Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. He started the project of formulating and proving the theorems of calculus in a rigorous manner and was thus an early pioneer of analysis. He also gave several important theorems in complex analysis and initiated the study of permutation groups. A profound mathematician, Cauchy exercised by his perspicuous and rigorous methods a great influence over his contemporaries and successors. His writings cover the entire range of mathematics and mathematical physics. Image File history File links This page is a candidate for speedy deletion. ...
August 21 is the 233rd day of the year (234th in leap years) in the Gregorian calendar. ...
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May 23 is the 143rd day of the year in the Gregorian calendar (144th in leap years). ...
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Calculus [from Latin, literally pebble (used in reckoning)] is a major area in mathematics, with applications in science, engineering, business, and medicine. ...
The Ã‰cole Nationale des Ponts et ChaussÃ©es (ENPC) (National school of Bridges and Roads), often referred to as les Ponts, is the worlds oldest engineering school and remains to this day one of the most prestigious French Grandes Ã‰coles of engineering. ...
Logo The Arms of the Ã‰cole Polytechnique The cadets of Polytechnique rushed to the defense of Paris against the foreign armies in 1814. ...
The Ã‰cole Nationale des Ponts et ChaussÃ©es (ENPC) (National school of Bridges and Roads), often referred to as les Ponts, is the worlds oldest engineering school and remains to this day one of the most prestigious French Grandes Ã‰coles of engineering. ...
In mathematics, the Cauchy integral theorem in complex analysis, named after Augustin Louis Cauchy, is an important statement about path integrals for holomorphic functions in the complex plane. ...
August 21 is the 233rd day of the year (234th in leap years) in the Gregorian calendar. ...
1789 was a common year starting on Thursday (see link for calendar). ...
May 23 is the 143rd day of the year in the Gregorian calendar (144th in leap years). ...
1857 was a common year starting on Thursday (see link for calendar). ...
Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ...
Calculus [from Latin, literally pebble (used in reckoning)] is a major area in mathematics, with applications in science, engineering, business, and medicine. ...
Analysis is the branch of mathematics most explicitly concerned with the notion of a limit, either the limit of a sequence or the limit of a function. ...
Complex analysis is the branch of mathematics investigating functions of complex numbers, and is of enormous practical use in many branches of mathematics, including applied mathematics. ...
In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself); the relationship is often written as (G,M). ...
Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories1. ...
Biography
Having received his early education from his father Louis François Cauchy (1760–1848), who held several minor public appointments and counted Lagrange and Laplace among his friends, Cauchy entered the École Centrale du Panthéon in 1802, and proceeded to the École Polytechnique in 1805, and to the École Nationale des Ponts et Chaussées in 1807. Having adopted the profession of an engineer, he left Paris for Cherbourg in 1810, but returned in 1813 on account of his health, whereupon Lagrange and Laplace persuaded him to renounce engineering and to devote himself to mathematics. He obtained an appointment at the École Polytechnique, which, however, he relinquished in 1830 on the accession of LouisPhilippe. He did this because he found it impossible to take the necessary oaths to the new government as he remained loyal to the House of Bourbon. A short sojourn at Fribourg in Switzerland was followed by his appointment in 1831 to the newlycreated chair of mathematical physics at the University of Turin. (Note: At that time, Turin was the capital of the Kingdom of Sardinia, which unified Italy in later history. Now Turin is just a city in northern Italy.) Louis FranÃ§ois Cauchy (17601848) was a senior French government official and the father of the mathematician Augustin Louis Cauchy. ...
1760 was a leap year starting on Tuesday (see link for calendar). ...
Year 1848 (MDCCCXLVIII) was a leap year starting on Saturday (link will display the full calendar) of the Gregorian Calendar (or a leap year starting on Monday of the 12day slower Julian calendar). ...
JosephLouis Lagrange, comte de lEmpire (January 25, 1736 â€“ April 10, 1813; b. ...
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Logo The Arms of the Ã‰cole Polytechnique The cadets of Polytechnique rushed to the defense of Paris against the foreign armies in 1814. ...
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The Ã‰cole Nationale des Ponts et ChaussÃ©es (ENPC) (National school of Bridges and Roads), often referred to as les Ponts, is the worlds oldest engineering school and remains to this day one of the most prestigious French Grandes Ã‰coles of engineering. ...
Year 1807 (MDCCCVII) was a common year starting on Thursday (link will display the full calendar). ...
Engineering is the design, analysis, and/or construction of works for practical purposes. ...
City flag City coat of arms Motto: Fluctuat nec mergitur (Latin: Tossed by the waves, she does not sink) Paris Eiffel tower as seen from the esplanade du TrocadÃ©ro. ...
CherbourgOcteville is a town and commune in Normandy, northwest France. ...
1810 was a common year starting on Monday (see link for calendar). ...
Year 1813 (MDCCCXIII) was a common year starting on Friday (link will display the full calendar). ...
Liberty Leading the People by EugÃ¨ne Delacroix commemorates the July Revolution 1830 (MDCCCXXX) was a common year starting on Friday (see link for calendar). ...
LouisPhilippe, King of the French (October 6, 1773 â€“ August 26, 1850) reigned as the OrlÃ©anist king of the French from 1830 to 1848. ...
Also see: Early Modern France The House of Bourbon is an important European royal house. ...
Fribourg (French; German: Freiburg or Freiburg im Ãœechtland, often Fribourg) is a city in the country of Switzerland and the capital of the Swiss Canton of Fribourg on the river Sarine/Saane. ...
Leopold I 1831 (MDCCCXXXI) was a common year starting on Saturday (see link for calendar). ...
The University of Turin (Italian UniversitÃ degli Studi di Torino, UNITO) is the university of Turin in the Piedmont region of northwestern Italy. ...
In 1833 the deposed king Charles X of France summoned Cauchy to be tutor to his grandson, the duke of Bordeaux, an appointment which enabled Cauchy to travel and thereby become acquainted with the favourable impression which his investigations had made. Charles created him a baron in return for his services. Returning to Paris in 1838, Cauchy refused a proffered chair at the Collège de France, but in 1848, the oath having been suspended, he resumed his post at the École Polytechnique, and when the oath was reinstituted after the coup d'état of 1851, Cauchy and François Arago were exempted from it. Subequently, Cauchy lived in the France ruled by the emperor Napoleon III until his death in 1857. 1833 was a common year starting on Tuesday (see link for calendar). ...
Charles X (October 9, 1757 â€“ November 6, 1836) ruled as King of France and Navarre from 1824 until the French Revolution of 1830, when he abdicated rather than become a constitutional monarch. ...
This article or section does not cite its references or sources. ...
Baron is a specific title of nobility or a more generic feudal qualification. ...
 JÃ¶ns Jakob Berzelius, discoverer of protein 1838 was a common year starting on Monday (see link for calendar). ...
Courtyard of the CollÃ¨ge de France. ...
Year 1848 (MDCCCXLVIII) was a leap year starting on Saturday (link will display the full calendar) of the Gregorian Calendar (or a leap year starting on Monday of the 12day slower Julian calendar). ...
A coup dÃ©tat (pronounced ), or simply coup, is the sudden overthrow of a government through unconstitutional means by a part of the state establishment â€” mostly replacing just the highlevel figures. ...
1851 (MDCCCLI) was a common year starting on Wednesday (see link for calendar) of the Gregorian calendar (or a common year starting on Friday of the 12dayslower Julian calendar). ...
FranÃ§ois Arago FranÃ§ois Jean Dominique Arago (February 26, 1786 â€“ October 2, 1853) was a French mathematician, physicist, astronomer, and politician. ...
Charles Louis Napoléon Bonaparte (April 20, 1808  January 9, 1873) was the son of King Louis Bonaparte and Queen Hortense de Beauharnais; both monarchs of the French puppet state, the Kingdom of Holland. ...
Cauchy married Aloise de Bure in 1818. She was a close relative of a publisher who published most of Cauchy's works. Cauchy had two brothers: Alexandre Laurent Cauchy (1792–1857), who became a president of a division of the court of appeal in 1847, and a judge of the court of cassation in 1849; and Eugène François Cauchy (1802–1877), a publicist who also wrote several mathematical works. 1792 was a leap year starting on Sunday (see link for calendar). ...
1857 was a common year starting on Thursday (see link for calendar). ...
1847 was a common year starting on Friday (see link for calendar). ...
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1877 (MDCCCLXXVII) was a common year starting on Monday (see link for calendar). ...
Spoke fluent Tanzamanian.
Work The genius of Cauchy was illustrated in his simple solution of the problem of Apollonius, i.e. to describe a circle touching three given circles, which he discovered in 1805, his generalization of Euler's formula on polyhedra in 1811, and in several other elegant problems. More important is his memoir on wave propagation, which obtained the Grand Prix of the Institut in 1816. His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced. These are mainly embodied in his three great treatises, Cours d'analyse de l'École Polytechnique (1821); Le Calcul infinitésimal (1823); Leçons sur les applications de calcul infinitésimal; La géométrie (1826–1828); and also in his Courses of mechanics (for the École Polytechnique), Higher algebra (for the Faculté des Sciences), and of Mathematical physics (for the Collège de France). In mathematics, an Apollonian gasket or Apollonian net is a fractal generated from three circles, any two of which are tangent to one another. ...
Circle illustration This article is about the shape and mathematical concept of circle. ...
1805 was a common year starting on Tuesday (see link for calendar). ...
It has been suggested that Vertex/Face/Edge relation in a convex polyhedron be merged into this article or section. ...
In mathematics, there are three related meanings of the term polyhedron: in the traditional meaning it is a 3dimensional polytope, and in a newer meaning that exists alongside the older one it is a bounded or unbounded generalization of a polytope of any dimension. ...
1811 was a common year starting on Tuesday (see link for calendar). ...
This article is about waves in the most general scientific sense. ...
1816 was a leap year starting on Monday (see link for calendar). ...
Logo The Arms of the Ã‰cole Polytechnique The cadets of Polytechnique rushed to the defense of Paris against the foreign armies in 1814. ...
The coronation banquet for George IV 1821 was a common year starting on Monday (see link for calendar). ...
1823 was a common year starting on Wednesday (see link for calendar). ...
The oldest surviving photograph, NicÃ©phore NiÃ©pce, circa 1826 1826 (MDCCCXXVI) was a common year starting on Sunday (see link for calendar) of the Gregorian calendar (or a common year starting on Tuesday of the 12dayslower Julian calendar). ...
1828 was a leap year starting on Tuesday (see link for calendar). ...
His treatises and contributions to scientific journals (to the number of 789) contain investigations on the theory of series (where he developed with perspicuous skill the notion of convergency), on the theory of numbers and complex quantities, the theory of groups and substitutions, the theory of functions, differential equations and determinants. He clarified the principles of the calculus by developing them with the aid of limits and continuity, and was the first to prove Taylor's theorem rigorously, establishing his wellknown form of the remainder. In mechanics, he made many researches, substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. In optics, he developed the wave theory, and his name is associated with the simple dispersion formula. In elasticity, he originated the theory of stress, and his results are nearly as valuable as those of Simeon Poisson. In calculus, Taylors theorem, named after the mathematician Brook Taylor, who stated it in 1712, gives the approximation of a differentiable function near a point by a polynomial whose coefficients depend only on the derivatives of the function at that point. ...
Mechanics (Greek ) is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment. ...
Table of Opticks, 1728 Cyclopaedia Optics ( appearance or look in ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. ...
Elasticity has meanings in two different fields: In physics and mechanical engineering, the theory of elasticity describes how a solid object moves and deforms in response to external stress. ...
Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ...
Simeon Poisson. ...
As to a number of significant contributions, Cauchy was the first to prove the Fermat polygonal number theorem. He created the residue theorem and used it to derive a whole host of most interesting series and integral formulas and was the first to define complex numbers as pairs of real numbers. He also discovered many of the basic formulas in the theory of qseries. His collected works, Œuvres complètes d'Augustin Cauchy, have been published in 27 volumes. Every positive integer is a sum of at most polygonal numbers. ...
The residue theorem in complex analysis is a powerful tool to evaluate path integrals of meromorphic functions over closed curves and can often be used to compute real integrals as well. ...
In mathematics, a qseries, also sometimes called a qshifted factorial, is defined as It is usually considered first as a formal power series; it is also an analytic function of q, in the unit disc. ...
Although generally rigourous, he was way ahead of the rest of his field at the time, and thus one of his theorems was exposed to a "counterexample" by Abel, later fixed by the inclusion of uniform continuity. In a paper published in 1855, two years before his death, he discussed some theorems, one of which is similar to the "Argument Principle" in many modern textbooks on complex analysis. In modern control theory textbooks, the Cauchy argument principle is quite frequently used to derive the Nyquist stability criterion, which can be used to predict the stability of negative feedback amplifier and negative feedback control systems. Thus Cauchy's work has strong impact on both pure mathematics and practical engineering. The contour C (black), the zeros of f (blue) and the poles of f (red). ...
The Nyquist stability criterion, named for Harry Nyquist, provides a simple test for stability of a closedloop control system by examining the openloop systems Nyquist plot. ...
A feedback amplifier, also known as negative feedback amplifier is an amplifier which uses a feedback network, generally for improving performance (gain stability, linearity, frequency response etc. ...
It has been suggested that this article or section be merged with Feedback loop. ...
Politics and religious beliefs Augustin Louis Cauchy grew up in the house of a staunch royalist. This made his father flee with the family to Arcueil during the French Revolution. Their life there was apparently hard and Cauchy spoke of living on rice, bread, and crackers during the period. In any event he inherited his father's staunch royalism and hence refused to take oaths to any government after the overthrow of Charles X. Arcueil is a commune of the ValdeMarne dÃ©partement, in France. ...
The French Revolution (1789â€“1799) was a period of political and social upheaval in the political history of France and Europe as a whole, during which the French governmental structure, previously an absolute monarchy with feudal privileges for the aristocracy and Catholic clergy, underwent radical change to forms based on...
He was an equally staunch Catholic and a member of the Society of Saint Vincent de Paul.[1] He also had links to the Society of Jesus and defended them at the Academy when it was politically unwise to do so. His zeal for his faith may have led to his caring for Charles Hermite during his illness and leading Hermite to become a faithful Catholic. It also inspired Cauchy to plea on behalf of the Irish during the Potato Famine. The Society of Saint Vincent de Paul is an international organization of Roman Catholic lay men and women of all ages, whose primary mission is to help the poor and less fortunate. ...
Seal of the Society of Jesus. ...
Charles Hermite (pronounced in IPA, , or phonetically airmeet) (December 24, 1822  January 14, 1901) was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. ...
Potato famine may mean or refer to: The Irish Potato Famine (1845â€“1849) The Highland Potato Famine (1846  1857) The potato famines of the mid 19th century arose from an infestation of potato blight, Phytophthora infestans, which spread across Europe in the 1840s. ...
His royalism and religious zeal also made him contentious, which caused difficulties with his colleagues. He felt that he was mistreated for his beliefs, but his opponents felt he intentionally provoked people by berating them over religious matters or by defending the Jesuits after they had been suppressed. Niels Henrik Abel called him a "bigoted Catholic" and added he was "mad and there is nothing that can be done about him," but at the same time praised him as a mathematician. Cauchy's views were widely unpopular among mathematicians and when Guglielmo Libri Carucci dalla Sommaja was made chair in mathematics before him he, and many others, felt his views were the cause. When Libri was accused of stealing books he was replaced by Joseph Liouville which caused a rift between him and Cauchy. Another dispute concerned Jean Marie Constant Duhamel and a claim on inelastic shocks. Cauchy was later shown, by JeanVictor Poncelet, that he was in the wrong. Despite that Cauchy refused to concede this and nursed a bitterness on the whole issue. Niels Henrik Abel (August 5, 1802â€“April 6, 1829), Norwegian mathematician, was born in Nedstrand, near FinnÃ¸y where his father acted as rector. ...
Count Guglielmo Libri Carucci dalla Sommaja (born January 1, 1803 in Florence, Italy; died September 28, 1869, in Fiesole, Italy) was an Italian mathematician and a book thief. ...
Joseph Liouville (born March 24, 1809, died September 8, 1882) was a French mathematician. ...
JeanVictor Poncelet (July 1, 1788 – December 22, 1867) was a mathematician and engineer who did much to revive projective geometry. ...
His daughter indicated his last moments brought him a certain calm and that his final words were "Jesus, Mary, and Joseph." (For corroboration of claims here see the link to MacTutor History of Mathematics archive for his and Hermite's biographies) The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ...
See also In mathematics, the Cauchy integral theorem in complex analysis, named after Augustin Louis Cauchy, is an important statement about path integrals for holomorphic functions in the complex plane. ...
In mathematics, Cauchys integral formula, named after Augustin Louis Cauchy, is a central statement in complex analysis. ...
In mathematics, the CauchySchwarz inequality, also known as the Schwarz inequality, the Cauchy inequality, or the CauchyBunyakovskiSchwarz inequality, named after Augustin Louis Cauchy, Viktor Yakovlevich Bunyakovsky and Hermann Amandus Schwarz, is a useful inequality encountered in many different settings, such as linear algebra applied to vectors, in...
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Cauchys theorem is a theorem in geometry, named after Augustin Cauchy. ...
The CauchyLorentz distribution, named after Augustin Cauchy, is a continuous probability distribution with probability density function where x0 is the location parameter, specifying the location of the peak of the distribution, and Î³ is the scale parameter which specifies the halfwidth at halfmaximum (HWHM). ...
In mathematics, the Cauchy determinant in linear algebra, named after Augustin Cauchy, is the determinant of the complex nÃ—n matrix CM with entries for Here it is assumed that The explicit formula for the determinant is Example The determinant of the Hilbert matrix is the case xi = yi = i...
The Cauchy formula for repeated integration allows one to compress antidifferentiations of a function into a single integral. ...
In mathematical analysis, a Cauchy sequence, named after Augustin Cauchy, is a sequence whose elements become close as the sequence progresses. ...
In mathematics, the CauchyRiemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, are two partial differential equations which provide a necessary but not sufficient condition for a function to be holomorphic. ...
Burnsides lemma, sometimes also called Burnsides counting theorem, Polyas formula or CauchyFrobenius lemma, is a result in group theory which is often useful in taking account of symmetry when counting mathematical objects. ...
In mathematics, the Cauchy product, named in honor of Augustin Louis Cauchy, of two strictly formal (not necessarily convergent) series usually, of real or complex numbers, is defined by a discrete convolution as follows. ...
In mathematics, the Cauchy principal value of certain improper integrals is defined as either the finite number where b is a point at which the behavior of the function f is such that for any a < b and for any c > b (one sign is + and the other is âˆ’). or...
In linear algebra, the CauchyBinet formula generalizes the multiplicativity of the determinant (the fact that the determinant of a product of two square matrices is equal to the product of the two determinants) to non_square matrices. ...
In mathematics, a CauchyEuler equation (also EulerCauchy equation) is a secondorder ordinary differential equation of the form These differential equations have one relatively simple solution xÎ±. Observe Since xÎ± is zero only when x is zero for positive Î± (which corresponds to a trivial solution) and never zero...
A plot of refactive index vs. ...
Consider a smooth hypersurface having a continuous, nontangential direction field described by unitary vectors , i. ...
In physics, a Cauchy horizon is a light_like boundary of the domain of validity of a Cauchy problem. ...
In mathematics, a Cauchy boundary condition imposed on an ordinary differential equation or a partial differential equation specifies both the values a solution of a differential equation is to take on the boundary of the domain and the normal derivative at the boundary. ...
This article is in need of attention from an expert on the subject. ...
In mathematics, the CauchyKovalevskaya theorem is the main existence and uniqueness theorem for analytic partial differential equations. ...
The integral test for convergence is a method used to test infinite series of nonnegative terms for convergence. ...
In mathematics, the root test is a test for the convergence of an infinite series. ...
Cauchy is a small lunar impact crater on the eastern Mare Tranquillitatis. ...
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In mathematics, specifically in the study of ordinary differential equations, the Peano existence theorem, Peano theorem or CauchyPeano theorem, named after Guiseppe Peano and Augustin Louis Cauchy, is a fundamental theorem which guarantees the existence of solutions to certain initial value problems. ...
The contour C (black), the zeros of f (blue) and the poles of f (red). ...
References  This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.
EncyclopÃ¦dia Britannica, the 11th edition The EncyclopÃ¦dia Britannica Eleventh Edition (1910â€“1911) is perhaps the most famous edition of the EncyclopÃ¦dia Britannica. ...
The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ...
External links  O'Connor, John J., and Edmund F. Robertson. "Augustin Louis Cauchy". MacTutor History of Mathematics archive.
 Cauchy criterion for convergence
 Œuvres complètes d'Augustin Cauchy Académie des sciences (France). Ministère de l'éducation nationale.
 [2]
Calculus [from Latin, literally pebble (used in reckoning)] is a major area in mathematics, with applications in science, engineering, business, and medicine. ...
August 21 is the 233rd day of the year (234th in leap years) in the Gregorian calendar. ...
1789 was a common year starting on Thursday (see link for calendar). ...
Street in the center of Dijon Arc de triomphe known as the Porte Guillaume, on Place Darcy in the center of Dijon Dijon and suburbs CathÃ©drale St BÃ©nigne  Dijon Wikimedia Commons has media related to: Dijon Dijon ( ) is a city in eastern France, the prÃ©fecture (administrative capital...
May 23 is the 143rd day of the year in the Gregorian calendar (144th in leap years). ...
1857 was a common year starting on Thursday (see link for calendar). ...
City flag City coat of arms Motto: Fluctuat nec mergitur (Latin: Tossed by the waves, she does not sink) Paris Eiffel tower as seen from the esplanade du TrocadÃ©ro. ...
