memorize the basic Laplace transformation rules.

there is a rule that says: for and is the Laplace transform parameter

thus: ......(the Laplace transform is like a linear operator in this sense, we can pull constants out when convenient)

and:

write as . now the power is not an integer. the Laplace transform is a bit more complicated. we would use the Gamma function here. the rule is: for

what do you think the Laplace transform is?

think of it as a change of variable. you are transforming a function in some variable, say x or t, into another variable s. this variable is brought about by the Laplace transform of the function in the original variable. and I suppose you know the definition of the Laplace transform.

2. And what mean parameter S in laplace transformation?

i answered this already

3. Let say I Have very trivial function: 2x and i wanna laplace transform that,

the rule to find the Laplace transform (which will not always be easy) for any function is:is there any integration/derivation type rules how I do it or do i have to memorize transformations or look from the transformation table?

but it is really a good idea to memorize the basic functions. i can give you a good list to know if you want.

not sure what you are talking about. we never did much with graphing Laplace transforms when i did differential equations. not sure exactly how such a graph would relate to the problem per say. maybe you could elaborate4. Finally, Am I miss something, I understand that with Laplace transformation you can for example digitalize sin / cosine curve and any analogical curve. However if I draw Laplace tranformed function I cant see any digitialization in chart. What Laplace function represents actually?