MaplePrimes Questions

Hi, 

I have an expression F that has an addend which is a definite integral,-(int(del_u0(x)*(diff(N_xx(x), x)), x = 0 .. L)), and addends that are not, all the rest of them.

How can I create an expression that is the integrated addend only without the other ones?

In other words, how do i separate the integral term from the rest of them?

F := -(int(del_u0(x)*(diff(N_xx(x), x)), x = 0 .. L))+del_u0(L)*N_xx(L)-del_u0(0)*N_xx(0)+ibp2+ibp3

Thanks!

Shai

 

I need to write a procedure that takes an integer N and a boolean function F as in14 as arguments, returns nothing, and plots a square N × N lattice of points, coloring the points (i, j) with F (i, j) true in red and the other ones blue. 

Thank you in advance. Any help with this would be apreciated. 

I've got a very complicated integral, generated by Maple (15), of the form:

Z:=a*Int(f(x),x=0..1);

I need to do some manipulations on the integrand.  So, I perform the following:

f(x)=GetIntegrand(Z);

f1:=perform operations on f(x)...etc

Z1:=a*Int(f1,x=0..1);

The trouble arises because sometimes Maple writes Z as shown above, and sometimes it writes it as:

Z:=-a*Int(-f(x),x=0..1);

and you can run the program twice in a row and you will get either form, randomly. So, sometimes Z1 will be wrong by a minus sign because you can't predict whether the minus sign is going to be embedded or not.

I've been complaining about this Maple property for years, to deaf ears within MapleSoft who insist it is not an issue, and it has been the subject of long discussions on this site that go nowhere.

So, the question becomes - how do I reliably extract the expression "a" from the expression for "Z" and how do I test whether it has a minus sign embedded within it, or explicitly showing.

This can drive you crazy if you are trying to do a calculation or write a program that always works.

write down the mapple procedure that finds the shape operator plus
gauss and primative curvatores and determines the surface characteristic
of a parametically given surface

 

best regards, ty

Dear All, I need your help to plot the numerical solution. many thanks.

The variable t in [0,T], x in [0,1], b in [0,2].

Difference finie for waves equation is :

pde:=diff(u(x, y,t), t$2) = c^2*(diff(u(x, y,t),x$2)+diff(u(x,y,t),y$2));

i: according to x, j according to y, and k according to t.

u[i,j,k+1]=2*u[i,j,k]-u[i,j,k-1]+(c*dt/dx)^2*(u[i-1,j,k]-2*u[i,j,k]+u[i+1,j,k])+ (c*dt/dy)^2*(u[i,j-1,k]-2*u[i,j,k]+u[i,j+1,k])

 

Boundary condition: u(t=0)=1, diff(u(x,y,t),t=0)=0, and the normal derivative on the boundary of Omega =0.

How can solve this problem and plot the numerical solution.

 

 

 

Using the two images from the branched question I tried to calculate the offset of the two images.  But it is too cumbersome and slow, can someone figure out a faster way?

Here's what I did,

I created both jpg images into a single row vector and then into an Array.  I then used a for loop with CircularShift to cycle one array and subtract it from the other.  I then took the absolute value and added all the values in the array and stored that value in another array.  The smallest value would indicate the highest probable position that both images have lined up.

Something like...

with(ArrayTools):

a:=convert(convert(img1,vector),Array)  #after img1 is padded to 184x184 from Markyan Hirnyk's answer
b:=convert(convert(img2,vector),Array)

for i from 1 to 100 do
  aa:=abs(CircularShift(a,i)-b):
  bb[i]:=add(k,k=aa):
end do:
min(convert(convert(bb,array),Array))


The problem is 100 shifts takes a long time, let alone go through the full image.  Is there a faster way to accomplish this?

Hi

As i asked at title; i want to determine natural frequency of a single or multi degree of freedom vibration system using MapleSim. but i can't and i don't know how i can do it. can every one help me plz?؟؟؟

Say I have a 3x3 matrix with real entries (like 3.4) and want to compute, say, A^(11). How can I do it and only have 5 digits in the output? I set Digits:=5; and used MatrixPower -- but got 10 digits, which is way too many for the classroom presentation.

Please see the attached worksheet for the error at the end, any idea what happens?

Besides, anyone know how to make plot array with each element has a plot and scatterplot in it?  I made my plot by making table first and then type the cmd individually.

Raw Data

restart

avicel102_aero200 := Matrix(12, 3, {(1, 1) = 50, (1, 2) = 1.6621, (1, 3) = .22, (2, 1) = 100, (2, 2) = 3.33221, (2, 3) = .103, (3, 1) = 150, (3, 2) = 4.95533, (3, 3) = 0.43e-1, (4, 1) = 200, (4, 2) = 5.62147, (4, 3) = 0.37e-1, (5, 1) = 50, (5, 2) = 1.88627, (5, 3) = .207, (6, 1) = 50, (6, 2) = 1.90375, (6, 3) = .199, (7, 1) = 100, (7, 2) = 4.04708, (7, 3) = 0.89e-1, (8, 1) = 100, (8, 2) = 4.20413, (8, 3) = 0.87e-1, (9, 1) = 150, (9, 2) = 5.50509, (9, 3) = 0.41e-1, (10, 1) = 150, (10, 2) = 4.90453, (10, 3) = 0.49e-1, (11, 1) = 200, (11, 2) = 6.22001, (11, 3) = 0.16e-1, (12, 1) = 200, (12, 2) = 6.24435, (12, 3) = 0.23e-1}); avicel102_syloid := Matrix(13, 3, {(1, 1) = 50, (1, 2) = 1.76578, (1, 3) = .235, (2, 1) = 100, (2, 2) = 4.08314, (2, 3) = .128, (3, 1) = 150, (3, 2) = 4.85921, (3, 3) = 0.73e-1, (4, 1) = 200, (4, 2) = 5.66786, (4, 3) = 0.51e-1, (5, 1) = 50, (5, 2) = 2.06221, (5, 3) = .224, (6, 1) = 50, (6, 2) = 2.17294, (6, 3) = .216, (7, 1) = 100, (7, 2) = 4.03728, (7, 3) = .109, (8, 1) = 100, (8, 2) = 3.67978, (8, 3) = .116, (9, 1) = 150, (9, 2) = 5.78427, (9, 3) = 0.6e-1, (10, 1) = 150, (10, 2) = 5.43599, (10, 3) = 0.59e-1, (11, 1) = 200, (11, 2) = 6.26332, (11, 3) = 0.38e-1, (12, 1) = 200, (12, 2) = 6.10814, (12, 3) = 0.39e-1, (13, 1) = 200, (13, 2) = 6.83857, (13, 3) = 0.25e-1}); avicel301_101_aero200 := Matrix(12, 3, {(1, 1) = 50, (1, 2) = 1.106, (1, 3) = .2597543205, (2, 1) = 50, (2, 2) = 1.06, (2, 3) = .2564849561, (3, 1) = 50, (3, 2) = 1.129, (3, 3) = .2552025392, (4, 1) = 100, (4, 2) = 2.865, (4, 3) = .1280363098, (5, 1) = 100, (5, 2) = 2.793, (5, 3) = .127659333, (6, 1) = 100, (6, 2) = 3.088, (6, 3) = .1347147061, (7, 1) = 150, (7, 2) = 4.216, (7, 3) = 0.802489497e-1, (8, 1) = 150, (8, 2) = 4.044, (8, 3) = 0.838493001e-1, (9, 1) = 150, (9, 2) = 4.071, (9, 3) = 0.855901289e-1, (10, 1) = 200, (10, 2) = 4.826, (10, 3) = 0.627298821e-1, (11, 1) = 200, (11, 2) = 4.924, (11, 3) = 0.614759445e-1, (12, 1) = 200, (12, 2) = 4.76, (12, 3) = 0.61001365e-1})

NULL

 

with(LinearAlgebra):

X[1] := Column(avicel102_aero200, 3):

X[2] := Column(avicel102_syloid, 3):

X[3] := Column(avicel301_101_aero200, 3):

S := Array(1 .. 3):

S[1] := ScatterPlot(X[1], Y[1], labels = [Porocity, Tensile*Strength], title = Compactability*of*Avicel102*with*Aerosil200):

with(plots):NULL

 

vSST := Array(1 .. 3):

tpfit := proc (x, y) options operator, arrow; Fit(a*exp(-k*p)+c, x, y, p, output = [leastsquaresfunction, residualsumofsquares, degreesoffreedom]) end proc:SST := proc (y) options operator, arrow; Variance(y)*(NumElems(y)-1) end proc:NULL

for i to 3 do fnTP[i] := tpfit(X[i], Y[i])[1] end do:

for i to 3 do fnPC[i] := Fit(c*p^2+b*p+a, P[i], X[i], p, output = [leastsquaresfunction, residualsumofsquares, degreesoffreedom])[1] end do:

NULL

for i to 3 do vSST[i] := SST(Y[i]) end do:

for i to 3 do pSST[i] := SST(X[i]) end do:

NULL

for i to 3 do vSSR[i] := tpfit(X[i], Y[i])[2] end do:

for i to 3 do Rsquare[i] := 1-vSSR[i]/vSST[i] end do:

NULL

``

s := Array(1 .. 3):

for i to 3 do s[i] := plot(fnTP[i], p = 0 .. .26, legend = typeset(fnTP[i], R^2, "= ", Rsquare[i])) end do

for i to 3 do ps[i] := plot(fnPC[i], p = 0 .. 200, legend = typeset(fnPC[i], R^2, "= ", pRsquare[i])) end do

G := Array(1 .. 3):

G[1] := [S[1], s[1]]:

pG := [[PS[1], ps[1]], [PS[2], ps[2]], [PS[3], ps[3]]]:NULL

NULL

Table 1: Compactability Curve

display(G[1])

 

NULL

display(G[2])

 

NULL

display(G[3])

 

NULL

NULL

NULL

Table 2: Compressibility Curve

display(pG[1])

 

NULL

display(pG[2])

 

NULL

display(pG[3])

 

NULL

``

ff := proc (x) options operator, arrow; unapply(x, p) end proc:

gtp := map(ff, fnTP):

gpc := map(ff, fnPC):

TS1 := proc (pressure) options operator, arrow; (`@`(gtp[1], gpc[1]))(pressure/Unit('MPa'))*Unit('MPa') end proc:

TS2 := proc (pressure) options operator, arrow; (`@`(gtp[2], gpc[2]))(pressure/Unit('MPa'))*Unit('MPa') end proc:

TS3 := proc (pressure) options operator, arrow; (`@`(gtp[3], gpc[2]))(pressure/Unit('MPa'))*Unit('MPa') end proc:

por1 := proc (p) options operator, arrow; gpc[1](p/Unit('MPa')) end proc:

(1)

por1(x*Unit('MPa'))

HFloat(0.36333333333333295)-HFloat(0.0036139999999999957)*x+HFloat(9.666666666666651e-6)*x^2

(2)

por1(x);

HFloat(0.36333333333333295)-HFloat(0.0036139999999999957)*x/Units:-Unit('MPa')+HFloat(9.666666666666651e-6)*x^2/Units:-Unit('MPa')^2

(3)

``

NULL

 

(4)

ts := 2/3*(10*P/(Pi*D^2*(2.84*t/D-.126*t/W+3.15*W/D+0.1e-1))):

Target Weight of Tablet, m__t:

m__t := 700*Unit('mg')

700*Units:-Unit('mg')

(5)

Tablet True Density:NULL

`ρ__true1` := 1.8*Unit('g'/'cm'^3)

1800.0*Units:-Unit(('kg')/('m')^3)

(6)

Width of tablet w;

d := 7.747*Unit('mm')

7.747*Units:-Unit('mm')

(7)

Length of tablet, l:

l := 17.018*Unit('mm')

17.018*Units:-Unit('mm')

(8)

Cup Depth, h:

hh := 1.6764*Unit('mm')

1.6764*Units:-Unit('mm')

(9)

Cup Volume", `v__cup`"

v__cup := 119.789438*Unit('mm'^3)

119.789438*Units:-Unit(('mm')^3)

(10)

Die cross sectional area, v__die:

a__die := 118.9610524*Unit('mm'^2)

118.9610524*Units:-Unit(('mm')^2)

(11)

Equation to solve tablet thickness using tablet dimension and porocity:

Tablet bulk density:

`ρ__bulk` := `ρ__true`*sf

`ρ__true`*sf

(12)

Tablet volume:``

V__tablet := 2*V__cup+A__die*(t-2*H)

2*V__cup+A__die*(t-2*H)

(13)

NULL

Tablet bulk Density:``

`ρ__bulk` := m__tablet/V__tablet

m__tablet/(2*V__cup+A__die*(t-2*H))

(14)

NULL

eq1 := m__tablet/(2*V__cup+A__die*(t-2*H)) = `ρ__true`*sf

m__tablet/(2*V__cup+A__die*(t-2*H)) = `ρ__true`*sf

(15)

Function for thickness:

thickness := unapply(simplify(solve(eq1, t), size), sf, A__die, H, V__cup, `ρ__true`, m__tablet)

proc (sf, A__die, H, V__cup, `ρ__true`, m__tablet) options operator, arrow; (2*sf*(A__die*H-V__cup)*`ρ__true`+m__tablet)/(A__die*sf*`ρ__true`) end proc

(16)

simplify(thickness(1-por[1](100*Unit(MPa)), a__die, hh, v__cup, `ρ__true1`, m__t))

HFloat(0.005719286791216391)*Units:-Unit('m')

(17)

t2 := proc (cc, A__die, H, V__cup, `ρ__true`, m__tablet) options operator, arrow; simplify(thickness(1-cc, A__die, H, V__cup, `ρ__true`, m__tablet)) end proc:

``

``

``

Tablet tensile strength:NULL

eq2 := `σ__t` = ts

`σ__t` = (20/3)*P/(Pi*D^2*(2.84*t/D-.126*t/W+3.15*W/D+0.1e-1))

(18)

Break force of tablet (N)

breakforce := unapply(subs(W = t-2*h, solve(eq2, P)), `σ__t`, D, h, t)

proc (`σ__t`, D, h, t) options operator, arrow; 0.9424777961e-3*`σ__t`*D*(5.*D*(t-2*h)-63.*t*D+1575.*(t-2*h)^2+1420.*t*(t-2*h))/(t-2*h) end proc

(19)

 

kp := simplify(breakforce(TS[1](100*Unit('MPa')), d, hh, 0.5719e-2*Unit('m')))

HFloat(286.99924404612904)*Units:-Unit('N')

(20)

convert(kp, units, kilopond)

HFloat(29.265778226624693)*Units:-Unit('kilopond')

(21)

t2(por[1](100*Unit('MPa')), a__die, hh, v__cup, `ρ__true1`, m__t)

HFloat(0.005719286791216391)*Units:-Unit('m')

(22)

``

hh

1.6764*Units:-Unit('mm')

(23)

simplify(breakforce(TS[1](100*Unit('MPa')), d, hh, t2(por[1](100*Unit('MPa')), a__die, hh, v__cup, `ρ__true1`, m__t)))

HFloat(287.02451456724083)*Units:-Unit('N')

(24)

Encounter problem while chaning variable

 BF:= 
proc (`σ__t`, D, p, A__die, hhh, V__cup, `ρ__true`, m__tablet) options operator, arrow; breakforce(`σ__f`, D, hhh, t2(p, A__die, hhh, V__cup, `ρ__true`, m__tablet)) end proc:

BF(TS1(100*Unit('MPa')), d, por1(100*Unit('MPa')), a__die, hh, v__cup, `ρ__true1`, m__t)

BF(HFloat(3.6712504621161846)*Units:-Unit('MPa'), 7.747*Units:-Unit('mm'), HFloat(0.09859999999999991), 118.9610524*Units:-Unit(('mm')^2), 1.6764*Units:-Unit('mm'), 119.789438*Units:-Unit(('mm')^3), 1420.00*Units:-Unit(('kg')/('m')^3), 667*Units:-Unit('mg'))

(25)

evalf(TS[1](100*Unit(MPa)))

HFloat(3.6712504621161846)*Units:-Unit('MPa')

(26)

plot(breakforce(TS1(x), d, hh, t2(por1(x), a__die, hh, v__cup, `ρ__true1`, m__t)), x = Unit('MPa') .. 200*Unit('MPa'), useunits = true)

Error, (in Units:-Standard:-+) the units `1` and `1/MPa` have incompatible dimensions

 

plot(t2(por1(x), a__die, hh, v__cup, `ρ__true1`, m__t), x = Unit('MPa') .. 200*Unit('MPa'), useunits = true)

Error, (in Units:-Standard:-+) the units `1` and `1/MPa` have incompatible dimensions

 

plot(evalf(por1(xx)), xx = 10 .. 200)

 

but por1 works fine on its own with units

por1(Units:-Standard:-`*`(200, Unit('MPa')))

HFloat(0.02719999999999989)

(27)

plot(evalf(por1(xx)), xx = 10 .. 200);

 

Unloading Units:-Standard

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Fitting_worksheet.mw

I also used a lot for for loop in this worksheet, can anyone suggest another way of doing it? And I think I initiated many Array(1..3) that is of no use.  But if I do not initiate and do the following

A[1]:=a : 

A[2]:=b:

A[3]:=c:

A;

output: A

Only if I initiate A:=Array(1..3) and then define the element I can see the complete A array at the end.

 

I am trying to write a procedure that have the following input:  expr, xdata,ydata. [dependent variables list]

I want a procedure to calculate Rsquare following the method described in 

http://www.mapleprimes.com/questions/120014-How-To-Calculate-Coefficient-Of-Determination

 

But I want the proc to take any abitary function and be able to identify the  dependent variable...how can I approach it? what function can I use to match [dependent variable list] in expr??

 

Thanks

 

 

Is it possible to set maple to fill in a header or footer for every new document I make?

Now i have to do it fot each new file by hand: 

View => Header footer ..=> 

 - select custom  - goto tab cusom headers put in the left textfield "&[File] pag. &[Page]/&[Pages]"

Hi,

I want to calculate a range.

eg. j=1...n-1 will use this equation

P(j,n):={((m/(2-1))(m/(2))^(j-1))/(2(m/(2))^(n)-1))} 

j=n will use other equation.

How to create the command? I keep receive errors.

 

Thank you.

Lina

 

 

what is the best maple book? could every one introduce books which have studied about maple !?? which is the best due to everyones opinion ? tnx for answering.

Hi,

I'm getting an error when I try to

plot(sin(x), x = -1..1, color = darkblue,tickmarks=[spacing(0.25),subticks=2]);

The error is
Error, (in plot) expecting option tickmarks to be of type list({"default", "piticks", "decimalticks", "pidefault", nonnegint, list(realcons), list(realcons = anything), spacing(realcons), spacing(realcons, realcons)}) but received [spacing(.25), subticks = 2]

What exactly am I doing wrong? After all, [...] is a list.

Even more confusingly, tickmarks=[[spacing(0.25),subticks=2],default] doesn't work either.

Any help appreciated!

Dear All,

 

I would like perform a symbolic integration to the following integrand with Heaviside function:

 

The integral I defined is as follows:

The output I got is

 

Could any one explain me how to avoid the undefined in the output. I tried to define the assumtions to constrain the solution. However, I failed to supress the undefined.

I expect a result of the integration should also be piecewise function.

 

Appreciate you constructive inputs.

 

Thanks!

 

 

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