Carl Neumann
Encyclopedia
Carl Gottfried Neumann was a German
mathematician
.
Neumann was born in Königsberg
, Prussia
, as the son of the mineralogist, physicist and mathematician Franz Ernst Neumann
(1798-1895), who was professor of mineralogy and physics at Königsberg University. Carl Neumann studied in Königsberg and Halle
and was a professor at the universities of Halle, Basel
, Tübingen, and Leipzig
.
Neumann worked on the Dirichlet principle
, and can be considered one of the initiators of the theory of integral equation
s. The Neumann series, which is analogous to the geometric series
but for infinite matrices
, is named after him.
Together with Alfred Clebsch
Neumann founded the mathematical research journal Mathematische Annalen
. He died in Leipzig.
The Neumann boundary condition
for certain types of ordinary and partial differential equation
s is named after him (Cheng and Cheng, 2005).
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Neumann was born in Königsberg
Königsberg
Königsberg was the capital of East Prussia from the Late Middle Ages until 1945 as well as the northernmost and easternmost German city with 286,666 inhabitants . Due to the multicultural society in and around the city, there are several local names for it...
, Prussia
Province of Prussia
The Province of Prussia was a province of the Kingdom of Prussia from 1829-1878 created out of the provinces of East Prussia and West Prussia....
, as the son of the mineralogist, physicist and mathematician Franz Ernst Neumann
Franz Ernst Neumann
Franz Ernst Neumann was a German mineralogist, physicist and mathematician.-Biography:Neumann was born in Joachimsthal, Margraviate of Brandenburg, located not far from Berlin. In 1815 he interrupted his studies at Berlin to serve as a volunteer in the Hundred Days against Napoleon, and was...
(1798-1895), who was professor of mineralogy and physics at Königsberg University. Carl Neumann studied in Königsberg and Halle
University of Halle-Wittenberg
The Martin Luther University of Halle-Wittenberg , also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg within Saxony-Anhalt, Germany...
and was a professor at the universities of Halle, Basel
University of Basel
The University of Basel is located in Basel, Switzerland, and is considered to be one of leading universities in the country...
, Tübingen, and Leipzig
University of Leipzig
The University of Leipzig , located in Leipzig in the Free State of Saxony, Germany, is one of the oldest universities in the world and the second-oldest university in Germany...
.
Neumann worked on the Dirichlet principle
Dirichlet problem
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation in the interior of a given region that takes prescribed values on the boundary of the region....
, and can be considered one of the initiators of the theory of integral equation
Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way...
s. The Neumann series, which is analogous to the geometric series
but for infinite matrices
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
, is named after him.
Together with Alfred Clebsch
Alfred Clebsch
Rudolf Friedrich Alfred Clebsch was a German mathematician who made important contributions to algebraic geometry and invariant theory. He attended the University of Königsberg and was habilitated at Berlin. He subsequently taught in Berlin and Karlsruhe...
Neumann founded the mathematical research journal Mathematische Annalen
Mathematische Annalen
Mathematische Annalen is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann...
. He died in Leipzig.
The Neumann boundary condition
Neumann boundary condition
In mathematics, the Neumann boundary condition is a type of boundary condition, named after Carl Neumann.When imposed on an ordinary or a partial differential equation, it specifies the values that the derivative of a solution is to take on the boundary of the domain.* For an ordinary...
for certain types of ordinary and partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s is named after him (Cheng and Cheng, 2005).
Works by Carl Neumann
- Das Dirichlet'sche Princip in seiner Anwendung auf die Riemann'schen Flächen (B. G. Teubner, Leipzig, 1865)
- Vorlesungen über Riemann's Theorie der Abel'schen Integrale (B. G. Teubner, 1865)
- Theorie der Bessel'schen functionen: ein analogon zur theorie der Kugelfunctionen (B. G. Teubner, 1867)
- Untersuchungen über das Logarithmische und Newton'sche potential (B. G. Teubner, 1877)
- Allgemeine Untersuchungen über das Newton'sche Princip der Fernwirkungen, mit besonderer Rücksicht auf die elektrischen Wirkungen (B. G. Teubner, 1896)
- Über die Methode des arithmetischen Mittels (S. Hirzel, Leipzig, 1887)
- Die elektrischen Kräfte (Teubner, 1873-1898)