His studies were affected by the troubles of the Napoleonic era.

Duhamel's principle, a method of obtaining solutions to inhomogeneous linear evolution equations, is named after him.

He was primarily a mathematician but did studies on the mathematics of heat, mechanics, and acoustics.

[3] In 1853 he published about an early recording device he called a vibroscope.

Like other similar devices, the vibroscope was a type of measuring device similar to an oscilloscope, and could not play back the etchings it recorded.