From Stroud's Further Engineering Maths..
Where L(F(t)) is the Laplace Transform of a function:
In determining the transform of any function, you will appreciate that the limits are subsituted for t so that the result will be a function of s:
I don't understand the jump from the first equation to the second, how does the Laplace Transform = f(s)?
Turn on thread page Beta
- Thread Starter
- 16-07-2008 20:26
- 16-07-2008 21:21
Well your transforming the function from one domain to another. In the first domain the variable is t and in the transformed domain the variable is s, and the laplace transformation maps the function F into the function f.
Its like if I said , I'm just carrying out an operation/transformation that takes one function into another.
But the laplace transformation is defined as:
In the transformed domain things are often easier to deal with (i.e. differential equations just become algebraic equations) so I can form a nice neat equation then do the inverse transformation to get the answer I require in terms of variables of my domain. Also the integral removes any t dependence since it is a definite integral, just as the inverse transformation gives back the t dependence but removes the s dependence.