190
2 Variational Problems with Fixed Boundaries
told him written by John Bernoulli in 1694, namely found the limit rule of a fraction when its numerator and denominator are both tending to zero, later it is called
the L’Hospital rule. There were the articles on geometry, algebra and mechanics
aspect. His posthumous manuscript was compiled into Traité analytique des sections
coniques et de leur usage pour la résolution des équations dans les problêmes tant
déterminés qu’indéterminés (Analytic treatise on conic sections, 1707, 1720).
Bernoulli (Johann, 1667.8.6–1748.1.1) Swiss mathematician and mechanician. Born
and died in Basel. Studied at University of Basel in 1683, received a master’s degree
in art in 1685, took a master’s degree in medicine in 1690, obtained a doctor’s degree
in medicine at the University of Basel in 1694. Served as a mathematical physics
professor at the University of Groningen Dutch in 1695. Served as a professor at the
University of Basel in 1705. Became foreign academician of the French Academy of
Sciences in 1699, became a member of the Royal Society in 1712, become a foreign
academician of the Italian Bologna Academy of Sciences in 1724, Becoming an
honorary academician of Saint Petersburg Academy of Sciences in 1725. Because
of the research achievements in mechanics, got the award of the French Academy
of Sciences three times. In June 1696 in Acta Eruditorum to challenge all European mathematicians, Proposed the famous “brachistochrone problem”, played a
promoting role for the development of variational method, was acclaimed as one of
the pioneers of the calculus of variations. Had achieved important results in calculus,
theory of differential equations, calculus of variations, geometry and mechanics etc.
aspects. The work had the book Lections Mathematies de Method Integralium (1742).
Euler (Léonhard, 1707.4.15–1783.9.18) Swiss mathematician, physicist, astronomer
and mechanician, the founder of the theoretical fluid dynamics, one of the founders
of the Berlin Academy of Sciences. Born in Basel, died in Saint Petersburg, Russian
Empire. Entered the University of Basel in 1720, to study under John Bernoulli.
received a master’s degree in 1723. Was elected the academician of the Saint Petersburg Academy of Sciences in 1733. In 1774, published the research achievements
of the variational problems in the book Methodus inveniendi lineas curvas maximi
minimive proprietate gaudentes, sive solutio problematis isoperimetrici latissimo
sensu accepti, thus founded the calculus of variations. In almost all the most important branches of mathematics, had his pioneering contributions, also used mathematics to almost the entire physical field. Was one of the most prominent figures in
the 18th century, Historians had listed him with Archimedes, Newton, Gauss as the
four mathematicians of the largest contribution in human history, was acclaimed as
a hero for mathematician. Published over 800 papers, there were Leonhardi Euleri
Opera Omnia 74 volumes. Was blind in his old age. Laplace once said: “Read Euler,
read Euler, he is the master of us all.”
Clairaut (Alexis Claude, 1713.5.13(7)–1765.5.17) French mathematician and
astronomer and geophysicist. Born and died in Paris. He was a child prodigy, at
the age of ten had read through L’Hospital’s Analyse des Infiniment Petits. Published
a book about the Recherches sur les courbes á double courbure in 1831, became a
member of the French Academy of Sciences in the same year. Became a member
of the Royal Society in 1737. In mathematics, established the total differential of
binary function, the general solution and special solution of first order differential
2 Variational Problems with Fixed Boundaries
told him written by John Bernoulli in 1694, namely found the limit rule of a fraction when its numerator and denominator are both tending to zero, later it is called
the L’Hospital rule. There were the articles on geometry, algebra and mechanics
aspect. His posthumous manuscript was compiled into Traité analytique des sections
coniques et de leur usage pour la résolution des équations dans les problêmes tant
déterminés qu’indéterminés (Analytic treatise on conic sections, 1707, 1720).
Bernoulli (Johann, 1667.8.6–1748.1.1) Swiss mathematician and mechanician. Born
and died in Basel. Studied at University of Basel in 1683, received a master’s degree
in art in 1685, took a master’s degree in medicine in 1690, obtained a doctor’s degree
in medicine at the University of Basel in 1694. Served as a mathematical physics
professor at the University of Groningen Dutch in 1695. Served as a professor at the
University of Basel in 1705. Became foreign academician of the French Academy of
Sciences in 1699, became a member of the Royal Society in 1712, become a foreign
academician of the Italian Bologna Academy of Sciences in 1724, Becoming an
honorary academician of Saint Petersburg Academy of Sciences in 1725. Because
of the research achievements in mechanics, got the award of the French Academy
of Sciences three times. In June 1696 in Acta Eruditorum to challenge all European mathematicians, Proposed the famous “brachistochrone problem”, played a
promoting role for the development of variational method, was acclaimed as one of
the pioneers of the calculus of variations. Had achieved important results in calculus,
theory of differential equations, calculus of variations, geometry and mechanics etc.
aspects. The work had the book Lections Mathematies de Method Integralium (1742).
Euler (Léonhard, 1707.4.15–1783.9.18) Swiss mathematician, physicist, astronomer
and mechanician, the founder of the theoretical fluid dynamics, one of the founders
of the Berlin Academy of Sciences. Born in Basel, died in Saint Petersburg, Russian
Empire. Entered the University of Basel in 1720, to study under John Bernoulli.
received a master’s degree in 1723. Was elected the academician of the Saint Petersburg Academy of Sciences in 1733. In 1774, published the research achievements
of the variational problems in the book Methodus inveniendi lineas curvas maximi
minimive proprietate gaudentes, sive solutio problematis isoperimetrici latissimo
sensu accepti, thus founded the calculus of variations. In almost all the most important branches of mathematics, had his pioneering contributions, also used mathematics to almost the entire physical field. Was one of the most prominent figures in
the 18th century, Historians had listed him with Archimedes, Newton, Gauss as the
four mathematicians of the largest contribution in human history, was acclaimed as
a hero for mathematician. Published over 800 papers, there were Leonhardi Euleri
Opera Omnia 74 volumes. Was blind in his old age. Laplace once said: “Read Euler,
read Euler, he is the master of us all.”
Clairaut (Alexis Claude, 1713.5.13(7)–1765.5.17) French mathematician and
astronomer and geophysicist. Born and died in Paris. He was a child prodigy, at
the age of ten had read through L’Hospital’s Analyse des Infiniment Petits. Published
a book about the Recherches sur les courbes á double courbure in 1831, became a
member of the French Academy of Sciences in the same year. Became a member
of the Royal Society in 1737. In mathematics, established the total differential of
binary function, the general solution and special solution of first order differential