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I am particularly interested in 'why' it Works for ac theory. I say 'why' because I know 'how' it works - ie. how to do the transform.

I am puzzled that combinations of voltage waveforms, together with integrated and differentiated waveforms, can be combined, transformed to another space, manipulated and transformed back and that they successfully solve a circuit problem. The maths works, but why does the Physics? I was hoping the maths would help me understand the Physics.

On comments: I can see exp(-st) as an eigenfunction - it doesn't change with d/dt, its job seems to be to cause the transformed values to be finite.

The Gibbs distribution may be along the lines I was thinking - which is that perhaps that the transformed function is an encapsulation of the energy beneath the decaying exp(-st) voltage.

Stieltjes didn't take me anywhere towards an understanding.

"Laplace transform is closely related to the Fourier transform." Yes I understand that. Laplace just adds a real part to s and that causes a decay - the transformed function then occupies 2D in the W plane with both real and imaginary axes.

You have given me more to think about, for which I am grateful, but it doesn't seem to be leading me to a physical reason for it's success. Some of your answers are going to take me quite a while to digest, but I so grateful thank you took the time to give me for them.

After being on MathFlow the other day I was led to this which helped quite a bit:

http://www.codee.org/library/articles/the-laplace-transform-motivating-the-definition

and file itself:

John

2 clarification

I am particularly interested in 'why' it Works for ac theory. I say 'why' because I know 'how' it works - ie. how to do the transform.

I am puzzled that combinations of voltage waveforms, together with integrated and differentiated waveforms, can be combined, transformed to another space, manipulated and transformed back and that they successfully solve a circuit problem. The maths works, but why does the Physics? I was hoping the maths would help me understand the Physics.

On comments: I can see exp(-st) as an eigenfunction - it doesn't change with d/dt, its job seems to be to cause the transformed values to be finite.

The Gibbs distribution may be along the lines I was thinking - which is that perhaps that the transformed function is an encapsulation of the energy beneath the decaying exp(-st) voltage.

Stieltjes didn't take me anywhere towards an understanding.

"Laplace transform is closely related to the Fourier transform." Yes I understand that. Laplace just adds a real part to s and that causes a decay - the transformed value function then occupies 2D in the W plane (with both real and imaginary axes)axes.

You have given me more to think about, for which I am grateful, but it doesn't seem to be leading me to a physical reason for it's success. Some of your answers are going to take me quite a while to digest, but I so grateful you took the time to give me them.

After being on MathFlow the other day I was led to this which helped quite a bit:

http://www.codee.org/library/articles/the-laplace-transform-motivating-the-definition

and file itself:

John

1

I am particularly interested in 'why' it Works for ac theory. I say 'why' because I know 'how' it works - ie. how to do the transform.

I am puzzled that combinations of voltage waveforms, together with integrated and differentiated waveforms, can be combined, transformed to another space, manipulated and transformed back and that they successfully solve a circuit problem. The maths works, but why does the Physics?

On comments: I can see exp(-st) as an eigenfunction - it doesn't change with d/dt, its job seems to be to cause the transformed values to be finite.

The Gibbs distribution may be along the lines I was thinking - which is that perhaps that the transformed function is an encapsulation of the energy beneath the decaying exp(-st) voltage.

Stieltjes didn't take me anywhere towards an understanding.

"Laplace transform is closely related to the Fourier transform." Yes I understand that. Laplace just adds a real part to s and that causes a decay - the transformed value then occupies 2D in the W plane (real and imaginary axes).

You have given me more to think about, for which I am grateful, but it doesn't seem to be leading me to a physical reason for it's success.

After being on MathFlow the other day I was led to this which helped quite a bit:

John