ME 201/MTH 281/ME 400/CHE 400
Links to Other Web Sites
Friedrich Wilhelm Bessel (1784 - 1846)
The links below give information on some of the mathematicians who played an important role in the development of this subject. The links are to biographies on the St. Andrews web site for the history of mathematics.
Joseph Fourier - Fourier is the discoverer of the fundamental ideas on which our course is based. Like many pioneers, he had severe critics, but his work has long outlived them.
Lord Kelvin - Lord Kelvin was a pioneer in the use of mathematical models to elucidate earth science. He also did work of major importance in thermodynamics and in electricity and magnetism. He was knighted for his successful work on the first transatlantic telegraph cable.
J. Willard Gibbs - Gibbs was one of the first great American theoretical physicists, and he is known for his work in thermodynamics and statistical mechanics. He was also a major contributor to the development of vector calculus. In our course, we encounter him through his explanation of the persistent oscillatory overshoots of Fourier series near discontinuities.
Friedrich Wilhelm Bessel - Bessel's accomplishments were major and diverse. He was one of the founding pioneers of precision measurements of stellar positions. He was one of the first to tackle the notoriously difficult three-body problem in gravitational theory. His now famous differential equation arose from his work on planetary perturbations.
Adrien-Marie Legendre - Legendre's long career included much work on number theory and on elliptic functions. The polynomials encountered in our course and named for him arose in his studies of the gravitational field of ellipsoids.
Augustin Louis Cauchy - Cauchy was one of the founders of modern analysis. His 789 papers dealt with most areas of mathematics known at the time of his work. He did not accept much of Fourier's work, and although Fourier was right, it took the mathematical community nearly a half-century to put it all on a rigorous foundation.
Johann Peter Gustav Lejeune Dirichlet - Dirchlet's interests included number theory (he proved the special case of n = 5 for Fermat's Last Theorem), potential theory, and Fourier series. He gave the first satisfactory proof of the convergence of Fourier series.
Jacques Charles Francois Sturm - Sturm worked on a variety of problems in differential equations and geometry. His famous work on eigenvalue problems with Liouville was done in 1836-1837.
Joseph Louiville - Louiville worked on problems in mathematics and physics. His name survives in a famous theorem about volumes in Hamiltonian phase spaces, and in his work with Sturm.
Marc-Antoine Parseval des Chênes - Not much is known about Parseval's life. The theorem which we now call Parseval's theorem was created in a context other than Fourier series (it was created at about the time Fourier's work was just becoming known).
ARTICLES OF INTEREST
Fourier's Series: The Genesis and Evolution of a Theory by R. E. Langer. This long and very detailed article, by a prominent mathematician of the mid-20th century, appeared in the American Mathematical Monthly, Volume 54, No. 7, Part II, 1947. Of Fourier, Langer said, "It was, no doubt, partially because of his very disregard for rigor that he was able to take conceptual steps which were inherently impossible to men of more critical genius."
Connections in Mathematical Analysis: The Case of Fourier Series by Enrique A. Gonzalez-Velasco. This very interesting article appeared in the American Mathematical Monthly, Vol. 99, No. 5, pp. 427-441, 1992. The article traces the connection between Fourier Series and the development of many important mathematical ideas in 19th century.
The links here are to downloadable versions on the JSTOR web site.
DEMOS ON THE WEB
There are a large number of Mathematica demos on the web site Wolfram Demonstrations Project. The URL is given below.
Once you get to the site, do a search on Fourier Analysis.