Hello,

I was wondering why there is difference in computer speed between two almost the same calculations.

Example:

61! + 1 costs 271 sec and 59! + 1 almost 0? Why is that? When there are small prime factors, the

calculation goes often faster, why? hanks in advance!

Dears,

I would like to draw a spectrum of plots. For example sin(mx) when m ∈ [1,2] and x ∈ [0,2] that is a spectrum of sinous plots. Obviously, if I write

plot(sin(m*x), m = 1 .. 2, x = 0 .. 2)

I will receive the error

Warning, expecting only range variable m in expression sin(m*x) to be plotted but found name x

I expect that there exist an alternative plot command in Maple, able to do that. I checked some members of Plots family that their name conducted me to check them. Moreover, I searched the web: but the most common retrieved results are related to drawing the area between two plots or under one plot.

A real example of what I am looking for is (not exaclty but something like) the below picure

Could you please let me know the alternative plot command, satisfying my requirement?

i am new on maple while usig maple i have to substitute a general value in an equation but could not do it like

> restart;
> taylor(f(x), x = gamma);

i typed this and want to replace x-gamma with e[n] which is easy and i did it but whn i want to substitute D(f)(gamma),(D@@2)(f)(gamma) and so on by (D@@k)(f)(gamma)=k!*c[k]*f(gamma) then i could not understand how can i do 2nd part 
pls help in this i m very thanlful to you

Hello!

I'd like to define a function after loading the Units package. But when using the defined function, Maple displays "Units:Standard-" everywhere. Even in labels of plots. I'd like to avoid that. A sample file is attached. Is there a better way of doing it?

Thanks.

Bruno

Test.mw

Hello, I am beginner with Maple 18, started recently, so I have some silly questions. I'm training the algebra study in Maple and got a list of exercises on the Internet, where they were asked to Prove it {5, 15, 25, 45, 55, 65} is a group with mod multiplication operation 90. If so, calculate the identity element and inverse of any element.

group.mw

Dear Maple users

Physical experiment: I dropped a ball with low mass from a height of approximately 7 meters and wanted to test if the air resistance was proportional to the square of the velocity. I filmed the fall and used the program Logger Pro to collect data: a number of datapoints (time,height) was collected. I copy/pasted the datapoints into MS Excel, from where I could import data into Maple via Tools > Assistants > Import Data ... Then I wanted to make a fit with the theoretical solution, given by a function having just one parameter: the Drag coefficient. Unfortunately I received an error "complex values encountered" (see below). I can solve the problem manual by making a number of guesses for the drag coefficient, until the theoretical curve approximates the data points well. I wanted to make Maple do the fitting job, though. I will appreciate if someone could give an idea how to fit the data properly.

NB! Mass m and g is defined above in the Maple document. The Statistics and plots package is called too.

Suppose we have a differential equation that it's order is 2. For example

diff(x(t), t, t)+(1000*(x(t)^2-1))*(diff(x(t), t))+x(t) = 0,

and we want to solve it numerically. When we use some initial values and dsolve it, the maple solves it very quickly. We can plot each new equations of x(t) without any problem respect of "t" or else.

But when we want to show the variation of "diff(x(t), t, t)" respect of "t" (when our derivation order is equal or upper than our differential equation order) our answer is 0 however dx(t)/dt is not 0 or constant!

What's happen here?

I tested it with all kind of methods as "rkf45","rosenbrock","lsode" etc.  but non of them showed me a correct answer.

How can I solve it correctly?
 
  
Please help me!

Hi all

How I use "solve" or "fsolve" for this equation ?

M2 := evalf[4](Matrix(4, 4, {(1, 1) = BesselJ(0, 0.5e-1*sqrt(0.1111111111e-16*omega^2-25.00027778)), (1, 2) = -BesselJ(0, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25)), (1, 3) = -BesselY(0, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25)), (1, 4) = 0, (2, 1) = (0.1111111111e-16*I)*omega*(1-25000000000000/omega^2)*BesselJ(1, 0.5e-1*sqrt(0.1111111111e-16*omega^2-25.00027778))/sqrt(0.1111111111e-16*omega^2-25.00027778), (2, 2) = -(0.4444444444e-16*I)*BesselJ(1, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (2, 3) = (0.4444444444e-16*I)*BesselY(1, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (2, 4) = 0, (3, 1) = 0, (3, 2) = BesselJ(0, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25)), (3, 3) = BesselY(0, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25)), (3, 4) = -BesselY(0, 0.60e-1*sqrt(0.1111111111e-16*omega^2-25)), (4, 1) = 0, (4, 2) = (0.4444444444e-16*I)*BesselJ(1, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (4, 3) = (0.4444444444e-16*I)*BesselY(1, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (4, 4) = -(0.1111111111e-16*I)*omega*BesselY(1, 0.60e-1*sqrt(0.1111111111e-16*omega^2-25))/sqrt(0.1111111111e-16*omega^2-25)})):

with(LinearAlgebra):
DETM2 := Determinant(M2):
solve(DETM2 = 0, omega);

Error, (in solve) cannot solve for an unknown function with other operations in its arguments

Is this Error because of combination of bessel functions? if I use asymptatic forms, does it work?

Thanks

Dear all;

Thanks in advance for helping me to plot the solution of this second order ode.

with(plots):
ode := diff(y(x), x, x) = x*y(x)+x^(17/12);
ics := y(1000) = 0, y(1001) = 1;
 dsolve({ics,ode}):

How can I plot the solution obtained in the range (1000, 1001).

Thanks

How to produce such a plot with Maple?


The difficulty is that the geom3d package does not include a command for a cylinder whereas
the plottools package has the cylinder command, but does not have a tool to determine whether
two random cylinders intersect.

I would like to plot the following singular double integral, but I cannot due to singularities...

where x>0, t=0.2 and m=0.2.

I defined f(y) function as f:=y->exp(-(y-4.68)^2/0.4):

I attached my file:
1st_try.mw

Thank you !

There is an error in my implementation as follow:

"Error, (in unknown) incorrect syntax in parse: `*` unexpected (near 1st character of parsed string)"

What I have to do to remove this error?

Hi, 

I have to plot in 2 different ways an ellipse that has been rotated in a plane. The equation of the ellipse is 

3x^2 - 3xy + 6y^2 -6x +7y =9

First of all I use the implicitplot which works great: 

restart;
f:=(x,y)->3*x^2-3*x*y+6*y^2-6*x+7*y-9;
with(plots):
implicitplot(f(x,y),x=-10..10,y=-10..10,numpoints=50000,scaling=constrained);

For the second method I really am not sure if what I'm doing is good. I tried with the plot3d, but it gave me some sort of weird shape, I really don't think it is what I am looking for. 

restart;
f:=(x,y)->3*x^2-3*x*y+6*y^2-6*x+7*y-9;
with(plots):
plot3d(f(x,y),x=-10..10,y=-10..10);

The I tried to reduce the equation to the form x^2/a^2 + y^2/b^2 = 1, but I could not, maybe because of the rotation. Still, I tried to take the ellipse function from Maple with some empirical numbers I just tried to create an ellipse looking like the first one. 

restart;
with(plottools):
with(plots):
a:=2.29:b:=1.38:x0:=0.8:y0:=-0.5:
elli:=ellipse([x0,y0],a,b,color=blue):
display(rotate(elli,0.4),scaling=constrained);
This time I get an ellipse similar to the first, but I don't really think it is legit to do it that way, in a sort of trial-and-error.

So I was wondering if there was another way like implicitplot to create the graph of that ellipse. 

This is the code hw2_final.mw

This is the warning 

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters )"

How to solve it?

Hello everyone,

I am trying to extract the coefficients from a differential poynomial. In general, this poynomial is in two variables, say u and v along with their differentials, i.e D(u) or D@@2(u) or so on. 

Coefficients of this polynomials are rational funcitons.

For instance- consider the following example:

a(x)*v*u+v*D(u)-D(v)*u

then output should be [a(x), 1, -1].

Thanks for your help.