The French mathematician Joseph Fourier addressed these questions in his The Analytical Theory of Heat (1822).
The equation was developed by the mathematician Baron Jean-Baptiste-Joseph Fourier and appeared in its final form in his 1822 book, The Analytical Theory of Heat.
Nowadays, trigonometric series solutions (12) are called Fourier series, after Joseph Fourier, who in 1822 published one of the great mathematical classics, The Analytical Theory of Heat.
The analytical theory of the neuroses is based upon three ground-pillars: the recognition of (1) "repression," of (2) the importance of the sexual instincts and of (3) "transference".
Comparisons with the analytical theory were also made.
In a word, the classic analytical theory is not applicable in this case.
Both the numerical and the analytical theory correspond quite well with obtained test results.
However, there is no rigorous analytical theory for this type of antenna.
We note that our analytical theory appropriately describes the increase of the mutual information for weak independent noise levels.
In analytical theory, Mill at first differed little from Ricardo, but in later editions of his Principles he came to modify those views.
An analytical theory of flame acceleration in cylindrical tubes with one end closed is developed.
