Carle David Tolmé Runge
Encyclopedia
Carl David Tolmé Runge (ˈʁʊŋə; 1856–1927) was a German mathematician
, physicist
, and spectroscopist.
He was co-developer and co-eponym
of the Runge–Kutta method , in the field of what is today known as numerical analysis
.
, where his father Julius Runge was the Danish consul. The family later moved to Bremen, where his father died early (in 1864).
In 1880, he received his Ph.D. in mathematics at Berlin
, where he studied under Karl Weierstrass
. In 1886, he became a professor in Hannover, Germany
.
His interests included mathematics, spectroscopy
, geodesy
, and astrophysics
. In addition to pure mathematics, he did a great deal of experimental work studying spectral line
s of various elements (together with Heinrich Kayser
), and was very interested in the application of this work to astronomical spectroscopy
.
In 1904, on the initiative of Felix Klein
he received a call to the Georg-August University of Göttingen
, which he accepted. There he remained until his retirement in 1925.
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....
, physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, and spectroscopist.
He was co-developer and co-eponym
Eponym
An eponym is the name of a person or thing, whether real or fictitious, after which a particular place, tribe, era, discovery, or other item is named or thought to be named...
of the Runge–Kutta method , in the field of what is today known as numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
.
Biography
He spent the first few years of his life in HavanaHavana
Havana is the capital city, province, major port, and leading commercial centre of Cuba. The city proper has a population of 2.1 million inhabitants, and it spans a total of — making it the largest city in the Caribbean region, and the most populous...
, where his father Julius Runge was the Danish consul. The family later moved to Bremen, where his father died early (in 1864).
In 1880, he received his Ph.D. in mathematics at Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
, where he studied under Karl Weierstrass
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass was a German mathematician who is often cited as the "father of modern analysis".- Biography :Weierstrass was born in Ostenfelde, part of Ennigerloh, Province of Westphalia....
. In 1886, he became a professor in Hannover, Germany
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...
.
His interests included mathematics, spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
, geodesy
Geodesy
Geodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...
, and astrophysics
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
. In addition to pure mathematics, he did a great deal of experimental work studying spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...
s of various elements (together with Heinrich Kayser
Heinrich Kayser
Heinrich Gustav Johannes Kayser was a German physicist.He was born at Bingen am Rhein. Kayser's early work was concerned with the characteristics of acoustic waves. He discovered the occurrence of helium in the Earth's atmosphere. Together with Carl Runge, he examined the spectra of chemical...
), and was very interested in the application of this work to astronomical spectroscopy
Astronomical spectroscopy
Astronomical spectroscopy is the technique of spectroscopy used in astronomy. The object of study is the spectrum of electromagnetic radiation, including visible light, which radiates from stars and other celestial objects...
.
In 1904, on the initiative of Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
he received a call to the Georg-August University of Göttingen
Georg-August University of Göttingen
The University of Göttingen , known informally as Georgia Augusta, is a university in the city of Göttingen, Germany.Founded in 1734 by King George II of Great Britain and the Elector of Hanover, it opened for classes in 1737. The University of Göttingen soon grew in size and popularity...
, which he accepted. There he remained until his retirement in 1925.
See also
- Runge's phenomenonRunge's phenomenonIn the mathematical field of numerical analysis, Runge's phenomenon is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree...
- Runge's method for diophantine equationDiophantine equationIn mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations...
s. - Laplace–Runge–Lenz vector
Works
- Ueber die Krümmung, Torsion und geodätische Krümmung der auf einer Fläche gezogenen Curven (PhD dissertation, Friese, 1880)
- Analytische Geometrie der Ebene (B.G. Teubner, Leipzig, 1908)
- Graphical methods; a course of lectures delivered in Columbia university, New York, October, 1909, to January, 1910 (Columbia University Press, New York, 1912)
- Carl Runge und Hermann König Vorlesungen über numerisches Rechnen (Springer, Heidelberg, 1924)
- Graphische Methoden (Teubner, 1928)