Problem with Laplace transform

[Natoe]

Hi !

When i want to do a Laplace transform like :

Laplace(u(t),t,p) i want to have for the result : 1/p but didn't have this ...

And when i do ILaplace(1/p) i have for result : Dirac/p ...

What is the problem ? Ans how can i fix it ?

Thanks and have a Nice day !

[JMB]

Hi

Both the "laplace" and "ilaplace" functions have three parameters: expression, variable of the expression, and variable of the result. The last two variables are optional, but it looks like if you don't specify them, the calculator uses the variable x as the default variable.

With firmware 2015 6 17 (8151), you have the following results:

laplace(1): 1/x

laplace(1,t,p): 1/p

ilaplace(1/x): 1

ilaplace(1/p): Dirac(x)/p ---> wrong

ilaplace(1/p,p,t): 1

So, it seems that sometimes the two last variables are necessary, in order to get correct answers.

I hope this heps.

[parisse]

The default variable is x, therefore nothing is wrong.

[JMB]

You're right.

The case ilaplace(1/p) = Dirac(x)/p is correct because p is interpreted by the HP Prime as a constant.

[Natoe]

Thanks ! , but for the U(t) like in this exemple :

http://image.noelshack.com/fichiers/2016...-titre.png

U(t) on Hp prime = "1" because U(t) = 1/P and when i did : "ilaplace(1/p,p,t)" the result is "1"

So i did on the hp prime :"Laplace((1+(t-2)².1(t-2),t,p) for the exercice and the result is wrong or not the same ...

And thanks for your answer !

[JMB]

I guess that by U(t) you mean the step function. In that case you need to use the HP Prime function Heaviside().

The step function at t=0 is Heaviside(t), and the step function at other values, say t=2, is Heaviside(t-2).

Using this function you get:

laplace(Heaviside(t),t,p) = 1/p

laplace(Heaviside(t-2),t,p) = e^(-2*p)/p

laplace(Heaviside(t)+(t-2)^2*Heavisede(t-2),t,p) = (p^2+2*e^(-2*p)) / p^3

[Grayhek]

I am having some issues that seem similar to this but I just cant get it to work. I am trying to get the Laplace function to work on my calculator but I keep running into errors. The only one I am able to get working is "laplace(1)".
laplace(1)->1/x
ilplace(1/x)->±∞
laplace((5/(16*x^2+10*x)))->Undef
"laplace(5/(16*x^2+10*x),x,s) -> Error: Bad Argument Value"

[JMB]

This is what I get in my G1 Prime, running software version 2.1.14425 (2020 01 16)
   

[Joe Horn]

(09-29-2020 05:31 PM)Grayhek Wrote:  I am having some issues that seem similar to this but I just cant get it to work. I am trying to get the Laplace function to work on my calculator but I keep running into errors. The only one I am able to get working is "laplace(1)".
laplace(1)->1/x
ilplace(1/x)->±∞ ...

I'm guessing that you have a zero stored in 'x'. Try again after purge(x).

[Grayhek]

(09-29-2020 10:42 PM)Joe Horn Wrote:  

(09-29-2020 05:31 PM)Grayhek Wrote:  I am having some issues that seem similar to this but I just cant get it to work. I am trying to get the Laplace function to work on my calculator but I keep running into errors. The only one I am able to get working is "laplace(1)".
laplace(1)->1/x
ilplace(1/x)->±∞ ...

I'm guessing that you have a zero stored in 'x'. Try again after purge(x).

purge(x) returns "No such variable x"
But when I run x it does return a number such as 0 or whatever is stored. I cleared all of the data on the calculator and then it worked but I deleted all my programs which I don't like. Purge does not seem to find or clear 'x'.

[cdmackay]

(09-29-2020 10:51 PM)Grayhek Wrote:  purge(x) returns "No such variable x"
But when I run x it does return a number such as 0 or whatever is stored. I cleared all of the data on the calculator and then it worked but I deleted all my programs which I don't like. Purge does not seem to find or clear 'x'.

purge() only works on CAS variables.

To clear Home variables, use the memory manager (Shift B) — User Variables, select, then delete or backspace.

[parisse]

laplace((5/(16*x^2+10*x))) is infinity because the integral is singular at x=0. I believe you want to compute ilaplace((5/(16*x^2+10*x)))

[Joe Horn]

(09-29-2020 10:51 PM)Grayhek Wrote:  

(09-29-2020 10:42 PM)Joe Horn Wrote:  I'm guessing that you have a zero stored in 'x'. Try again after purge(x).

purge(x) returns "No such variable x"
But when I run x it does return a number such as 0 or whatever is stored. I cleared all of the data on the calculator and then it worked but I deleted all my programs which I don't like. Purge does not seem to find or clear 'x'.

Sounds like the difference between 'X' and 'x' is not well understood, not to mention the difference between Home and CAS. If purge(x) says "No such variable x" then you CANNOT get a value by executing x (lowercase letter x). But you will ALWAYS get a value after executing X (uppercase letter X) because X is a permanently existing Home variable which always contains a real number, and cannot be purged. It's not intended for symbolic math work, which is done in CAS using lowercase variables.

[cdmackay]

hah! I didn't even notice the significance of the particular variable it was, sigh; thanks Joe.