What are interpolationand extrapolation?
Interpolation in mathematics involves finding a value (or outcome) of a function
between already known values; in other words, it is a method of estimating the values
in between sampled data points. Extrapolation in mathematics is estimating the value
of a problem beyond the range covered by the existing data. Both methods are used a
great deal in engineering.What is a Fourier series?
The idea for the Fourier series was developed by French mathematician and physicist
Baron Jean Baptiste Joseph Fourier (1768–1830) as an alternate method of expressing
324 a function by the expansion of the function. A Fourier series is actually a specific type
What are some details of Jean Baptiste Fourier’s life?
T
he accomplishments of French mathematician and physicist Baron Jean Bap-
tiste Joseph Fourier (1768–1830) prove that not all famous mathematicians
did just math. Fourier was a teacher, became involved in the messy French Rev-
olution, and was arrested for his views and imprisoned in 1794. For a time, he
even feared the guillotine, but political changes resulted in Fourier being freed.
By 1798 Fourier joined Napoleon’s army in its invasion of Egypt as a scientific
adviser. After Napoleon lost the Battle of the Nile to Nelson and was confined to
Malta, Fourier continued his work in Egypt, establishing educational facilities
there and carrying out archeological explorations. Back in France with Napoleon
in 1801, he supervised the draining of the swamps of Bourgoin and the con-
struction of a highway from Grenoble to Turin. He also spent time writing
Description of Egypt,a book that Napoleon edited, and included some historical
rewrites (by the second edition of the book, Napoleon himself would be com-
pletely edited out of the text).
As if he wasn’t busy enough, during this time Fourier wrote his now-famous
1807 paper, On the Propagation of Heat in Solid Bodies,a mathematical work
on the theory of heat that presented one of his major contributions: the Fourier
series. But it was an uphill battle to get approval from his peers. In 1811 he sub-
mitted his 1807 ideas for a mathematics prize, along with additional work on the
cooling of infinite solids and on terrestrial and radiant heat. Only one other
entry was received, making Fourier’s work the obvious winner. Finally, by 1822,
he published his 1811 essay, making the techniques of Fourier analysis available
to everyone. To this day, the functions that he worked out have a multitude of
applications in engineering, science, and mathematics.