## Inverse Laplace Transform...

I take the Inverse Laplace Transform on a specific function and the shown result is still an integral.

Would you like to explain it to me?

Thanks.

## Inverse laplace transform...

I can't take the inverse laplace transform of one kind of functions.

Would you like to help me?

Thanks.

## Inverse CDF of the Standard Normal Distribution...

Is there a command in Maple to produce a table of z values given F(z) where F is the CDF of the Standard Normal Distribution? I know of the command ProbabilityTable to generate a table of z, F(z) values.  What I would really like is F, Inv(F) table of values. I guess  I could write my own code to do this but was wondering if there is an easier way to do this.

## issues with angular displacement in given inverse ...

Hi,

I was playing around with the example "Simple Inverse Kinematic Problem" and found somethings to be odd:

the angular motion seems to be calculated from between pi and negative pi and this has some effects when using position block to move a joint.

the original angular displacement is graph below

the angular displacement after ik calculations have been performed:

if you run the simulation it seems to copy and mirror the input pendulum, however if you disable one of the IK solutions you see that infact its motion isn't like the input.

this becomes more prevailant when you use a position block to force rotation on a joint instead of using the 'prescribed rotation' blocks that comes with the example.

My question then:
why does this happen?
how do I work around this?

the importance that the motion is follow precisely becomes more prevailent when we want to extract other values such as vel, accel, torque. they are incorrect and very jumpy. Also simply put the angular displacement is wrong, how do I fix it?

(side note: I'm thinking  it has to do with the way arctan is calculated in maple limits it to stay in range -pi to pi
"For real arguments x, y, the two-argument function arctan(y, x), computes the principal value of the argument of the complex number x+Iy, so −π < arctan(y,x) ≤ π." from https://www.maplesoft.com/support/help/Maple/view.aspx?path=invtrig)

pjf

## Den Iseger algorithm for numerical Laplace transfo...

Dear Community,

Would someone have a good and easy to understand/implement description of the Den Iseger algorithm for the numerical inversion of Laplace transform? Even better if someone would have a Maple script to do it, that would be superb.

best regards

Andras

## how to evaluate numerical inverse Laplace transfor...

I would like to apply inverse Laplace transform to U(x,p), which is defined by

For simplicity with my calculations, I assumed p:=i*beta^2. That is why I have the following equation after applying Laplace transform

(beta=0 is not a pole, that is why I removed the last term in my calculations later. Because there is no contribution) where

Here p and beta are complex values, we can write Re(p)=-2*Re(beta)*Im(beta), Im(p)=(Re(beta))^2-(Im(beta))^2 due to p:=i*beta^2. I numerically compute the roots of h(beta), you can find the numerical values of beta (I assumed digits are 50 due to accuracy ) betap.mw

Finally, I would like to plot U(x,t) with the values t=0.8, lambda=1, L=10, k=1. For checking the figure give t=0 and observe that U(x,0)=0.

I am expecting the plot is more or less like the following figure

PS: I already tried to solve and plot the problem, but I could not find where I make a mistake. I  share the worksheet below. Thank you!

complexplot.mw

## Matrix and inverse matrix...

Hello all

I try to make matrix of size 21*21 but maple doen't run , I don't Know why ?

Also I want to comput the inverse but I get the same problem.

Do you have any idea .

Thank you

## expression with inverse trig funtion...

Hello

I am having issue in finding the explanation on how to solve inverse trig funtion and expression with inverse trig funtions. I do not understand my school book and I was hoping that the software would have given me an extra help in understanding my school problems.

Thank you very much

Regards,

Perla D'andrea

HOW DO I GET A STEP BY STEP SOLUTION FOR INVERSE Z TRANSFORM HELPPP!!!!!!

## Levi-Civita symbol and inverse of matrix...

Hi

We know determinant of a square matrix A[ij] (i,j ∈ {1,2,3}) is equal to the following expression

det(A) = 1/6 * e[ijk] * e[pqr] * A[ip] * A[jq] * A[kr]

in which e[ijk] is a third order Tensor (Permutation notation or Levi-Civita symbol) and has a simple form as follows:

e[mnr] = 1/2 * (m-n) * (n-r) * (r-m).

The (i,j) minor of A, denoted Mij, is the determinant of the (n − 1)×(n − 1) matrix that results from deleting row i and column j of A. The cofactor matrix of A is the n×n matrix C whose (i, j) entry is the (i, j) cofactor of A,

C[ij]= -1 i+j * M[ij]

A-1=CT/det(A)

The general form of Levi-Civita symbol is as bellow:

I want to write a program for finding inverse of (NxN) matrix:

N=2 →

restart;
N := 2:
with(LinearAlgebra):
f := (1/2)*(sum(sum(sum(sum((m-n)*(p-q)*A[m, p]*A[n, q], q = 1 .. 2), p = 1 .. 2), n = 1 .. 2), m = 1 .. 2)):
A := Matrix(N, N, proc (i, j) options operator, arrow; evalf((37*i^2+j^3)/(2*i+4*j)) end proc):
f/Determinant(A);

N=3 →

restart;
N := 3:
with(LinearAlgebra):
f := (1/24)*(sum(sum(sum(sum(sum(sum((m-n)*(n-r)*(r-m)*(p-q)*(q-z)*(z-p)*A[m, p]*A[n, q]*A[r, z], m = 1 .. N), n = 1 .. N), r = 1 .. N), p = 1 .. N), q = 1 .. N), z = 1 .. N)):
A := Matrix(N, N, proc (i, j) options operator, arrow; 10*i^2/(20*i+j) end proc):
f/Determinant(A);

The results of above programs are equal to 1 and validation of method is observed.

If we can write the general form of determinant then we can find the inverse of any square non-singular matrices.

Now I try to write the mentioned program.

restart;
with(linalg):
N := 7:
Digits := 40:
e := product(product(signum(a[j]-a[i]), j = i+1 .. N), i = 1 .. N):
ML := product(A[a[k], b[k]], k = 1 .. N):
s[0] := e*subs(`\$`(a[q] = b[q], q = 1 .. N), e)*ML:
for i to N do
s[i] := sum(sum(s[i-1], a[i] = 1 .. N), b[i] = 1 .. N)
end do:
A := Matrix(N, N, proc (i, j) options operator, arrow; evalf((3*i+j)/(i+2*j)) end proc): # arbitrary matrix
CN:=simplify(s[N]/det(A));

Therefore det(A)= CN-1 * e[a1,a2,..an] * e [b1,b2,.., bn] * A[a1,b1] * A[a2,b2] * ... * A[an,bn].

The correction coefficient is CN(for N)/CN(for N-1) = N!/(N-1)! =N.

restart:
with(linalg): N := 4: Digits := 20:
e := product(product(signum(a[j]-a[i]), j = i+1 .. N), i = 1 .. N):
ML := product(A[a[k], b[k]], k = 1 .. N):
s[0] := e*subs(`\$`(a[q] = b[q], q = 1 .. N), e)*ML:
for r to N do s[r] := sum(sum(s[r-1], a[r] = 1 .. N), b[r] = 1 .. N) end do:
A := Matrix(N, N, proc (i, j) options operator, arrow; evalf((3*i+2*j)/(i+2*j)) end proc):
DET:=S[N]:
for x to N do for y to N do
e := product(product(signum(a[j]-a[i]), j = i+1 .. N-1), i = 1 .. N-1):
ML := product(AA[a[k], b[k]], k = 1 .. N-1):
S[0, x, y] := e*subs(`\$`(a[q] = b[q], q = 1 .. N-1), e)*ML:
for r to N-1 do S[r, x, y] := sum(sum(S[r-1, x, y], a[r] = 1 .. N-1), b[r] = 1 .. N-1) end do:
f[y, x] := (-1)^(x+y)*subs(seq(seq(AA[t, u] = delrows(delcols(A, y .. y), x .. x)[t, u], t = 1 .. N-1), u = 1 .. N-1), S[N-1, x, y])
end do: end do:
Matrix(N, N, f)/(DET)*(24/6);
A^(-1);

CN for N=4 and N=3 is 24 and 6 respectively i.e. CN(4)/CN(3)=24/6.

When I use bellow procedure the error "(in S) bad index into Matrix" is occurred.

Thank you

restart; with(linalg): Digits := 40: n := 7:
S := proc (N) local e, ML, s, i:
e := product(product(signum(a[j]-a[i]), j = i+1 .. N), i = 1 .. N):
ML := product(A[a[k], b[k]], k = 1 .. N):
s[0] := e*subs(`\$`(a[q] = b[q], q = 1 .. N), e)*ML:
for i to N do s[i] := sum(sum(s[i-1], a[i] = 1 .. N), b[i] = 1 .. N) end do
end proc:
A := Matrix(n, n, proc (i, j) options operator, arrow; evalf((3*i+j)/(i+2*j)) end proc): # arbitrary matrix
CN := simplify(S(n)/det(A))

## How do I plot a function...?...

I have a function like

w=f(r) on the other hand

z=g(r) wher r is common between these two.

how i could plot w in term of z?

## Inverse function in restricted domain...

Hello,

I've tried to find the solution to my problem, but none of my attempts was succesful.

I have a function which is one-to-one in a particular domain which I am interested in. I would like to get the inverse function of it only in this domain. Here is my function and plot for xp=0..10000:

x := xp-> (-1)*720.5668720*sinh(0.2043018094e-3*xp-0.8532729286)+84952.59423+4.014460003*10^5*arcsinh(0.1219272144e-1*sinh(0.2043018094e-3*xp-0.8532729286)-0.2032498888)

I would appreciate any help,

Iza

## Can I solve this Inverse Laplace?...

Hello,

I tried to solve below equation, but it gives me zeros result. Please help me to find their inverse laplace.

It will be clearer if was pasted on Maple:

restart

Ps := [P[0], P[1], P[2], P[3], P[4]]:

eqs := [P[0](s) =~ (P[1](s)*mu[1]+P[2](s)*mu[2]+P[3](s)*mu[3]+P[4](s)*mu[4])/(s+lambda[1]+lambda[2]+lambda[3]+lambda[4]), P[1](s) = lambda[1]*P[0](s)/(s+mu[1]), P[2](s) = lambda[2]*P[0](s)/(s+mu[2]), P[3](s) = lambda[3]*P[0](s)/(s+mu[3]), P[4](s) = lambda[4]*P[0](s)/(s+mu[4])];

Ls := solve(eqs, Ps(s))[];

P(t)=~inttrans[invlaplace]~(rhs~(Ls), s, t);

Thank you

## How to find invlaplace?...

Hello

I have a complex set of Markov Processes in reliability application. To make them simpler for me, as a beginner in Maplesoft, I solve them manually to reach a point where I need inverse Laplace for a set of equations. For illustration, I used a simple example below. If I get the concepts for below example, I can apply them on more complicated systems, as following:

P0(s) = 1/(s+λ)+υ*P1(s)/(s+λ)

P1(s)=γ*P0(s)/(s+υ)

Mannuly I find that:

P0(t)=υ/(s+λ)+λ*exp(-(λ+υ)t)/(υ+λ)

P1(t)=υ/(s+λ)-λ*exp(-(λ+υ)t)/(υ+λ)

Thank you,