Laplace transform

There is a description of this mathematical technique and its applications to be found in many encyclopaedia.

Becoming intimately familar with it is within the province of a third-year option in a degree course in Chemical Engineering.

Laplace Transform - its just a method of solving differential equations... thats all!

Fourier Transform (not furrier) - its a mathematical method of converting a signal into frequency domain in an attempt to make analysis easier.

They are completely different things.

Guest, you're a UTS student? lol...

You can, considering the R, sL and 1/sC (some use pL and 1/pC - where s or p are jω), put any electrical (even electronic) circuit under an equation. Than, using Ohm's law, apply it to the circuit expressed as a Laplace fraction, use the signal Laplace transform of the signal (there are tables with all those transforms)and the resulting equation you will inverse Laplace transform and, voila, the response. It works well for transitory response, sinusoidal, even polygonal signals. Start small, with a step pulse on an RC circuit to get the decay response. It is fun. BTW, stability conditions can be derived, too, from a Laplace circuit equation.

Fourier, Laplace and Z transforms are used in several branches of engineering and physics. (All covered in depth in second year maths if I remember correctly.) The transforms on their own as well as the inherent relationships between them is exploited to solve numerous problems related to differential equations. From second year physics I remember using the relationship between Laplace and Fourier to get a solution for certain Green's functions and from third year signals and systems I remember using the unilateral Laplace transform to "fix" certain signals where the Fourier integral does not converge. (Still use the tricks learned in real life.)

Furrier transforms, there is a woolly concept!!

Hope this helps.

To the point of posted ques: Here's impossible to enumerate all applications of LT. But just for engineering field. Yes it gives us good developed and excelent formalized way to resolve system of diff. equations(DE). DE represents compound dynamic object irrespectively its nature.

1st advantage is: replacing DE(s) by means of algebraic equations which are thought to be much more easy for processing.

2nd adv: Mentioned replacing (transforming) is really easy and we can use whether simplest rulers or tables of standard pre-calculated conversions d/dt -> s; int f(t)dt --> 1/s and so on;

3rd adv: We can represent complex dynamic system graphically applying so called transfer functions and observe analyzed system as block diagram with all feedbacks, loops, inputs etc.

Some restrictions of relatively comfortable treating of LT is desirableness of zero/null initial conditions for all DE (just for TF). But it is not serious obstacle.

Regardless LT was created in 19 Cent it's actual up to now and very good suited to computer software (Matlab, Simulink, Scilab ....).

Every engineering and not only engineering field can apply LT for getting good relevant results.Fourier transform can be obtained from LT by mean of formal replacing Laplace variable s-->jw.

Hope it help you.

In school I used them in my control systems class after not seeing them for 2 years after differential equations. I was mighty surprised that I had actually learned something from that class! Also mighty disappointed that I now had to apply it in a chemical engineering class. It went well though because LaPlace is surprisingly easy and effective in the right setting.

Doesn't a Laplace transform have to do with changing genitals from a male to a female...

Maybe that's called a sword....

oops