Dear Maple friends~

Recently I am thinking a question about how to use Maple to prove an equation based on a known partial differential equationand its boundary conditions.

Although I can Prove it with hand computation ,it still has some difficulty and it will be really hard if its partial differential equation become more complex(As a matter of fact, it will happen).So I think of Maple and want to take advantage of computer.However,I get few ideas how to realize it .The details are as follows：

alias(u=u(x,t)):
pde:=diff(u,t)-diff(u,x$2,t)+4*u^2*diff(u,x)=3*u*diff(u,x)*diff(u,x$2)+u^2*diff(u,x$3);
N:=5;#actually N can be any positive integer!
bcs:=eval(u,x=-infinity)=0,seq(eval(diff(u,x$ha),x=-infinity)=0,ha=1..N),eval(u,x=infinity)=0,seq(eval(diff(u,x$ha),x=infinity)=0,ha=1..N);
E:=Int(u^4+2*u^2*diff(u,x)^2-diff(u,x)^4/3,x=-infinity..infinity);

#try to prove the following equation
diff(E,t)=0

The written proof is as follows:

Therfore,I submit such a problem and look forward your solutions and suggestions sincerely~

Hello,

How I can write a code for the determination of Laplacian in a new form that is introduced in the maple code (First line).

Thank you.

FOR

Maple Worksheet - Error

Failed to load the worksheet //convert/FOR
 

Download FOR

How may I please use maple tools in communication engineering applications. May I please have any example model

I'm trying to use the ExpectedValue function to get the next close value of a stock.

restart; with(Finance)

W := WienerProcess()

T := 1.0

S := SamplePath(W(t), t = 0 .. T, timesteps = 100, replications = 10^4)

A := S[1 .. 10^4, 50]

TI := 1

AN := 100 (Start Value)

sigma := 3.5 (volatility)

r := 0.5e-1    (interest)

ANF := AN*exp((r-(1/2)*sigma^2)*TI+sigma*W(TI))       (ANF: is the forecasting Value)

ExpectedValue(ANF, timesteps = 100, replications = 10^3)

Is this approach right?

How i can generate P_r matrix when P_r = -x and x₀=-1 , x₁=-2/3 , x₂=-1/3 , and x₃=0 with the help loop?

Hello, i am experiencing some problems when trying to open the maple 2018 software*
I have tried unistalling and download it again.
I have tried to search for sollution but there is very ittle intel
When i open Maple 2018 it just lingeres on the start up (pic below) and just disappears after 10 seconds

Can someone please help i have a very important examination upcoming

how we can get matrix of p[2],p[0] and p[1] when p[2]=1,p[0]=1 and  p[1]=-x and x[0]=-1,x[1]=-2/3 ,x[3]=0 when the general matrices of p are given below.....and answer should be p[2]=p[0]= identity matrix and p[1]= only diagonal values are 1,2/3,1/3,0..

I am using external library function but it shows following error. please help.

dll.mw

I am trying to derive Heisenberg's equation of motion for an observable given by two Fermionic operators. The Hamiltonian has both Fermionic and Bosonic creation and annihilation operators.  

H := sum(g[`qαβ`]*C[alpha]*v[beta]*b[q]-g[`qαβ`]*B[q]*V[beta]*c[alpha], `qαβ`)

When I take the commutator with 

A := C[nu]*c[nu]

and try to simplify down it will only go so far. I know the final answer and have checked what it gives by hand, but it will not sum over the different indexes. 

Hello everyone, Greetings!

I am facing a really strange problem. I need to write an expression, however, maple out of nowhere assigns values to the variable used. only to those which are written inside sin (). In previous versions the out put is fine. Is there a new way to write expressions in maple 2019? I am not sure.

Download strngmpl.mw

Hi,

While trying to run this code :

pde := diff(u(x, t), t) = k*diff(u(x, t), x, x);
bc := u(x, 0) = T, u(0, t) = a*t + b, u(L, t) = T;
pdsolve([pde, bc], u(x, t)) assuming (0 < k, 0 < L, 0 < a, 0 < b, 0 < T, 0 <= t, 0 <= x and x <= L);

I get the following error :

Error, (in assuming) when calling 'factor'. Received: 'floating point coefficients are incompatible with field extension; use 'real' or 'complex' instead'

Any idea why ?

When I try to get a higher resolution plot using numpoints, the lines are jagged and look lower resolution.

You can see the difference, the first does not look anti-aliased whil ethe second does(although the 2nd looks far better on my comp)

Give the following functions find Domain, Range, Possible Asymptotes, Intercepts, Critical Points, Intervals of Increase, Decrease, Relative and Absolute Extrema, and Concavity.

A) f(x)=x(x^2-6x+8)

B) f(x) =x^3/4 -3x

Sorry,

I have been away from Maple for a year.
Then, when I used op command, I am puzzed to notice the results were different from those I know.

>op((x+5)^2*(x+y));
      _EXPSEQ((x+5)^2, x+y)

Result I know is 

        (x+5)^2, x+y

Has a modifire such as _EXPSEQ   automatically come to be attatched?
Or, can I have maple express it  in the form I know:  (x+5)^2, x+y?

Thank you in advance.

taro

Hi all, I would be most grateful if I could get some help with solving the tasks below using Maple.

Given the function: mx''(t)+cx'(t)+kx(t)= F_y(t)

1. Rewrite the equation above to a system of 1. order differential equations, by defining the two variables x_1(t) = x(t) and x_2(t)=x'(t) (Hint what is x'(t)?) This gives the first differential equation in the system. What is x_2'(t)?
    
2. Write the equations as a linear system when the outer force F_y(t) is the influence and the position x_1(t) is the answer, in other words give the system matrix A and the vectors b and r.
    
3. I'm given the constants m = 5kg, c = 3Ns/m and k = 20 N/m and I'm trying to find the transfer function of the system.
    
4. Give the systems transfer function H(s) and draw the graphs for the amplitude and phase characteristic.

Thank you!