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Wronski Determinant
In mathematics, the Wronskian (or Wrońskian) is a determinant introduced by and named by . It is used in the study of differential equations, where it can sometimes show linear independence in a set of solutions. Definition The Wronskian of two differentiable functions and is . More generally, for real- or complex-valued functions , which are times differentiable on an interval , the Wronskian as a function on is defined by W(f_1, \ldots, f_n) (x)= \begin f_1(x) & f_2(x) & \cdots & f_n(x) \\ f_1'(x) & f_2'(x) & \cdots & f_n' (x)\\ \vdots & \vdots & \ddots & \vdots \\ f_1^(x)& f_2^(x) & \cdots & f_n^(x) \end,\quad x\in I. That is, it is the determinant of the matrix constructed by placing the functions in the first row, the first derivative of each function in the second row, and so on through the th derivative, thus forming a square matrix. When the functions are solutions of a linear differential equation, the Wronskian can be found explicitly using Abel's ident ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variation Of Parameters
In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations. For first-order inhomogeneous linear differential equations it is usually possible to find solutions via integrating factors or undetermined coefficients with considerably less effort, although those methods leverage heuristics that involve guessing and do not work for all inhomogeneous linear differential equations. Variation of parameters extends to linear partial differential equations as well, specifically to inhomogeneous problems for linear evolution equations like the heat equation, wave equation, and vibrating plate equation. In this setting, the method is more often known as Duhamel's principle, named after Jean-Marie Duhamel (1797–1872) who first applied the method to solve the inhomogeneous heat equation. Sometimes variation of parameters itself is called Duhamel's principle and vice versa. History Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Differential Equations
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathesis (journal)
''Mathesis: Recueil Mathématique'' was a Belgian scientific journal for elementary mathematics, established in 1881 by Paul Mansion and Joseph Jean Baptiste Neuberg Joseph Jean Baptiste Neuberg (30 October 1840 – 22 March 1926) was a Luxembourger mathematician who worked primarily in geometry. Biography Neuberg was born on 30 October 1840 in Luxembourg City, Luxembourg. He first studied at a local scho .... An earlier Belgian mathematics journal, ''Nouvelle Correspondance Mathématique'', was established in 1874 by Mansion and Neuberg together with Eugène Catalan. In 1880, ''Nouvelle Correspondance'' ceased publication, and Mansion and Neuberg together launched its successor, ''Mathesis'', in 1881. ''Mathesis'' ceased publication in 1915 because of the war in Europe, but restarted again under the editorship of Neuberg and Adolphe Mineur in 1922 as the official journal of the Belgian Mathematical Society, which itself was founded in 1921. It continued in publication unt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East Orange, New Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor & Francis
Taylor & Francis Group is an international company originating in England that publishes books and academic journals. Its parts include Taylor & Francis, Routledge, F1000 (publisher), F1000 Research or Dovepress. It is a division of Informa, Informa plc, a United Kingdom–based publisher and conference company. Overview The company was founded in 1852 when William Francis (chemist), William Francis joined Richard Taylor (editor), Richard Taylor in his publishing business. Taylor had founded his company in 1798. Their subjects covered agriculture, chemistry, education, engineering, geography, law, mathematics, medicine, and social sciences. Francis's son, Richard Taunton Francis (1883–1930), was sole partner in the firm from 1917 to 1930. In 1965, Taylor & Francis launched Wykeham Publications and began book publishing. T&F acquired Hemisphere Publishing in 1988, and the company was renamed Taylor & Francis Group to reflect the growing number of Imprint (trade name), imp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transactions Of The American Mathematical Society
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 printed pages. See also * ''Bulletin of the American Mathematical Society'' * '' Journal of the American Mathematical Society'' * ''Memoirs of the American Mathematical Society'' * ''Notices of the American Mathematical Society'' * ''Proceedings of the American Mathematical Society'' External links * ''Transactions of the American Mathematical Society''on JSTOR JSTOR (; short for ''Journal Storage'') is a digital library founded in 1995 in New York City. Originally containing digitized back issues of academic journals, it now encompasses books and other primary sources as well as current issues of j ... American Mathematical Society academic journals Mathematics journals Publications established in 1900 {{math-journal-st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. It is one of the highest-ranked universities in the world. The institution moved to Newark, New Jersey, Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. It is a member of the Ivy League. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vandermonde Matrix
In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an matrix :V=\begin 1 & x_1 & x_1^2 & \dots & x_1^\\ 1 & x_2 & x_2^2 & \dots & x_2^\\ 1 & x_3 & x_3^2 & \dots & x_3^\\ \vdots & \vdots & \vdots & \ddots &\vdots \\ 1 & x_m & x_m^2 & \dots & x_m^ \end, or :V_ = x_i^ \, for all indices and . Some authors define the Vandermonde matrix as the transpose of the above matrix. The determinant of a square Vandermonde matrix is called a ''Vandermonde polynomial'' or ''Vandermonde determinant''. Its value is the polynomial :\det(V) = \prod_ (x_j - x_i) which is non-zero if and only if all x_i are distinct. The Vandermonde determinant was sometimes called the ''discriminant'', although, presently, the discriminant of a polynomial is the square of the Vandermonde determinant of the roots of the polynomial. The Vandermonde determinant is an alternating form in the x_i, meaning that exchang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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