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Johann Friedrich Pfaff
Johann Friedrich Pfaff (sometimes spelled Friederich; 22 December 1765 – 21 April 1825) was a German mathematician. He was described as one of Germany's most eminent mathematicians during the 19th century. He was a precursor of the German school of mathematical thinking, which under Carl Friedrich Gauss and his followers largely determined the lines on which mathematics developed during the 19th century. Biography He received his early education at the Carlsschule, where he met Friedrich Schiller, his lifelong friend. His mathematical capacity was noticed during his early years. He pursued his studies at Göttingen under Abraham Gotthelf Kästner, and in 1787 he went to Berlin and studied practical astronomy under J. E. Bode. In 1788, Pfaff became professor of mathematics in Helmstedt, and continued his work as a professor until that university was abolished in 1810. After this event, he became professor of mathematics at the University of Halle, where he stayed for the rest of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stuttgart
Stuttgart (; Swabian: ; ) is the capital and largest city of the German state of Baden-Württemberg. It is located on the Neckar river in a fertile valley known as the ''Stuttgarter Kessel'' (Stuttgart Cauldron) and lies an hour from the Swabian Jura and the Black Forest. Stuttgart has a population of 635,911, making it the sixth largest city in Germany. 2.8 million people live in the city's administrative region and 5.3 million people in its metropolitan area, making it the fourth largest metropolitan area in Germany. The city and metropolitan area are consistently ranked among the top 20 European metropolitan areas by GDP; Mercer listed Stuttgart as 21st on its 2015 list of cities by quality of living; innovation agency 2thinknow ranked the city 24th globally out of 442 cities in its Innovation Cities Index; and the Globalization and World Cities Research Network ranked the city as a Beta-status global city in their 2020 survey. Stuttgart was one of the host cities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pfaffian Function
In mathematics, Pfaffian functions are a certain class of functions whose derivative can be written in terms of the original function. They were originally introduced by Askold Khovanskii in the 1970s, but are named after German mathematician Johann Pfaff. Basic definition Some functions, when differentiated, give a result which can be written in terms of the original function. Perhaps the simplest example is the exponential function, ''f''(''x'') = ''e''''x''. If we differentiate this function we get ''ex'' again, that is :f^\prime(x) = f(x). Another example of a function like this is the reciprocal function, ''g''(''x'') = 1/''x''. If we differentiate this function we will see that :g^\prime(x) = -g(x)^2. Other functions may not have the above property, but their derivative may be written in terms of functions like those above. For example, if we take the function ''h''(''x'') = ''e''''x'' log(''x'') then we see :h^\prime(x) = e^x\log x+x^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Form
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For instance, the expression is an example of a -form, and can be integrated over an interval contained in the domain of : :\int_a^b f(x)\,dx. Similarly, the expression is a -form that can be integrated over a surface : :\int_S (f(x,y,z)\,dx\wedge dy + g(x,y,z)\,dz\wedge dx + h(x,y,z)\,dy\wedge dz). The symbol denotes the exterior product, sometimes called the ''wedge product'', of two differential forms. Likewise, a -form represents a volume element that can be integrated over a region of space. In general, a -form is an object that may be integrated over a -dimensional manifold, and is homogeneous of degree in the coordinate differentials dx, dy, \ldots. On an -dimensional manifold, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to Numerical methods for partial differential equations, numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematics, pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Calculus
In mathematics, an integral assigns numbers to Function (mathematics), functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are posi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Series
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance. For a long time, the idea that such a potentially infinite summation could produce a finite result was considered paradoxical. This paradox was resolved using the concept of a limit during the 17th century. Zeno's paradox of Achilles and the tortoise illustrates this counterintuitive property of infinite sums: Achilles runs after a tortoise, but when he reaches the position of the tortoise at the beginning of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Halle
Martin Luther University of Halle-Wittenberg (german: Martin-Luther-Universität Halle-Wittenberg), also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg and the largest and oldest university in the German state of Saxony-Anhalt. MLU offers German and international (English) courses leading to academic degrees such as BA, BSc, MA, MSc, doctoral degrees, and Habilitation. The university was created in 1817 through the merger of the University of Wittenberg (founded in 1502) and the University of Halle (founded in 1694). MLU is named after Protestant reformer Martin Luther, who was a professor in Wittenberg. Today, the university campus is located in Halle, while ''Leucorea Foundation'' in Wittenberg serves as MLU's convention centre. Both Halle and Wittenberg are about one hour from Berlin via the Berlin–Halle railway, which offers Intercity-Express (ICE) trains. History University of Wittenberg (''Universität Wittenbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmstedt
Helmstedt (; Eastphalian: ''Helmstidde'') is a town on the eastern edge of the German state of Lower Saxony. It is the capital of the District of Helmstedt. The historic university and Hanseatic city conserves an important monumental heritage of Romanesque and Renaissance buildings, as well as numerous timber framed houses. During the German partition the nearby Bundesautobahn 2 was the site of the Helmstedt–Marienborn border crossing, the most important on the former inner German border as starting point of the shortest land route between West Germany and West Berlin. Geography Helmstedt is situated in a basin between the Elm and Lappwald hill ranges, at the transition area between the northern foothills of the Harz mountains and the North German Plain. It is surrounded by the Elm-Lappwald Nature Park. The town centre is located about east of Braunschweig, west of Magdeburg, and east of the state capital Hanover. The municipal area includes the localities of Barmke and E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. Due to its l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Gotthelf Kästner
Abraham Gotthelf Kästner (27 September 1719 – 20 June 1800) was a German mathematician and epigrammatist. He was known in his professional life for writing textbooks and compiling encyclopedias rather than for original research. Georg Christoph Lichtenberg was one of his doctoral students, and admired the man greatly. He became most well known for his epigrammatic poems. The crater Kästner on the Moon is named after him. Life Kästner was the son of law professor Abraham Kästner. He married Anna Rosina Baumann in 1757 after a 12-year engagement. She died on 4 March 1758, less than a year later, of a lung disease. Later Kästner had a daughter Catharine with his cleaning lady. Kästner studied law, philosophy, physics, mathematics and metaphysics in Leipzig from 1731, and was appointed a Notary in 1733. He gained his habilitation from the University of Leipzig in 1739, and lectured there in mathematics, philosophy, logic and law, becoming an associate professor in 17 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Schiller
Johann Christoph Friedrich von Schiller (, short: ; 10 November 17599 May 1805) was a German playwright, poet, and philosopher. During the last seventeen years of his life (1788–1805), Schiller developed a productive, if complicated, friendship with the already famous and influential Johann Wolfgang von Goethe. They frequently discussed issues concerning aesthetics, and Schiller encouraged Goethe to finish works that he had left as sketches. This relationship and these discussions led to a period now referred to as Weimar Classicism. They also worked together on ''Xenien'', a collection of short satirical poems in which both Schiller and Goethe challenge opponents of their philosophical vision. Early life and career Friedrich Schiller was born on 10 November 1759, in Marbach, Württemberg, as the only son of military doctor Johann Kaspar Schiller (1733–1796) and Elisabetha Dorothea Schiller (1732–1802). They also had five daughters, including Christophine, the eldest. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carlsschule
Hohe Karlsschule (''Karl's High School'') was the strict military academy founded by Karl Eugen, Duke of Württemberg in Stuttgart, Germany. It was first founded in 1770 as a military orphanage, but then converted into a military academy in 1773 for the duke. Politically the duke was quite unimportant and with this school he wanted to enhance his prestige. In 1770, it was moved to Castle Solitude, and in 1775 into the city. Raised in 1781 by Emperor Joseph II to university status under the name ''Karls Hohe Schule'', it was disbanded after the death of Duke Carl Eugen by his brother Ludwig Eugen, Duke of Württemberg in 1794. The building, situated behind Neues Schloss, was destroyed in World War II. Alumni Friedrich Schiller was one of its alumni.Barbara Schubert-Felmy, ''Die Räuber und andere Räubergeschichten'', Schöningh, 1999. . p. 217. He spent eight years of his life in this academy and suffered a lot in his first years of his stay. At first he was considered an averag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
