Question

Please help me to conceive and designing an engineering mathmatical which can use laplace transform, the problem closed to our daily live is best.

Answer 1

1) One uses the Laplace transform to study the transient response of a circuit. Like, when you turn it on, what happens as current flows to charge the capacitors in the circuit to their normal operating voltage. With the proper use of the transform one can see the transient voltage drop in each resistor caused by the charging current.

For the steady state response one uses the Fourier transform, which has many similarities with the Laplace transform.

2) I can't really give you a good example a problem where you need it exactly, but I can maybe try to explain why it's useful. The LaPlace transform takes a differential equation and turns it into a linear equation, so it's easier to solve by algebra, rather than calculus. Then we can take the inverse LaPlace transform and solve for the answer.

3) Laplace transform is integral transform named after its discoverer named Pierre Simon Laplace. It can be used as follows:

It is used in nuclear physics.

It is used in determining structure of astronomical object from spectrum

4) Stability is a concern in any 'real' system. So yes, Laplace transform is used in real life.

If your question is 'Why is the Laplace transform used for stability analysis?', then take a look at my answers here: