Question

Why do we use laplace transformation?

Answer 1

http://en.wikipedia.org/wiki/Laplace_transform

Answer 2

Laplace transformations can basically reduce a DE to algebra

Answer 3

http://tutorial.math.lamar.edu/Classes/DE/IVPWithLaplace.aspx
if you notice, in these examples, no integration or differentiation is explicitly required (given that the transforms are on our table and we don't have to derive them from the definition)

Answer 4

I see :) I just stared learning it. I saw that we use limits to evaluate an indefinite integral during laplace transformation. How are we able to do that?

Answer 5

it's an improper integral, meaning it has at least one integration bound at infinity. since infinity isn't a number, we handle it the way we always do in calculus: as a limit
just like in the definitions of the derivative and definite integral, when we need an infinitely small unit of time or infinitely many rectangles to calculate our area, we take a limit to get around actually having infinity in the equation, which would obviously wreck everything

Answer 6

it's just an integral of this type:
http://tutorial.math.lamar.edu/Classes/CalcII/ImproperIntegrals.aspx

Answer 7

I see. So does all laplace questions involve that limit step?

Answer 8

Only if you need to derive what the transform is from the definition. However, people in the practice of solving a DE almost always refer to a table, since far better mathematicians than us have derived almost all the transforms that aren't mind-bendingly difficult to derive. Usually using the definition to derive the transform of a function is just an exercise as far as I have encountered. Maybe not for real mathematicians.

Answer 9

If I were actually using laplace transforms to solve a DE, I'd be hoping that all the terms in it could be worked through a bit of algebra into a form that fits on a table like this http://tutorial.math.lamar.edu/Classes/DE/Laplace_Table.aspx

Answer 10

Typically how many are you supposed to remember? The entire table?

Answer 11

I haven't really ever had to memorize them. When I was actually doing a class on this stuff I remembered maybe 5 or 7, but usually the table was allowed

Answer 12

This was a first course in DE's mind you, I don't know about more advanced levels

Answer 13

Well I was just going through the first year books so I think its not at an advanced level. My class starts only after a month.

Answer 14

Anyways thanks for the help. I will be back with more doubts since I am learning this on my own due to interest. :)

Answer 15

Yeah, for now, I think mostly relying on the table in practice is sufficient, but knowing the definition and how a few of the derivations work is definitely something you want

Answer 16

welcome :)