Maple Questions and Posts

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I have a problem about the integration of a function. The maple returns mathematical form of the given command

the function is

fn :=(-4.079067798*10^(-16)+3.422708023*10^(-16)*I)*(3.363377947*10^(-11)+5.977507284*10^(-12038)*I+(3.363377947*10^(-11)+4.678081798*10^(-22)*I)*erf(1.664331698*10^15*qq-0.2503507367e-1-4.649313602*I)) *exp(-2.77*(qq/(tau*tau))^2)*exp(-I*w0*qq)*exp(-(ss-qq)/T_pop)

qq is the integration variable qq=-inf..ss

w0=10^15

tau=10^(-15)

T_pop=30e-15

I have this matrix

A := Matrix([[x+I*y, z+I*w], [-z+I*w, x-I*y]])

and I want a matrix which components are de real parte of the components of A. I have tried this:

Re(A)

but it doesn't work.

What is wrong?

Thank you so much.

I have this two matrices

uA := Matrix([[-w^2+x^2+y^2-z^2, -2*(w*y+x*z), 2*(-w*x+y*z)], [2*(-w*y+x*z), w^2+x^2-y^2-z^2, -2*(w*z+x*y)], [2*(w*x+y*z), 2*(-w*z+x*y), -w^2+x^2-y^2+z^2]])

and

 

UA := eval(uA, {w = -w, x = -x, y = -y, z = -z})

 

and I want to check that their are the same. I have tried

evalb(uA = UA)

 

but it says it false. It should say that is true, because - I think- this two matrices are the same.

Does anyone know what is wrong?

 

Many thanks

Can anyone offer an explanation why the following error occurs, and how it can be avoided? Thanks!

 

plots:-shadebetween(2, 1/sqrt(-x^2+1), x = 0 .. (1/2)*sqrt(3))

Error, (in t) invalid input: nops expects 1 argument, but received 0

 

``

 

Download error.mw

In preparation for learning GR, I need somme trick on how to use the DifferentialGEometry package or else. So I want to show you what I want to do (see the link to the document below) and I would like some help on how to do it with tensor.  That would help me a lot.  Then, I will extansion it on a 3-D problem and next in 4-D.

 

Thank you in advance dor your help

 

here is the file : Finding_covariant_and_contravariant.mw

 

--------------------------------------
Mario Lemelin
Maple 2015 Ubuntu 14.04 - 64 bits
Maple 2015 Win 10 - 64 bits messagerie : mario.lemelin@cgocable.ca téléphone :  (819) 376-0987

For the life of me I cannot find the method to do so.

 

So the solution would look like:

1. Euation

2 Step 2

3 Step 3

4 step 3+n

where n is the number of steps reuired.

Any help will be appreciated so very much.

.

.TIA

Larry C

 

 

I have this matrix

 

uA := Matrix([[-w^2+x^2+y^2-z^2, -2*(w*y+x*z), 2*(-w*x+y*z)], [2*(-w*y+x*z), w^2+x^2-y^2-z^2, -2*(w*z+x*y)], [2*(w*x+y*z), 2*(-w*z+x*y), -w^2+x^2-y^2+z^2]])

and I would like to evaluate the variables like this

 

x = -x, y = -y, z = -z, w = -w

I tried this

Eval(uA, x = -x, y = -y, z = -z, w = -w)

but it didnt work.

 

Any suggestions??

 

Thank you so much

 

 

I want to compute some matrix multiplications and i need this expression to be 1 always, i.e,

x^2+y^2+z^2+w^2=1

for every calculation I do.

I have tried x^2+y^2+z^2+w^2:=1 and assign(x^2+y^2+z^2+w^2,1) but it doesn't work.

What I should type to make it work?

 

Thank you

 

 

Hi,

In line with my previous questions

http://www.mapleprimes.com/questions/201944-Convergence-Problem-In-My-Algorithm-DSOLVE

I write a code with different variables and odes. However I tried to get the solution, I cannot get the results. I think it should be some problems with my Guess procedure. The code is attached. I would be most grateful if you help me on this problem.

code.mw

Thank you.

Amir

The engineering design process involves numerous steps that allow the engineer to reach his/her final design objectives to the best of his/her ability. This process is akin to creating a fine sculpture or a great painting where different approaches are explored and tested, then either adopted or abandoned in favor of better or more developed and fine-tuned ones. Consider the x-ray of an oil painting. X-rays of the works of master artists reveal the thought and creative processes of their minds as they complete the work. I am sure that some colleagues may disagree with the comparison of our modern engineering designs to art masterpieces, but let me ask you to explore the innovations and their brilliant forms, and maybe you will agree with me even a little bit.

Design Process

Successful design engineers must have the very best craft, knowledge and experience to generate work that is truly worthy of being incorporated in products that sell in the tens, or even hundreds, of millions. This is presently achieved by having cross-functional teams of engineers work on a design, allowing cross checking and several rounds of reviews, followed by multiple prototypes and exhaustive preproduction testing until the team reaches a collective conclusion that “we have a design.” This is then followed by the final design review and release of the product. This necessary and vital approach is clearly a time consuming and costly process. Over the years I have asked myself several times, “Did I explore every single detail of the design fully”? “Am I sure that this is the very best I can do?” And more importantly, “Does every component have the most fine-tuned value to render the best performance possible?” And invariably I am left with a bit of doubt. That brings me to a tool that has helped me in this regard.

A Great New Tool

I have used Maple for over 25 years to dig deeply into my designs and understand the interplay between a given set of parameters and the performance of the particular circuit I am working on. This has always given me a complete view of the problem at hand and solidly pointed me in the direction of the best possible solutions.

In recent years, a new feature called “Explore” has been added to Maple. This amazing feature allows the engineer/researcher to peer very deeply into any formula and explore the interaction of EVERY variable in the formula. 

Take for example the losses in the control MOSFET in a synchronous buck converter. In order to minimize these losses and maximize the power conversion efficiency, the most suitable MOSFET must be selected. With thousands of these devices being available in the market, a dozen of them are considered very close to the best at any given time. The real question then is, which one is really the very best amongst all of them? 

There are two possible approaches - one, build an application prototype, test a random sample of each and choose the one that gives you the best efficiency.  Or, use an accurate mathematical model to calculate the losses of each and chose the best. The first approach lacks the variability of each parameter due to the six sigma statistical distribution where it is next to impossible to get a device laying on the outer limits of the distribution. That leaves the mathematical model approach. If you take this route, you can have built-in tolerances in the equations to accommodate all the variabilities and use a simplified equation for the control MOSFET losses (clearly you can use a very detailed model should you chose to) to explore these losses. Luckily you can explore the losses using the Explore function in Maple.

The figure below shows a three dimensional plot, plus five other variables in the formula that the user can change using sliders that cover the range of values of interest including Minima and Maxima, while observing in real time the effects of the change on the power loss.

This means that by changing the values of any set of variables, you can observe their effect on the function. To put it simply, this single feature helps you replace dozens of plots with just one, saving you precious time and cost in fine-tuning your design. In my opinion, this is equivalent to an eight-dimensional/axes plot.

I used this amazing feature in the last few weeks and I was delighted at how simple it is to use and how much it simplifies the study of my approach and my components selection, in record times!

with(DynamicSystems)

T:= a vector

Iwant to make a single plot of:

DiscretePlot(T,x1,stile=stair); DisdretPlot(T,x2,stile=stair)

The usal way: DiscreePlot(T,[x1,x2]... ain't work

Thansk for helping

I am trying to solve a PDE which is converted to ODE when we assign one of the  variables some value. The boundary conditions given to the PDE are numerical values given for fixed numerical values to the two independent variables. I am trying to solve the PDE with the staandard syntax:

pds := pdsolve(pde,[ibc],numeric,time=z,range=0..beta);

The error message I get is:  

Error, (in pdsolve/numeric/process_PDEs) PDEs can only contain dependent variables with direct dependence on the independent variables of the problem, got {theta(z, 0)}

The pde and boundary conditions are as follows:

PDE:   pde := diff(theta(z, 0), z, z)+theta(z, 0)

Where zero is the fixed value for an independent variable

Boundary Condition:  ibc:={theta(0,0)=beta,D[1](theta)(0,0)=0};

When I try to solve it as an ODE the error is:

Error, (in dsolve) not an ODE system, please try pdsolve

 

Hello

i was stuck with some simple problem. I tried using if condition in program that involves a truth condition. If maple cannot determine the condition is true or false i want to assign o to a particular varable. I  show a similar program.

 

restart;


h[1] := -1;

for i from 1 by 1 while(i<150 and h[i]<0) do


p1[i] := .989347189582843*x^2-0.139423979061219e-1*x-1.82559474469870*10^8*x^15+1.30761381361453*10^8*x^16-6.88520063191821*10^7*x^17+2.51079317463498*10^7*x^18-5.66094206949155*10^6*x^19+5.94129446612678*10^5*x^20-6812.74182685426*x^5+59230.0931084044*x^6-3.83520584559500*10^5*x^7+1.90126822307036*10^6*x^8-7.34991883857609*10^6*x^9+2.24203561757434*10^7*x^10-5.43284775909785*10^7*x^11+1.04806113793011*10^8*x^12-1.60600324339222*10^8*x^13+1.94090536353833*10^8*x^14+559.557918804679*x^4-30.6576714427729*x^3-3.93727537464007*10^(-15)-i^2-i; fsolve(p1[i]-0.312e-1, x, -1 .. 1);


if fsolve(p1[i]-0.312e-1, x, -.2 .. 0) < 0 then h[i+1] := fsolve(p1[i]-0.312e-1, x, -.2 .. 0) elif FAIL then h[i+1] := 0 end if;

print(i, h[i])

end do;

i got an error message

Error, cannot determine if this expression is true or false: () < 0

how can i get a value of 0 for h[i] if the error comes.

 

Thanks.

Aditya



 

Hello,

I would like to change the numbering of my equation.

For the moment, the numbering of my equations is : 4.2.4 for Section 4, Subsection 2 and 4th equations.

I would like to keep the number for the section but to remove the numbers for the subsections.

Consequently, I would like to have this kind of result only : 4.4 for Section 4, Equation 4.

Do you have some ideas to do this changement ?

Thanks a lot for your help.

 

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