Please help me to solve this integration

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity);

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity)

I need to show that the following expression,
a^3b-a^3c+a^3z+a^3x+a^3y-a^2bx+a^2by+a^2cx-a^2cy-a^2zx+a^2zy-a^2x^2+a^2y^2-abcz-abcx-aczx-acx^2+b^2c^2+2bc^2x+c^2x^2-b^2c-2bcx-cx^2,

is positive

given that:

1. a,b,c,x,y,z are positive real numbers

2. a>b+x

3. c<b+y

I know a priori that the expression is indeed positive, but I do not know how to show it, or how to use Maple to do it?

Specifically, how can I use Maple to **partially factorize** the expression in terms of the expressions a-b-x and c-b-y?

Thanks for any help.

I have created and saved a MAPLE module in an .mla archive. The module contains three procedures A, B, C, where

A calls, B and C.  

Once the module library has been loaded, A acccepts inputs and generates outputs.

Is it possible to create a MAPLE player worksheet which calls the module and share it with a Maple Player (only) user, so that they can then supply the inputs and observe the outputs from A using the Maple Player programme components?

Can anyone help?

MRB

I have created and saved a MAPLE module in an .mla archive. The module contains three procedures A, B, C, where

A calls, B and C.  

Once the module library has been loaded, A acccepts inputs and generates outputs.

Is it possible to create a MAPLE player worksheet which calls the module and share it with a Maple Player (only) user, so that they can then supply the inputs and observe the outputs from A using the Maple Player programme components?

Can anyone help?

MRB

For the past thirty years, I have used several mathematical packages for problem solving and graphing. It all started with spreadsheet software that really helped speedup calculations compared to calculators. As many people do, once I had one tool I then started looking for another that would offer even more capabilities and features. I tested several of the very early math software but none really did all that I wanted until I came across Maple while I was working at SPAR Aerospace in Canada. For me, the rest is history. As long as I had a copy of Maple, it was all that I needed.

On occasions when I did not have a copy of this amazing software, I resorted to spreadsheets once more to complete fairly large and complex projects involving large databases and large numbers of calculations, especially when performing What-If scenarios. One distinct disadvantage of using a spreadsheet was the cryptic form of equation writing. I had to divide one long equation into several sections in different cells and then add them all up, which clearly is not good for documentation of the calculations. It is also very confusing for other engineers to know what that equation is or what it does. The development of the full engineering spreadsheet took months to complete, debug and verify. During this process, when I had errors, it was often very difficult to track exactly where the problem was, making the debugging process time consuming and sometimes very frustrating.

Having worked with Maple before, I remembered how easy it was to enter equations in a very familiar, readable math format. The real power of this software is that it allows you to write the equation(s) anyway you like and solve for any given parameter, unlike spreadsheets where you have to solve the problem first, by hand, for the parameter you want and then get the spreadsheet to calculate the value. I remember one time a few years ago when I wrote nine or ten simultaneous differential equations all in symbolic form and asked Maple to calculate certain parameters in a fully symbolic form. To my utmost disbelief, the answer came back within few minutes. With results in hand, I was able to quickly finish my research, and the results were published at PCIM Europe 2005 in “Distributed Gate ESR and its Effect on Shoot Through Performance at the Die Level”. I would never have gotten the results I needed if I was using a spreadsheet.

Even with much simpler systems of equations, finding solutions with a paper and pencil was never an easy task for me. It took a very long time, and even then there was no guarantee that I did not make copying errors, accidentally leave out a term, or make a calculation error. After I found the correct solution, I then had the problem of plotting the results, which I often needed in 3-D. Plotting allowed much deeper insights into the interdependency of all the parameters and made it easy for me to concentrate on the important ones without wasting any time. I was very happy when I could pass all these tasks onto Maple, which could do them much faster and more reliably then I ever could. Maple is a software that allows me to go beyond routine engineering calculations and gives me the tools to reach levels of insight and understanding that were completely out of reach of the average engineer until a few years ago.

For the record, I have no business affiliations with Maplesoft. I’m writing this article because Maple makes such a difference in my work that I feel it is important to share my experiences so other engineers can get the same benefits.

Hi everybody:

I'm going to learn programming with maple 18, are there any good and new pdf files for learn it?

with regards...

Consider the following situation: I have a function f, say

f:=x -> 1+x^2/n;

I want to compute the composition of f with itself; e.g.

g:=f@@n;
eval(g(x),n=3);

So it appears eval does evaluate the threefold composition but not at n=3. Obviously I can wrap this example in a subs() or another eval to get the replacement done; but it is a bit curious and I wonder whether this behaviour is as designed or an "undocumented feature."

I ran across this when investigating whether or how to do the composition for an arbitrary n (so I can e.g. find the limit for n=infinity) and really wanted to ask about that, but I see that such a question was dealt with before by Joe Riel using rsolve so I'll see first how far that approach gets me. In my case the function will be a polynomial vector function with vectorial arguments, providing for some additional challenge.

Mac Dude.

for example

There is a Matrix A:=Matrix([[1,2,3],[4,5,6]]), which function can help me find if 4 is an entry of  this Matrix?

Hello,

From a simulation software, I obtain in a matlab file my differential equations in the following way :

C_p_e = C_state/C_c;
C_p_f = I_state/I_i;
R_p_e = R_r*C_p_f;
I_p_e = (Se_p_e-R_p_e)-C_p_e;

For theses expressions, I would like to do two operations :
1) Transform it into equations
2) Conduct substitutions so as to change the names of the variables with nicer names.

For this objectives, I could do with the following code:

restart;
eq1:=C_p_e = C_state/C_c;
eq2:=C_p_f = I_state/I_i;
eq3:=R_p_e = R_r*C_p_f;
eq4:=I_p_e = (Se_p_e-R_p_e)-C_p_e
allsubs:= proc(XX )
subs(C_p_e=fs(t),C_p_f=v(t),R_p_e=fd(t),I_p_e=fm(t),C_c=1/k,I_i=m,R_r=c,Se_p_e=fe(t),I_state=int(fm(t),t),C_state=int(v(t),t),XX)
end proc:
eq1_a:=allsubs(eq1);
eq2_a:=allsubs(eq2);
eq3_a:=allsubs(eq3);
eq4_a:=allsubs(eq4);

Now, I would like to automatisation the creation of the equations eq1, eq2, eq3, eq4. For the moment, to create these equations, I have done copy/ paste from matlab.

But, I would like to create these equations eq1, eq2, eq3, eq4 with a automative process from my matlab equations. The reason comes from the fact that I would like to make the same work on bigger system which are composed with numerous equations.

How can I create equations labeled eq1, ...eqn from a list of expressions from matlab ?

Thank you for your help

Hello everybody,

I'm trying to solve two ODEs analytically but it returns this 'Warning, it is required that the numerator of the given ODE depends on the highest derivative. Returning NULL'. See the worksheet Parallel_flow.mw

Thanks.

I am not sure how/why, but here is the worksheet.

test.mw

The function evalutes fine and can be used for sequence. But it does not seem to be working with plot or Maximize.

V is assumed to between 0 and 1.

Need some help.

Thanks,

casper

Dear all,

I have to differential equations that I'd like to linearise, that is all higher order (>1) derivatives (like diff(uu[0],x$2)) and parameters (like beta^2) and the products of any derivatives with the parameters uu[0] and beta are zero (as they are assumed small).

The two equations considered are displayed below:

Up to now, I perform a very tedious substitution which is based on looking at the equations above and decide which terms I want to get rid of. Something like this, where K =1:KFBCLin:=simplify(eval(KFBC, [beta^3 = 0, beta^2 = 0,
seq(subs((diff(uu[n], x$3)) = 0),n=0..K),
seq(subs((diff(uu[n], x$2)) = 0),n=0..K),
seq(subs((diff(uu[n], t))*beta = 0),n=0..K),
seq(subs((diff(uu[n], x))^2 = 0),n=0..K),
seq(subs(g*diff(beta, x)*beta = 0),n=0..K),
seq(subs((d^2*diff(uu[n], x,t)*diff(beta,x)=0)),n=0..K),
seq(subs(-2*d*diff(uu[n], x,t)*beta*diff(beta,x)=0),n=0..K),
seq(subs((d^2*diff(uu[n], x$2,t)*beta=0)),n=0..K),
seq(subs((diff(uu[n], x)*uu[n])=0),n=0..K),
seq(subs((diff(uu[n], x)*uu[n]*beta)=0),n=0..K),
seq(subs((diff(uu[n], x)*uu[n]*d)=0),n=0..K),
seq(subs((diff(beta, x)*uu[n])=0),n=0..K),
seq(subs((diff(uu[n], x)*beta)=0),n=0..K)]));As there is a lack of automatisation, this procedure is not very helpful. Life would be easier if there was a command (or the like) that says "get rid of higher order derivatives".Any help is appreciated.Best regards,

I have purchased Maple 2015 Student Edition a few months ago.  Now, I was about to buy MapleSim Student Edition and I saw that MapleSim include a license of Maple. 

If I buy MapleSim and Maple,  I would pay 198$ even if I could have bought only MapleSim and still get both products? 

Can I get MapleSim Student without Maple at a lower price? 

Maybe the version of Maple included in MapleSim has less features and that's why the cost of MapleSim and Maple are the same? 

Thanks in advance!  

I did some search on Google and on this website, but I haven't found anything. 

please demonstrate to me how to set up a maple document to solve a simple beam design from the scratch.

S. Hassan

I'm using commands evalDG and LieBrackets to calculate Lie Brackets of infinitisemal operators.

But how (using Maple) can i extract component from the result?

For example, I had a result:

T = (f'(x) - f(x)) D_x + D_y

I need to get its component for x - f'(x) - f(x) and y - 1.

Is there a command for this operation?