I would like to find the derivative for f(x)=min(x^2 +1, 2x+3) and plot f(x) and its derivative on the same graph. I know the "diff" command works on functions, but I'm not sure how to use it on this one. Suggestions would be appreciated. Thanks!

It seems Maple has no Clear(variable); function build in, and one must type

         variable := 'variable`; 

for each variable to be cleared. This is a little too verbose. In Mathematica one types "Clear[variable1,variable2]" which requires much less typing than the Maple way of doing it. (About 1/2 as much, if one has to clear few variables each time).

Doing restart is not a good solution all the time, since that will clear everything.

Strange why Maple can not provide such a function, and inside it, it can do these calls.

So, I was wondering if someone has written such a function. I can try to write one myself, but I am not very good in Maple, and I think a professionally written one by an expert would be more robust and will do more checking as needed to make sure it works correctly.

So, my question is, why Maple does not provide such a function as build-in? And does one know of a good implementation of one that exist?

Fail to do Volume of Revolution when rotate in y-axis by using student calculus 1 packege.

It is good in any x-axis thorugh.

the erorr looks like this, I follow the direction on Maple website and enter axis = vertical, but it give me something like this.

I type vertical := x = 0 somewhere, I was wondering the Maple think vertical = x = 0, so O change the
vertical := x = 0 to v := x = 0(like first image), but after I run the whole thing it still give me same error.

The weirdest part is I actually run the second one scuccess first time, but second time it failed and I don't know why. I input exactly samething but it failed, weird!!

How do you express sin(4x)^2 in terms of powers of cos(x) in Maple 17?

Different evalf results.

evalf(3/Pi);
                         .9549296583

evalf(3/Pi,1);
                         .9

evalf(3/Pi,2);
                         .96

evalf(3/Pi,3);
                          .954

evalf(.9549296583,1)
                                    1.

evalf(.9549296583,2)
                                    0.95

evalf(.9549296583,3)
                                    0.955

This is probably a floating point issue but shouldn't the results be the same?

q[1] = sqrt(x)*alpha-lambda(sqrt(x)*alpha-lambda*q[1]*q[3]-p[2])*(sqrt(x)*alpha-lambda*q[1]*q[2]-p[3])-p[1]

I am looking for q[1] solution. When I solve for q[1], maple gives me following answer:

q[1] = RootOf(-_Z+sqrt(x)*alpha-lambda(sqrt(x)*alpha-lambda*_Z*q[3]-p[2])*sqrt(x)*alpha+lambda(sqrt(x)*alpha-lambda*_Z*q[3]-p[2])*lambda*_Z*q[2]+lambda(sqrt(x)*alpha-lambda*_Z*q[3]-p[2])*p[3]-p[1])

Is it possible to obtain a classical solution for the calculations above. (can not understand the meaning of: RootOf and _Z. I need q[1] in order to solve further in my system of eqautions for  q[2],  q[3]

could you help me please to find a solution for this issue...
I would like to thank you in advance 
Best regards,

D.L.

Hi folks,

from an experiment I gathered some data which I am now trying to display in a nice plot. The data contains x and y values (as well as errors for the y values, that are not part of my problem however). It appears that 'ErrorPlot' (Statistics package) seems to be the tool to use in my case, however I am not able to figure out how to assign the x values to the y values. By default Maple uses positive integers as the x values for any input set. Let's say my data is

x:=[1,5,8,9,10,15]

y:=[4,3,2,8,9,9] (with errors yr:=[0.5,0.5,0.5,0.5,0.5,0.5])

then, now matter how I try, the x values assigned are always 1,2,3,.. . Doing sth. like

> ErrorPlot([x,y]);

displays the sets of x and y each being assigned to integers rather than plotting y over x.
Can anybody help me with this issue?

tl;dr

How do I assign individual x values for my set of data using 'ErrorPlot' (from the Statistics pkg)?

Thank you very much!

Greets,
mulo

hello

how can i solve a nonlinear integral equation with maple?

thanks

Hi 

Fairly new to Maple and having trouble with the result displayed when using exponential functions. 

So I have the following function h(r), in which f1 - f5 are unknown constants that are to be calculated. [I am attempting to set up the equations needed to do so]:

h := r → exp(f1 + f2r + f3r² + f4r³ + f5r⁴ + f6r⁵)

Firstly, I need to evaluate h(r) at the point A. But, on entering the evaluate command, the general expression for h is re-produced:

A := 0.2

evalf(h(A)) 

exp(f6r^5+f5r^4+f4r^3+f3r^2+f1+f2r)

Further, I need to take the natural logarithm of h(A), which produces:

evalf(ln(h(A))

ln(exp(f6r^5+f5r^4+f4r^3+f3r^2+f1+f2r))

How do I get Maple to output the actual result of the substitution of r=A and the logarithm?

i.e. how do I get maple to display:

f1 + 0.2f2 + 0.04f3 + 0.008f4 + 0.0016f5 + 0.00032f6

Apologies if this is a very basic question. 

Cheers

((-1+lambda(lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))^2)*k[1](lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))+(-lambda*lambda(lambda*alpha[1]*k[1]+alpha[2](k[1]*lambda^2-2*k[1]-2))^2+lambda)*k[2](lambda*alpha[1]*k[1]+alpha[2](k[1]*lambda^2-2*k[1]-2))-k[1]*(-alpha[1]+lambda*alpha[2])*lambda(2+5*k[2])^2+lambda^5*alpha[2]*k[1]*k[2]-alpha[1]*k[1]*lambda^4*k[2]-2*lambda^3*alpha[2]*k[2]+2*alpha[1]*k[2]*lambda^2+(4*alpha[2]*(1+k[2])*k[1]+4*alpha[2]+4*k[2]*alpha[2]+2)*lambda-4*alpha[1]*(1+k[2])*k[1]-4*alpha[1]-4*alpha[1]*k[2]-2)*(-(lambda(lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))-1)*(lambda(lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))+1)*(-1+k[1]*lambda^2-k[1])*k[1](lambda*k[2]*alpha[2]+alpha[1](k[2]*lambda^2-2*k[2]-2))+(-lambda*lambda(lambda*alpha[1]*k[1]+alpha[2](k[1]*lambda^2-2*k[1]-2))^2+lambda)*k[2](lambda*alpha[1]*k[1]+alpha[2](k[1]*lambda^2-2*k[1]-2))-k[1]*(-alpha[1]+lambda*alpha[2])*lambda(2+5*k[2])^2+lambda^5*alpha[2]*k[1]*k[2]-alpha[1]*k[1]*lambda^4*k[2]-2*lambda^3*alpha[2]*k[2]+(2*k[1]+2*alpha[1]*k[2])*lambda^2+(4*alpha[2]*(1+k[2])*k[1]+4*alpha[2]+4*k[2]*alpha[2]+2)*lambda-(4*(1+k[1]))*(alpha[1]+alpha[1]*k[2]+1/2))*x

I am looking to simplify this long term...

could you help me please to find a solution for this issue...

I would like to thank you in advance

Best regards,

D.L.

Good afternoon sir.

I request your kind suggestion to the above cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

Hi,

I am doing calculation with binomial numbers with some parameters. Usually the result is correct, but this time a strange notation "table" appears. I do not know how does this happen?

Thank you!

Yan

Hi,

1-Triying to plot a function divided by its maximum value,sometimes it works with some parameters that means, the max.value of the plot is 1.

But when i change the data the max. value in the plot in graeter than 1 which is wrong!! should be 1.

dont know why??

2- Changing different data in the parameters, the programme takes long long time then i stop it?

please help me with these two problems.

restart:
>
------------------------- Defining the nature of the variables used ----------------------
assume(T,real):Digits:=25:n:=1:tau:=Pi:
theta:=0:phi:=0:
lambda:=n;Omega:=1:Gamma:=0.01:
--------------------- Input---------------------------------
1

J1

term1:=(exp((Gamma+I*d)*tau)-1)/(2*(Gamma+I*d)):
Ak1:=d->(exp((Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))+(exp((Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma)):
Ak2:=d->(exp((Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))+(exp((Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma)):
term2:=(evalf(-0.25*sum(BesselJ(k,Omega*Gamma/(4*n))*Ak1(d)+BesselJ(k,-(Omega*Gamma)/(4*n))*Ak2(d),k=0..50))):
J1:=(term1+term2):
J1mod:=(Re(J1))^2+(Im(J1))^2:
###### J2#########################
Ak1:=d->(exp((Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))-(exp((Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma)):
Ak2:=d->(exp((Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))-(exp((Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma)):

J2:=(evalf(-0.25*sum(BesselJ(k,Omega*Gamma/(4*n))*Ak1(d)+BesselJ(k,-Omega*Gamma/(4*n))*Ak2(d),k=0..100))):
######################

J2mod:=(Re(J2))^2+(Im(J2))^2:
J3 same as J1differ in sign
term1:=(exp((Gamma+I*d)*tau)-1)/(2*(Gamma+I*d)):
Ak1:=d->(exp((Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega-2*lambda*k/Gamma))+(exp((Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega+2*lambda*k/Gamma)):
Ak2:=d->(exp((Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d-0.5*Omega-2*lambda*k/Gamma))+(exp((Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma))*tau)-1)/(Gamma+I*(d+0.5*Omega+2*lambda*k/Gamma)):
term2:=(evalf(0.25*sum(BesselJ(k,Omega*Gamma/(4*n))*Ak1(d)+BesselJ(k,-Omega*Gamma/(4*n))*Ak2(d),k=0..100))):
J3:=term1+term2:
J3mod:=(Re(J3))^2+(Im(J3))^2:
J4 same as J2 but -0.25-->2

J4:=-2*J2:
######################

J4mod:=(Re(J4))^2+(Im(J4))^2:

calculate the spectrum

Spec:=d->(exp(-2*Gamma*tau)*(J1mod*cos(theta/2)^2+J2mod+J3mod*sin(theta/2)^2-0.5*Re(J3*J4*sin(theta)*exp(I*phi))+0.5*Re(J1*J4*sin(theta)*exp(-I*phi)))):

with(plots):

tit:=sprintf("l=%g,W=%g,G=%g",lambda,Omega,Gamma):
Smax1:=max(seq(evalf(Spec(d)),d=-100..100)):
plot(evalf(Spec(d)/Smax1),d=-15..15,axes=boxed,title=tit,color=black,font=[2,3,18],thickness=2,tickmarks=[3,3],titlefont=[SYMBOL,14],font=[1,1,18],linestyle=1);

I have a multivariate polynomial P (written with the order "tdeg")in the (x_i)_i ; the coefficients are functions of the (a_i)_i. I'd want the set of the monomials that appear in the development of P. For instance P=a_1xy^2z^3+a_2x^4yz^2+a_3 is associated to {xy^2z^3,x^4yz^2,1}. Does there exist a command to do that ?

In a second time, I'd want the coefficients of {xy^2z^3,x^4yz^2,1} in the same order. Does there exist a command to do that ?

Thanks in advance.

Suppose one sets a system of differental equations in vector form, say 2 ODE's, like this:

restart;
with(LinearAlgebra):
ode:=Vector([diff(x(t),t),diff(y(t),t)])=Vector([2*x(t)+y(t),3*y(t)-x(t)]);

Then to solve these, what would be an easy way to do it, without having to rewrite them again manually as a set, as what one would normally do. Clearly one needs to map dsolve, and also convert the vectors to a set somewhere? I am not able to get the syntax right.

Is there an easy way to automatically convert/rewrite the above to

ode2:= diff(x(t),t)=2*x(t)+y(t)  ,   diff(y(t),t)=3*y(t)-x(t);

so that I can just do

dsolve({ode2},{x(t),y(t)});

Or, a way to map dsolve directly into the first from as shown?( the Vector = Vector form).