Question

Can someone explain how to do a Laplace operator, when should it be used and what is its purpose?

Answer 1

Hi, Salvador,
Are you talking about the DEFINITION of the Laplace transform, or about the conversion of a time function to a Laplace transform using a table of Laplace transform pairs?

Laplace transforms are often introduced in Differential Equations as an alternative method of solving such equations. They're especially helpful in solving 2nd order or higher differential equations.

Are you working on a specific problem? If so, perhaps we could solve it using Laplace transforms.

Answer 2

I am trying to understand the Schrodinger equation, I have everything pretty much figured out but I dont yet understand the laplace
\[i \frac{ h }{ 2 \pi }\frac{ d }{ dt }\Psi=-\frac{ (\frac{ h }{ 2 \pi })^2 }{ 2m }\Delta^2 \Psi+V \Psi\]

Answer 3

(I used delta because I coulndt find the symbol for the laplace xD)

Answer 4

@mathmale ??

Answer 5

I think I need an explanation on what the transform is, not only the definition because it is a little cryptic

Answer 6

This topic is indeed a bit abstract because we don't run into Laplace transforms in many settings other than Differential Equations and Electrical Engineering.

Again, Laplace transforms are introduced because they give us an additional method for solving differential equations.

I think our best bet would be to try solving some actual problems with Laplace transforms, and so again ask you whether you've been given any homework problems in which you're supposed to apply Laplace transforms. If no, then I could invent a differential equation / initial value problem and attack it with your help.

Answer 7

You might want to take a look at this web page, Salvador:

http://tutorial.math.lamar.edu/Classes/DE/LaplaceIntro.aspx

Notice that the very first thing mentioned has to do with Laplace transforms being used in solving differential equations.

Answer 8

no, I'm still in high school, but I wan't to be an engineer and I am very interested in the topic, as well as differential equations, although it's hard when I don't have a teacher to tell me how to do all this stuff or like specific topics I should study, so I guess I become a little erratic

Answer 9

Not erratic at all! I'd be glad to help you learn how to apply Laplace transforms to solving easy differential equations problems, since that's a major reason for our learning about such transforms. Later we could branch into other aspects of the subject.

Sal, do you happen to have available a "table of Laplace transforms?"

Answer 10

If not, and you're interested, you could consider downloading this one:

http://tutorial.math.lamar.edu/pdf/Laplace_Table.pdf

Answer 11

that's great! what I saw in a web page was that it can be useful to know how to do it "by hand" instead of using a table. Is that true?

Answer 12

how does the table work?

Answer 13

I may last a little while in answering brb

Answer 14

You're expected to know the definition of the Laplace transform, but once you're beyond that, there's not much practical use for the "by hand" derivation of the transforms.

How does the table work?
If you were given the time function f(t) = t, you'd look up "t" on the left side of the table and find the corresponding Laplace transform on the right; it is 1/(s^2). This comes from Transform Pair #3 in the table I've sent you (let n=1).

Message me (mathmale) when you're back.

Answer 15

This (different) table might be more appropriate for your use, given that you're just starting out.

http://www.math.ucsd.edu/~helton/20Dweb2011/files/laplace_table.pdf

Answer 16

okaaay I see, so in this case what does the 1/s^2 represent?

Answer 17

Good question. Here, I've given you the example time function f(t) = t (or you could write that as f(t) = t^1 where n=1).

We say that 1/s^2 is the corresponding Laplace transform.

One's in the time domain (functions of time); the other's in the "frequency domain," functions of frequency "s".

By itself, Salvador, this Laplace transform pair doesn't have much use!

But in a table, it would be like having one of many tools to choose from, when needed.

Go ahead and ask more questions. i can't spend a lot of time on this tonight, but would be happy to continue this discussion later on. I admire your interest and perseverance!

Answer 18

so it represent some kind of derivative applied in 2 domains of the same function?

Answer 19

*represents

Answer 20

Not necessarily "some kind of derivative." But the rest of your statement is clear and relevant: yes, we do describe the same function in two different domains, primarily because problem solving (especially in differential equations) is easier in the frequency domain (which brings in Laplace transforms).