Soft question - Laplace transformation historical development

Question

This is a soft question

I'm looking for a book that explains in detail at least some of this points regarding Laplace transform:

• Motivations that led to the development of the transform.
• Detailed proof of the theorem.
• Why it can be used to transform a function from contínuos time to discrete time and back.
• Some physical intuition regarding the transform.

I know Laplace transformation is special case of Fourier transformation so any recommendation about the later will be appreciated.

Answer 1

• The development of the Laplace transform, 1737–1937
• The development of the Laplace Transform, 1737–1937 II. Poincaré to Doetsch, 1880–1937
• The ascendancy of the Laplace transform and how it came about