Hi, I've been doing Laplace transforms lately...the sums are pretty simple (as much as there is in our syllabus),and I've been practising hard...but the problem is, I don't really understand what I'm doing or why what I am dong is justified at all..... I want to know certain things like... 1, The general rule for transformation of a function f(t) is to integrate it w.r.t 's' (after multiplying with e^-st) within the limits 0 to infinity,in order to transform it into a function of 's'.....why? How can we take this as a general rule to convert a function of 't' to that of 's' ? 2. Does the laplace transform have any geometrical interpretation? If so, please tell me about it. 3. It also says in my book that all values of 't' in the function should be greater than zero...why? 4. Condition for existance of the laplace transform of f(t) is that its magnitude should be greater than M(e^-kt) for some constant value of M and k....please explain this. Besides, how should we find the values of M and k? 5.I feel that the laplace transform for a function need not be unique...we could perhaps find the same transform for two functions by using algaebric manipulation....yet my book says this isn't possible....how can we explain this? 6. What is 's'? Could it be any variable at all? Sorry if I asked too many questions.....I googled for ages,trying to find the answers,but I couldn't...besides,my teacher's really no good.