4, orientation = [-140, 60], scaling = constrained, style = patchnogrid)

I get this mess. The picture on the help page doesn't look any better.Setting the range 0..2 Pi looks fine though. So I think it is a bug.

What I was trying to do is plot 3/4 of a torus i.e circle disk swept in 3/4 of a carcle with capped ends. What is a good way?

I am trying to use a do loop with if/else statements to create a 5x5 unit matrix. I made an empty array. Converted it to a matrix. Then made a do loop where I was trying to get the matrix elements where i=j to be 1 and all else to be 0. It didn't spit out a matrix.

Any advice? I assume I must have missed a small detail in syntax.

Download fail_unit_matrix_loop.mw

By the way, I am open to completely different methods, also! I was just trying to use loops to do it rather than inbuilt commands.