80
1 Preliminaries
complex function theory, Fourier series, differential geometry, algebraic geometry
and theory of differential equations etc., and wrote the paper in physics. Proposed
the Riemann integral and founded the Riemannian geometry, the latter provided
the most appropriate mathematical tools for Einstein’s general theory of relativity.
The main works had Grundlagen für eine Allgemeine Theorie der Funktionen einer
Veränderlichen Complexen Grösse (1851), Partielle Differentialgleichungen und
deren Anwendung auf physikalische Fragen (1869) and Über Elliptische Funktionen
(1899) etc., published Bernhard Riemann’s Gesammelte Mathematische Werke und
Wissenchaftkicher Nachlass in 1876.
Du Bois-Reymond (Paul David Gustav, 1831.12.2–1889.4.7) German mathematician. Born in Berlin, died in Freiburg. Entered the University of Zürich to study
medicine in 1853, then transferred to the University of Könisberg to study mathematics and physics. Received a doctor’s degree in the University of Berlin in 1859.
Latter went to the liberal arts school of Friedrich-Werder in Berlin to teach. Taught
at the University of Heidelberg in 1865. From 1870 to 1874 served as a professor at
the University of Freiburg, from 1874 to 1884 served as a professor at the University
of Tübingen, from 1884 to 1889 served as a professor at the Technical University
of Berlin. Consolidation of the of the Mainly researched theory of differential equations, analysis, theory of real variable functions and variational methods, etc., made
a large contribution especially to the Fourier series and partial differential equations.
For the first time to classify the linear partial differential equations of second order by
characteristic line method, for the first time to prove the definite integral mean value
theorem in 1868. Put forward the embryonic form of measure concept and proposed
the term of integral equation in 1888. The works had De Aequilibrium Fluidorum
(1859), Über die Fourierschen Reihen (1873), Allgemeine Functionentheorie (1882)
and Über die Grundlagen der Erkenntnis in den exacten Wissenschaften (1890) etc.
Schwarz (Karl Hermann Amandus, 1843.1.25–1921.11.30) German mathematician.
born in Hermsdorf, died in Berlin. Was graduated from Technical University of
Berlin in 1864, got a Ph.D. degree. Served as a professor at the University of Halle
in 1867. Served as a professor at the Swiss Federal Institute of Zürich in 1869. Took
charge of the mathematics lecture of University of Göttingen. Served as a professor
at the University if Berlin in 1892. The academician of the French Academy of
Sciences, the Berlin Academy of Sciences and the Bavarian Academy of Sciences.
The mathematical achievement mainly involved the analysis, theory of differential
equation, geometry and variational methods etc., made outstanding contribution to
the study of minimal surface. The inequality named after his name is often used in
mathematics. Presented the strict theory of Poisson integral. Introduced the special
function in terms of analytic theory of differential equations, later it was called the
Schwarz function. In 1873, proved the mixed derivative equation for the first time.
In the study of angle-preserving mapping, gave the generally analytical formula that
an arbitrary polygon is transformed to the function of the half plane. The works had
Bestimmung einer speziellen Minimalfläche (1871) and Gesammelte Mathematische
Abhandlungen (two volumes, 1890).
1 Preliminaries
complex function theory, Fourier series, differential geometry, algebraic geometry
and theory of differential equations etc., and wrote the paper in physics. Proposed
the Riemann integral and founded the Riemannian geometry, the latter provided
the most appropriate mathematical tools for Einstein’s general theory of relativity.
The main works had Grundlagen für eine Allgemeine Theorie der Funktionen einer
Veränderlichen Complexen Grösse (1851), Partielle Differentialgleichungen und
deren Anwendung auf physikalische Fragen (1869) and Über Elliptische Funktionen
(1899) etc., published Bernhard Riemann’s Gesammelte Mathematische Werke und
Wissenchaftkicher Nachlass in 1876.
Du Bois-Reymond (Paul David Gustav, 1831.12.2–1889.4.7) German mathematician. Born in Berlin, died in Freiburg. Entered the University of Zürich to study
medicine in 1853, then transferred to the University of Könisberg to study mathematics and physics. Received a doctor’s degree in the University of Berlin in 1859.
Latter went to the liberal arts school of Friedrich-Werder in Berlin to teach. Taught
at the University of Heidelberg in 1865. From 1870 to 1874 served as a professor at
the University of Freiburg, from 1874 to 1884 served as a professor at the University
of Tübingen, from 1884 to 1889 served as a professor at the Technical University
of Berlin. Consolidation of the of the Mainly researched theory of differential equations, analysis, theory of real variable functions and variational methods, etc., made
a large contribution especially to the Fourier series and partial differential equations.
For the first time to classify the linear partial differential equations of second order by
characteristic line method, for the first time to prove the definite integral mean value
theorem in 1868. Put forward the embryonic form of measure concept and proposed
the term of integral equation in 1888. The works had De Aequilibrium Fluidorum
(1859), Über die Fourierschen Reihen (1873), Allgemeine Functionentheorie (1882)
and Über die Grundlagen der Erkenntnis in den exacten Wissenschaften (1890) etc.
Schwarz (Karl Hermann Amandus, 1843.1.25–1921.11.30) German mathematician.
born in Hermsdorf, died in Berlin. Was graduated from Technical University of
Berlin in 1864, got a Ph.D. degree. Served as a professor at the University of Halle
in 1867. Served as a professor at the Swiss Federal Institute of Zürich in 1869. Took
charge of the mathematics lecture of University of Göttingen. Served as a professor
at the University if Berlin in 1892. The academician of the French Academy of
Sciences, the Berlin Academy of Sciences and the Bavarian Academy of Sciences.
The mathematical achievement mainly involved the analysis, theory of differential
equation, geometry and variational methods etc., made outstanding contribution to
the study of minimal surface. The inequality named after his name is often used in
mathematics. Presented the strict theory of Poisson integral. Introduced the special
function in terms of analytic theory of differential equations, later it was called the
Schwarz function. In 1873, proved the mixed derivative equation for the first time.
In the study of angle-preserving mapping, gave the generally analytical formula that
an arbitrary polygon is transformed to the function of the half plane. The works had
Bestimmung einer speziellen Minimalfläche (1871) and Gesammelte Mathematische
Abhandlungen (two volumes, 1890).