Studying for the FE test, never learned LaPlace Transforms.

[jasc15]

I began studying with a friend of mine for the FE (fundamentals of engineering) test and we began with the math section. We came across a LaPlace transform problem and we had never learned it before. Is this something I can learn relatively quickly (within the week)? I have taken calculus 1 2 & 3 as well as differential equations, although its been about 2 years since I've actually used any of it. I'll have to dig up my old calculus books for sure, but i just wanted to know the level of difficulty of LaPlace transforms.

 

[J77]

Easy, if you know how to do limits and integration.

Just remember the formula:

$$\int_0^\infty e^{-st}f(t)dt$$

$$f(t)$$ will probably be given and you'll be asked to find its Laplace transform.

Stick it in the above formula, evaluating between 0 and T, then take the limit of the answer as $$T\rightarrow\infty$$

 

[jasc15]

Thanks a lot. I've seen tables for common transforms, are they just the worked out integrals for common f(t)'s?
Edit: I also notice that after the transform, the independent variable changes. What is the significance of this?

 

[J77]

You go from the time domain (t) to the frequency domain (s).

edit: you'll probably want to do the inverse to get back to the time domain in some questions - go through an engineering math textbook and you'll get the idea.

 

[FrogPad]

My differential equation teacher put it something like this:

The Laplace transform is a machine that eats differential equations and ouputs algebraic expressions.

With circuits it simplfies things dramatically because you work in the s domain, hence the change of variable.

The inverse laplace transform requires a course in complex analysis, so typically you will instead go through the back door and learn how to do partial fraction expansions, and use tables to get back to the time domain.

A basic rundown of what you typically use it for is,

1) Use Laplace transform (typically using tables) to convert from t-domain to s-domain.
2) Perform necessary algebra.
3) Partial fraction expansion of expression, and perform inverse Laplace transform to convert (typically using tables) from s-domain to t-domain.