Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

sys_ode.mw 

sys := -diff(g(x), x)*e^(c*x)*c/(3*t) + f(x) = 0, t*(c*e^(2*c*x)*diff(g(x), x) + t*e^(c*x)*(2*c^2 + 3*f(x) - 1))*diff(f(x), x) + 6*c^2*(diff(f(x), x, x)*t*e^(2*c*x) + diff(f(x), x, x, x)*e^(3*c*x)/3) = 0. I have attached worksheet. Please solve this system,of ODE.

So Maple 2019 seems to be unable to evaluate a relatively easy integeral for a positive integer, but when the obvious substitution u=cos(x) is made it is able to evaluate the integral.  Is there some setting I am using that is causing Maple to give up without much effort?  
 

restart

assume(n::integer, n > 0)

about(n)

Originally n, renamed n~:
  is assumed to be: AndProp(integer,RealRange(1,infinity))

 

int(sin(x)^(2*n+1), x = 0 .. Pi)

int(sin(x)^(2*n+1), x = 0 .. Pi)

(1)

for j to 5 do int(sin(x)^(2*j+1), x = 0 .. Pi) end do

4/3

 

16/15

 

32/35

 

256/315

 

512/693

(2)

int((-u^2+1)^n, u = -1 .. 1)

GAMMA(n+1)*Pi^(1/2)/GAMMA(n+3/2)

(3)

for j to 5 do int((-u^2+1)^j, u = -1 .. 1) end do

4/3

 

16/15

 

32/35

 

256/315

 

512/693

(4)

``


 

Download walter.mw

I am brand new to Maple, both as a specific program and as an example of symbolic mathematical software (although years ago I spent some time with MathCad).

I am interested in referrals to online resources which can help me progress down the learning curve. I have a substantial background in application computer programming, mostly in C#.

So if there's such a thing as "Maple for Programmers" that might be ideal...particularly since I find Maple's syntax and semantics to be "just similar enough" to coding that it causes me a lot of frustration. As in, simply entering the examples from the online manual Just Doesn't Work :).

Thanx!

- Mark

help.mw

How to solve Linear first-order PDE by the Lagrange method?

dx/(x) =dy/0=dt/0=du/3=dv/v=dw/w, where x,y,t are independent variables and u,v,w are dependent variables.

Hi,

 

I want my vector field plot to have more arrows, and am wondering how to do this.  Here is the file:

How_to_add_more_arrows.mw

 

Thanks in advance!

 

Hi everyone, i'm working on a project and i'm having a problem as such:

I got t1 already (t1=26,88) by solving s(t)=0 and when I try to calculate s(t) with t=t1, i type s(t1) Maple give me 1.10^(-6) as result but the result should be 0.22144. Here are my codes:

system_of_PDE.pdf

How to solve the system of partial differential equations in Maple.  I have attached a pdf file, please check it. Kindly help me.

Thank you

[Edit: I've also atached the OP's worksheet below.--Carl Love]

not_solve_sys_pde.mw

Hello there, 

Would you allow me to ask this question?

What I tried in the worksheet below is to map an expression to x-axis and another expression to y-axis, while both expressions have the same input (or independent variable). However, the resulting plot still shows those two expressions as two separate curves. Would you tell me how to map or assign the expressions to each axis?


 

restart;

with(LinearAlgebra):

Digits := 6:

j := I:

L__adpu := 1.66;
L__aqpu := 1.61;
L__lpu := 0.15;
R__apu := 0.003;
E__tpu := 1.0;
MVA := 555;

1.66

 

1.61

 

.15

 

0.3e-2

 

1.0

 

555

(1)

A__sat := 0.0312500:
B__sat := 6.93147:

I__tpu_compare := (P__t - j* Q__t) / E__tpu;

-(1.00000*I)*Q__t+1.00000*P__t

(2)

I__tpu_a := abs(I__tpu_compare);

abs(-(1.00000*I)*Q__t+1.00000*P__t)

(3)

Phi := arccos(P__t / (I__tpu_a * E__tpu));

arccos(1.00000*P__t/abs(-(1.00000*I)*Q__t+1.00000*P__t))

(4)

E__a__tilde := E__tpu + (R__apu + j * L__lpu) * I__tpu_compare;

1.0+(0.3e-2+.15*I)*(-(1.00000*I)*Q__t+1.00000*P__t)

(5)

psi__at := abs(E__a__tilde);

abs(1.0+(0.3e-2+.15*I)*(-(1.00000*I)*Q__t+1.00000*P__t))

(6)

psi__I := A__sat * exp(B__sat * (psi__at - 0.8));

0.312500e-1*exp(6.93147*abs(1.0+(0.3e-2+.15*I)*(-(1.00000*I)*Q__t+1.00000*P__t))-5.54518)

(7)

K__sd := psi__at / (psi__at + psi__I);

abs(1.0+(0.3e-2+.15*I)*(-(1.00000*I)*Q__t+1.00000*P__t))/(abs(1.0+(0.3e-2+.15*I)*(-(1.00000*I)*Q__t+1.00000*P__t))+0.312500e-1*exp(6.93147*abs(1.0+(0.3e-2+.15*I)*(-(1.00000*I)*Q__t+1.00000*P__t))-5.54518))

(8)

K__sq := K__sd;

abs(1.0+(0.3e-2+.15*I)*(-(1.00000*I)*Q__t+1.00000*P__t))/(abs(1.0+(0.3e-2+.15*I)*(-(1.00000*I)*Q__t+1.00000*P__t))+0.312500e-1*exp(6.93147*abs(1.0+(0.3e-2+.15*I)*(-(1.00000*I)*Q__t+1.00000*P__t))-5.54518))

(9)

X__ad := K__sd * L__adpu:

X__d := X__ad + L__lpu:

X__aq := K__sq * L__aqpu:

X__q := X__aq + L__lpu:

delta__i := arctan((X__q * I__tpu_a * cos(Phi) - R__apu * I__tpu_a * sin(Phi))/(E__tpu + R__apu * I__tpu_a * cos(Phi) + X__q * I__tpu_a * sin(Phi))):

e__q := E__tpu * cos(delta__i):

i__d := I__tpu_a * sin(delta__i + Phi):

i__q := I__tpu_a * cos(delta__i + Phi):

i__fd := (e__q + R__apu * i__q + X__d * i__d)/(X__ad):

i_armature := sqrt(i__d^2 + i__q^2):

i_armature2 := subs(P__t = 0, i_armature):

i_armature3 := subs(P__t = 0.5, i_armature):

i_armature4 := subs(P__t = 1.0, i_armature):

plotA := plot(i_armature2, Q__t = -0.6..0.6):

plotB := plot(i_armature3, Q__t = -0.6..0.6):

plotC := plot(i_armature4, Q__t = -0.6..0.6):

plots:-display([plotA, plotB, plotC]);

 

i__fd2 := subs(P__t = 0, i__fd):

i__fd3 := subs(P__t = 0.5, i__fd):

i__fd4 := subs(P__t = 1.0, i__fd):

 

plotD := plot(i__fd2, Q__t = -0.6..0.6):

plotE := plot(i__fd3, Q__t = -0.6..0.6):

plotF := plot(i__fd4, Q__t = -0.6..0.6):

plots:-display([plotD, plotE, plotF]);

 

plot([i__fd2, i_armature2, Q__t = -0.6..0.6]); #failed, two expressions are plotted seperately.

 

 

 


Best Regards, 

In Kwon Park 

Download Q20210416.mw

How to solve the Linear first-order partial differential equation by the Lagrange method. Suppose u and v are dependent variables and x,y,z are independent variables of a partial differential equation of the form:

dx/f(x,y,z)=dy/g(x,y,z)=dz/h(x,y,z)=du/k(x,y,z)=dv/s(x,y,z). I need its solution in the form of u and v . How to find it ?

Hi!

How to get the plot of the system of the equation below:

Tau >=0.Plot.mw

I did not succeed.

Thanks

Hello there, 

Would you tell me how to treat differentiation as an operator?

Here is a simple example:

(The content of the worksheet is supposed to be here, but that did not work)

Download Q20210407.mw

The 'coeff' operation shows 'psi__d0' as the only coefficient of 'Delta__delta(t)', while what I wanted to see is the 'Desired' expression in the worksheet, '(psi__d0 + psi__q0 / omega__0 * D)' as the coefficients. Here, 'D' represents the differentiation. 

Thank you, 

In Kwon Park 

Hi!

I am double checking some textbook methods involving the arc length of a parabolic function of y.  I need to calculate the x coordinate that represents half the arc length of the parabola from x=0 to x=1

I have included my work in the form of a maple worksheet.  Help on this would be appreciated.

Have a great day!Test_solve_for_x.mw

I am trying to find Lie subalgebra for finding optimal solutions directly with the help of MAPLE.  Please help me to find it. Share MAPLE code please.

Just A Simple Fouier Transform Example:

Given x(t) = exp(-2*t) u(t) and X(ω) is equal to 1/(j*omega + 2);

Use The Frequency Differentiation of Fourier Transform to the Given Problem and Plot With An Amplitude Spectrum Graph:

Sorry Everyone: I am trying To Learn This Software and Need A Bit Of Help: I am Trying To Solve & Plot With An Amplitude Spectrum Graph #A & Problem #B. Can Anyone Help: 

Sorry I Do Not Know How & I Can Find Very Little Via Google a Google Search and Thank You A Million Times For Anyone That Can Help Me With Problems. 

#A). t*x(t)
#B). t^2*X(t)

#Solution To Example Problem #A 't*x(t)':

(t)^nX(t)->(j)^n*((ⅆ)^n)/((ⅆ)^( )omega^n)(X(omega));

n := -1;
                        
X := omega -> 1/(2 + j*omega);


diff([j^n*diff(X(omega), [omega $ n])], omega);

Greetings!

I am unable to evaluate an improper integral involving rational, exponential and Bessel functions. Can Maple do it? if not is there a way around.

test.mw

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