41. EP 501 - Numerical Methods For Engineers And Scientists equation. Mean Value Theorem and Taylor's Theorem joseph raphson. EXAMSCHEDULE. LIBRARY. HOMEWORK / PROJECTS. Last modified 17 May 2002. http://faculty.erau.edu/reynolds/ep501/ep501_F02.html

EP 501 - Numerical Methods for Engineers and Scientists Embry-Riddle University Fall 2002 Anthony Reynolds INFORMATION This is the one of five required core courses in the MS in Space Sciences degree. We will cover Prerequisites: MA 345 (Differential Equations), as much mathematics as possible For undergraduates, it is recommended that you have taken at least PS 215, 208, 219 (Physics I, II, III), ES 201, 202, 204, 206 (Statics, Dynamics, Solids, Fluids). Text: to be determined See the syllabus for more detailed information. NEWS LINKS HISTORY What is a Computer? MATHEMATICAL TRICKS AND TRIVIA Solving the quadratic equation and some history about this equation. Mean Value Theorem and Taylor's Theorem Joseph Raphson EXAM SCHEDULE LIBRARY HOMEWORK / PROJECTS Last modified 17 May 2002

42. Www.ecs.fullerton.edu/~mathews/n2003/newtonsmethod/Newton SMethodMod.nb Newton.\ html , None}, ButtonStyle Hyperlink , FontColor- RGBColor1, 0, 1, (1643-1727) and , StyleBoxButtonBox joseph raphson , ButtonData { URL http://www.ecs.fullerton.edu/~mathews/n2003/newtonsmethod/Newton'sMethodMod.nb

43. Publications By David E. Bernholdt Adjusted Newtonraphson Algorithm for Finding Local Minima on Molecular PotentialEnergy Surfaces, J. Computat. Chem. 11, 58 (1990). 24 joseph D. Augspurger http://www.npac.syr.edu/users/bernhold/publication-list/publication-list.html

Publications by David E. Bernholdt John B. Nicholas, David E. Bernholdt, and Benjamin P. Hay, Conformational Analysis of Tetramethoxycalix[4]arene, in preparation. David E. Bernholdt, Scalability of Correlated Electronic Structure Calculations on Parallel Computers: A Case Study of the RI-MP2 Method, Parallel Computing (submitted). David E. Bernholdt and Rodney J. Bartlett, A Critical Assessment of Multireference Fock-Space CCSD and Perturbative Third-Order Triples Approximations for Photoelectron Spectra and Quasidegenerate Potential Energy Surfaces, Adv. Quantum Chem. David E. Bernholdt, Geoffrey C. Fox, Roman Markowski, Nancy J. McCracken, Marek Podgorny, Thomas R. Scavo, Debasis Mitra, and Qutaibah Malluhi, Synchronous Learning at a Distance: Experiences with TANGO, in SC'98 Conference , Institute of Electrical and Electronics Engineers and Association for Computing Machinery, 1998. D. Bernholdt, G. C. Fox, W. Furmanski, B. Natarajan, H. T. Ozdemir, Z. Odcikin Ozdemir, and T. Pulikal, WebHLA - An Interactive Programming and Training Environment for High Performance Modeling and Simulation, in 8th DoD HPC User Group Conference , Department of Defense High Performance Computing Modernization Program, 1998, in press.

44. Newton's Method And High Order Iterations Newton's iteration History, convergence results, Halley's iteration and high order new iterations .Category Science Math Numerical Analysis...... A few years later, in 1690, a new step was made by joseph raphson (16781715) whoproposed a method 6 which avoided the substitutions in Newton's approach. http://numbers.computation.free.fr/Constants/Algorithms/newton.html

Newton's method and high order iterations (Click here for a Postscript version of this page). Introduction It is of great importance to solve equations of the form f(x)=0, in many applications in Mathematics, Physics, Chemistry, ... and of course in the computation of some important mathematical constants or functions like square roots. In this essay, we are only interested in one type of methods : the Newton's methods. Newton's approach Around 1669, Isaac Newton (1643-1727) gave a new algorithm [ ] to solve a polynomial equation and it was illustrated on the example y 5=0. To find an accurate root of this equation, first one must guess a starting value, here y 2. Then just write y=2+p and after the substitution the equation becomes p Because p is supposed to be small we neglect p compared to 10p 1 and the previous equation gives p 0.1, therefore a better approximation of the root is y 2.1. It's possible to repeat this process and write p=0.1+q, the substitution gives q hence q 0.0054... and a new approximation for y 2.0946... And the process should be repeated until the required number of digits is reached.

45. UMPG II Chapter Xx Math & Algorithms Fromjnhall@sat.mot.com (joseph Hall) Subject Re long integer square root. One isa Newtonraphson iterator, the other a hybrid of three different subroutines http://mxmora.best.vwh.net/umpg/UMPG_II_Math&Algorithms.html

Contents Re: long integer square root Re: long integer square root Re: long integer square root Re: Fixed Math sqrt, asin, acos ... Pascal From:jnhall@sat.mot.com (Joseph Hall) Subject: Re: long integer square root estevez@atp3100.tuwien.ac.at (Ernesto Estevez) writes ... Does somebody has a code or algorithm for extracting a long integer square root and returning a integer. I suggest looking at Newton's iteration in any decent CS book on the subject. With a sufficiently good first guess you can do it in about 12 instructions on a 68020+. And yes, I have done it, and no, you can't have it. It belong to the company I work for. I pulled this one from my personal inventory. I hereby assign it to the public domain. Enjoy. * ISqrt * Find square root of n. This is a Newton's method approximation, * converging in 1 iteration per digit or so. Finds floor(sqrt(n) + 0.5). */ From: jimc@tau-ceti.isc-br.com (Jim Cathey) Subject: Re: long integer square root I'm personally fond of the non-Newton version, because the algorithm only uses shifts and adds, so it could be implemented in microcode with about same speed as a divide. From: k044477@hobbes.kzoo.edu (Jamie R. McCarthy)

46. Chapter 4: Lesson 5 function roots. joseph raphson, a contemporary of Newton, also developeda method of approximation similar to that of Newton. In http://coolschool.k12.or.us/courses/205800/lessons/assignments/04/lesson5.html

Getting Started Assignments Progress Timeline ... Chapter 3 Chapter 4 Calculus I: Differential Calculus (Chapter Four suggested timeline is 25 school days) Chapter Four Lesson Five: Linearization and Newton's Method INSTRUCTOR'S NOTES: Prior to scientific calculators, slides and primitive calculating devices, mathematicians relied upon algebraic and geometric skills to accomplish fairly complex problems. This lesson provides an historical look at the evolution of the derivative. DISCUSSION: Consider when you first learned how to take the square root of a number, like 30. You knew the answer had to be located between 5 and 6, because of your knowledge of perfect squares. But in order to find a more reasonable approximation, you had to take multiple iterations of the algorithm. Linearization is similar to taking multiple iterations in that the closer one gets to a target value in a function, the better the approximation of the linearization to the actual differential of that function. A good explanation can be found

47. ENCH250, Spring 2002 computes the steady state gas composition using the Newtonraphson method. Hartzell,Mike; Ibidapo, Ayodeji Olumide djdapson@hotmail.com; Iwanczuk, joseph Peter. http://www.isr.umd.edu/~adomaiti/ench250/project.html

48. Neue Seite 1 Translate this page Ramsey, Frank (1903 - 1930). Rankine, William (1820 - 1872). raphson, joseph (1651- 1708). Rayleigh, Lord John (1842 - 1919). Razmadze, Andrei (1889 - 1929). http://www.mathe-ecke.de/mathematiker.htm

Abbe, Ernst (1840 - 1909) Abel, Niels Henrik (5.8.1802 - 6.4.1829) Abraham bar Hiyya (1070 - 1130) Abraham, Max (1875 - 1922) Abu Kamil, Shuja (um 850 - um 930) Abu'l-Wafa al'Buzjani (940 - 998) Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843) Aepinus, Franz Ulrich Theodosius (13.12.1724 - 10.8.1802) Agnesi, Maria (1718 - 1799) Ahlfors, Lars (1907 - 1996) Ahmed ibn Yusuf (835 - 912) Ahmes (um 1680 - um 1620 v. Chr.) Aida Yasuaki (1747 - 1817) Aiken, Howard Hathaway (1900 - 1973) Airy, George Biddell (27.7.1801 - 2.1.1892) Aithoff, David (1854 - 1934) Aitken, Alexander (1895 - 1967) Ajima, Chokuyen (1732 - 1798) Akhiezer, Naum Il'ich (1901 - 1980) al'Battani, Abu Allah (um 850 - 929) al'Biruni, Abu Arrayhan (973 - 1048) al'Chaijami (? - 1123) al'Haitam, Abu Ali (965 - 1039) al'Kashi, Ghiyath (1390 - 1450) al'Khwarizmi, Abu Abd-Allah ibn Musa (um 790 - um 850) Albanese, Giacomo (1890 - 1948) Albert von Sachsen (1316 - 8.7.1390)

49. 1-1997 Thesis Geometry-Based Three Dimensional Hp Finite Element Slimane Adjerid, Mohammed Aiffa and joseph E. Flaherty. in time using an implicitfinite difference scheme, and solved using the Newtonraphson method. http://www.scorec.rpi.edu/reports/97.html

Thesis Geometry-Based Three Dimensional hp Finite Element Modeling and Computations S. Dey A. Suvorov Proc Software Framework for Mechanism-Based Design of Composite Structures R.Wentorf M.S. Shephard G.J. Dvorak J. Fish M.W. Beall R. Collar K.-L. Shek Proc. Modeling and Adaptive Numerical Techniques for Oxidation of Ceramic Composites S. Adjerid M. Aiffa J.E. Flaherty J.B. Hudson M.S. Shephard Journal Geometry Representation Issues Associated with p -Version Finite Element Computations S. Dey M.S. Shephard J.E. Flaherty Journal Adaptive Local Refinement with Octree Load- Balancing for the Parallel Solution of Three- Dimensional Conservation Laws J.E. Flaherty R.M. Loy M.S. Shephard B.K. Szymanski J.D. Teresco L.H. Ziantz Proc Predictive Load Balancing for Parallel Adaptive Finite Element Computation J.E. Flaherty R.M. Loy M.S. Shephard B.K. Szymanski J.D. Teresco L.H. Ziantz A Geometry-Based Framework for Reliable Numerical Simulations M.W. Beall M.S. Shephard Report A Posteriori Error Estimation for the Finite Element Method-of-Lines Solution of Parabolic Problems S. Adjerid I. Babuska

50. Great Mathematicians joseph raphson 1648 – 1715. joseph raphson was an English mathematician,a Fellow of the Royal Society of London and a friend of Newton. http://www.me.metu.edu.tr/me310/mathematicians/mathematicians.html

Great Mathematicians See the Web site, http://scienceworld.wolfram.com/biography/topics/Mathematicians.html , for the bios of many famous scientists and mathematicians. Many of the methods and equations used in numerical methods are associated with the names of famous mathematicians and scientists. Here, we provide biographical sketches of the more notable pre-twentieth century figures of the modern mathematical era. As will be seen in the sketches, even the most well recognized pure mathematicians worked on applied problems; indeed, some of their advances were made on the way to solving such problems. To appreciate their work, we must remember that they did not have the tools we take for granted - they developed them! To help with their places in history, the figure below shows the life-spans of those that are discussed. John Couch Adams [1819-1892] Adams was born in Cornwall and educated at Cambridge University. He was later appointed Lowndean Professor and Director of the Observatory at Cambridge. In 1845, he calculated the position of a planet beyond Uranus that could account for perturbations in the orbit of Uranus. His requests for help in looking for the planet, Neptune; met with little response among English astronomers. An independent set of calculations was completed in 1846 by Leverrier, whose suggestions to the German astronomer Johann Galle led to Neptune's discovery. Adams published a memoir on the mean motion of the Moon in 1855 and computed the orbit of the Leonids in 1867. The Leonids are meteor showers that appear to originate in the constellation Leo. They were especially prominent every 33 years from 902 to 1866.

51. Using Homotopy Methods For Designing Perfect Reconstruction Filter Banks (Resear popular method for solving a nonlinear equation is the Newtonraphson method Markov-BasedChannel Model Algorithm for Wireless Networks - Konrad, joseph, Ludwig http://citeseer.nj.nec.com/251349.html

Using Homotopy Methods for Designing Perfect Reconstruction Filter Banks (Make Corrections) Almudena P. Ordonez Home/Search Context Related View or download: berkeley.edu/~almuden final_paper.pdf Cached: PS.gz PS PDF DjVu ... Help From: berkeley.edu/~almudena research (more) (Enter author homepages) Rate this article: (best) Comment on this article (Enter summary) Abstract: Solving nonlinear equations often arises in engineering problems and it is seldom a trivial task. Maximizing the coding gain of a digital filter bank, for example, is equivalent to solving a set of nonlinear equations. The most popular method for solving a nonlinear equation is the Newton-Raphson method. Unfortunately, this method sometimes fails, especially in cases when nonlinear equations possess multiple solutions (zeros). An emerging family of methods that can be used in such cases are... (Update) Active bibliography (related documents): More All Teaching Simple Sound Synthesis: Real-Time, Numeric and Symbolic.. - Jacker (Correct) ... (Correct) Similar documents based on text: More All A Markov-Based Channel Model Algorithm for Wireless Networks - Konrad, Joseph, Ludwig.. (2001)

52. Newton's Method HTML Page that last reference does not spend too much time talking about Newton's Method, youmight want to consider the interesting page on the life of joseph raphson. http://www.math.umn.edu/itcep/delta-m/tse/NewtonsMethod.html

Chapter 7 Section 6 Newton's Method for solving equations back to Delta-M project page GNU General Public License The goal of this section is for you to learn how to use techniques from calculus to approximate the roots of equations. You may be surprised to learn that in order to understand one of the most widely used methods of approximating roots of equations, you need only to understand how to take derivatives. The method of approximating solutions to equations that we will cover in this section is called Newton's method. This section will have the following structure Introduction: An interesting history of Newton's method The Main Idea: ... Exercises Here is one possible way that you could use this section. The Introduction provides a brief history of Newton's method. There is no mathematics in this part of the paper ( but it is still interesting!!). So, if you are interested in a little history, you might want to read this part. The Main Idea of Newton's method comes next. Recall that throughout the book we have been emphasizing this idea from calculus - approximate solutions to a new problems by relating the new problem to one that you already know how to solve, then look at the limiting case. We present Newton's method from this point of view. This part is

53. Papers - 4th USENIX Conference On Object-Oriented Technologies And Systems, 1998 joseph (Yossi) Gil. IBM TJ Watson Research Center. A primary example of such analgorithm is the Newtonraphson method for finding the roots of a function. http://www.usenix.org/publications/library/proceedings/coots98/full_papers/gil/g

COOTS 1998 Technical Program Proceedings Compile Time Symbolic Derivation with C++ Templates Joseph (Yossi) Gil IBM T.J. Watson Research Center P.O. Box 704 Yorktown Heights, NY 10598 yogi@watson.ibm.com yogi@cs.technion.ac.il Zvi Gutterman Faculty of Computer Science Technion Israel Institute of Technology Haifa 32000, Israel zvik@cs.technion.ac.il Abstract C++ templates are already recognized as a powerful linguistic mechanism, whose usefulness transcends the realization of traditional generic containers. In the same venue, this paper reports on a somewhat surprising application of templates—for computing the symbolic derivative of expression. Specifically, we describe a software package based on templates, called SEMT, which allows the programmer to create symbolic expressions, substitute variables in them, and compute their derivatives. SEMT is unique in that these manipulations are all done at compile time. In other words, SEMT effectively coerces the compiler to do symbolic computation as part of the compilation process. Beyond the theoretical interest, SEMT can be practically applied in the efficient, generic and easy to use implementation of many numerical algorithms. KEYWORDS: SCIENTIFIC COMPUTING, GENERIC PROGRAMMING, NUMERICAL ALGORITHMS, SYMBOLIC DERIVATION.

54. Mathematics Archives - Topics In Mathematics - Calculus Materials, Lecture notes, Laboratories, HW Problems SOURCE joseph M. Mahaffy FixedPoints, Fundamental Theorem of Algebra, Newtonraphson Method, Lagrange http://archives.math.utk.edu/topics/calculus.html

Topics in Mathematics Calculus Calculus Resources On-Line ADD. KEYWORDS: Initiatives, Projects and Programs, Articles, Posters, Discussions, Software, Publisher sites, Other listings of calculus resources Aid for Calculus ADD. KEYWORDS: Solving problems in calculus AP Calculus on the Web ADD. KEYWORDS: Textbooks, 1998 Syllabus, Approved Calculators, Resources Are You Ready for Calculus? What you should know! Area of a Circle SOURCE: Tom Richmond, Western Kentucky University TECHNOLOGY: Animated Gif Basic EXCEL-skills for calculus and differential equations ADD. KEYWORDS: Sample worksheets, Sample problems / skills Better File Cabinet ADD. KEYWORDS: Database of calculus problems SOURCE: Eric Hsu and University of Texas at Austin Bisection Method Tutorial Cal Poly Linked Curriculum Program Interdisciplinary Projects ADD. KEYWORDS: Projects Calculus Calculus I Home Page ADD. KEYWORDS: Sample CBL Experiment: Newton's Law of Cooling, TI-85 Programs and CBL Experiment Data, Mathematica Notebooks Calculus 1 - Problems and Solutions ADD. KEYWORDS:

55. CALCUL NUMERIQUE joseph raphson? Quifut Thomas Simpson? Feuilles d'exercices à rendre en cours de rédaction. http://www.phys.univ-tours.fr/~nicolis/deugsm2.html

[PostScript PDF] Un cours sur le FORTRAN 77 (en anglais) sous forme [PostScript PDF] Le Pendule de Foucault Le Monde des Milieux Granulaires ... PDF] Corrigé : cf. corrigé TD3 [PostScript PDF] [PostScript PDF] ... PDF] Logiciels Disponibles gnuplot ici *b.zip ainsi que le fichier readme.1st , qui contient les instructions d'installation; voir aussi . Le logiciel gnuplot gpt35w32.zip (version 32 bits) et gpt35w16.zip (version 16 bits) En plus vous pouvez chercher les logiciels d'affichage Ghostview,GhostScript et GSview pour les fichiers de type PostScript ainsi que le logiciel d'affichage Acrobat Reader www.linux.org

56. Earliest Known Uses Of Some Of The Words Of Mathematics (A) Algorithm is found in English in 1715 in The Theory of Fluxions by joseph raphson Now from this being known as the Algorithm, as I may say of this Calculus http://members.aol.com/jeff570/a.html

Earliest Known Uses of Some of the Words of Mathematics (A) Last revision: March 16, 2003 ABELIAN EQUATION. Leopold Kronecker (1823-1891) introduced the term Abelsche Gleichung in an 1853 paper on algebraically soluble equations. He used the term to describe an equation which in modern terms would be described as having cyclic Galois group [Peter M. Neumann]. ABELIAN FUNCTION. C. G. J. Jacobi (1804-1851) proposed the term Abelsche Transcendenten (Abelian transcendental functions) in Crelle's Journal 8 (1832) (DSB). Abelian function appears in the title "Zur Theorie der Abelschen Functionen" by Karl Weierstrass (1815-1897) in Crelle's Journal, Weierstrass' first publications on Abelian functions appeared in the Braunsberg school prospectus (1848-1849). ABELIAN GROUP. Camille Jordan (1838-1922) wrote in 1870 in Mathematische Annalen, 20 (1882), 301329. The term is used in the first paragraph of the paper without definition; it is given an explicit definition in the middle of p. 304. [Peter M. Neumann and Julia Tompson] ABELIAN INTEGRAL appears in English in 1847 in the Report of the British Association for the Advancement of Science (1846): "What are the corresponding functions to which the hyper-elliptic or Abelian integrals are inverse, and how by means of them can Abel’s theorem be stated?" (OED2).

57. Quelques Bons Anciens élèves Abel Niels Henri 1802 1829 Translate this page Bézout, Etienne, 1730, 1783, Krönecker, Leopold, 1823, 1891. Binet, Jacques,1786, 1856, Lagrange, joseph Louis (Comte de), 1736, 1813. Diophante, 325, 409,raphson, http://vivent.les.math.free.fr/matheux.html

Abel Niels Henri Hadamard Jacques Salomon Agnesi Maria-Gaetan Hamilton William Rowan Heine Heinrich Eduard Hermite Charles Hilbert David Baire Otto Banach Stefan Bernoulli Daniel William George Bernoulli Jacques Huygens Christiaan Bernoulli Jean Jacobi Carl Gustav Jacob Bernstein Serguei Natanovic Jordan Camille Marie Ennemond Bertrand Kepler Johannes Bessel Friedrich Wilhem Klein Etienne Leopold Binet Jacques Lagrange Joseph Louis (Comte de) Bolzano Bernhard Laguerre Edmond Nicolas Boole Georges Landau Edmund Georg Hermann Bourbaki Laplace Pierre Simon (Marquis de) Buffon Georges Louis Leclerc (compte de) Lebesgue Cantor Georg Ferdinand Ludwig Philipp Legendre Adrien Marie Cardan Hieromino Leibniz Gottfried Wilhelm Carmichael Robert Daniel Lipschitz Rudolf Otto Sigismund Cassini Jean-Dominique Machin John Catalan Mac Laurin Colin Cauchy Augustin-Louis Minkowski Hermann Cayley Arthur Augustus Ferdinand Cesaro Ernesto Moivre Abraham (de) Chasles Michel Monge Gaspard Chebycheff Pafnuti Livovic Napier ou Neper John (baron de Merchiston) Clairaut Alexis Claude Newton Isaac Coriolis Gustave Ostrogradski Michel Vassilievitch Cornu Marie-Alfred Marc Antoine Cramer Gabriel Pascal Blaise d'Alembert Jean le Rond Peano Giuseppe Darboux Jean-Gaston Julius Descartes Poisson Dini Ulysse Pythagore -VI -VI -II -II Raabe Josef Ludwig Diophante Raphson Dirichlet Peter Gustav Lejeune Ricatti Jacopo Francesco (comte) Duhamel Jean Marie Constant Riemann Georg Friedrich Bernhard Eisenstein Ferdinand Gotthold Rolle Michel Euclide Sarrus Pierre Euler Leonhard Schmidt Erhard Farey John Schwarz Hermann Amandus Leopold Simpson Thomas Fermat Pierre Simon de Stirling

58. Collections: Columbia Rare Book & Manuscript Library Euclid and Newton; among the Newton holdings are several volumes from his library,including a volume of mathematical works by joseph raphson, Giovanni Cassini http://www.columbia.edu/acis/textarchive/rare/rare12.html

T HE R ARE B OOK AND M ANUSCRIPT L IBRARY OF C OLUMBIA U NIVERSITY Collections By Kenneth A. Lohf M AJOR libraries have achieved their standing because of the specialized collections of books and related materials which they have gathered over long periods of time for the purposes of preserving the records of civilization and making those records available for research. The largest of the academic libraries, Columbia among them, could not have achieved those goals if it had not been for those dedicated and generous collectors whose gifts in kind and in endowments have formed them into formidable research repositories of rare printed and manuscript materials. The unusual collections under the stewardship of the Rare Book and Manuscript Library require distinctive conditions of housing, use, cataloging, preservation and security. This is readily apparent when one considers the range of holdings which, in addition to rare printed works, cylinder seals, cuneiform tablets, papyri, coptic ostraca, medieval and renaissance manuscripts, and literary and art posters, include as well authors' manuscripts from the sixteenth century to Herman Wouk and Allen Ginsberg, files of correspondence from John Milton to Hart Crane, and archives as varied as those of the Carnegie Endowment for International Peace, Daly's Theatre of New York City, the Citizens Union and the Woman Suffrage Association. On our premises are entire libraries of printed materials devoted to special subjects, such as Greek and Roman authors, the Knickerbocker School of writers, history of economics and banking, American theater, accountancy, weights and measures, the New York Society of Tammany, Joan of Arc, Mary Queen of Scots, Hector Berlioz, mathematics and astronomy. Broadening the extraordinary diversity of the holdings are substantial or representative collections of Greek and Roman coins, historical bindings, mathematical instruments, portraits of literary figures, original drawings of illustrators, railroad colorprints, fore-edge paintings, miniature books, and the like. However extensive and impressive present day resources are, their beginnings more than two centuries ago illustrate an early and equally profound recognition of the importance of books and manuscripts to the academic community.

59. Earliest Known Uses Of Some Of The Words Of Mathematics (A) Apparently the earliest English translation was carried out by joseph raphson inThe Theory of Fluxions, Shewing in a compendious manner The first Rise of, and http://mail.mcjh.kl.edu.tw/~chenkwn/mathword/a.html

¦­´Á¼Æ¾Ç¦r·Jªº¾ú¥v (A) Last revision: July 29, 1999 ABELIAN EQUATION. Leopold Kronecker (1823-1891) introduced the term Abelsche Gleichung in an 1853 paper on algebraically soluble equations. He used the term to describe an equation which in modern terms would be described as having cyclic Galois group [Peter M. Neumann]. ABELIAN FUNCTION. C. G. J. Jacobi (1804-1851) proposed the term Abelsche Transcendenten (Abelian transcendental functions) in Crelle's Journal 8 (1832) (DSB). Abelian function appears in the title "Zur Theorie der Abelschen Functionen" by Karl Weierstrass (1815-1897) in Crelle's Journal, Weierstrass' first publications on Abelian functions appeared in the Braunsberg school prospectus (1848-1849). ABELIAN GROUP. Camille Jordan (1838-1922) wrote groupe ab?lien in 1870 in Trait? des Substitutions et des Equations Alg?braiques. However, Jordan does not mean a commutative group as we do now, but instead means the symplectic group over a finite field (that is to say, the group of those linear transformations of a vector space that preserve a non-singular alternating bilinear form). In fact, Jordan uses both the terms "groupe ab?lien" and "?quation ab?lienne." The former means the symplectic group; the latter is a natural modification of Kronecker's terminology and means an equation of which (in modern terms) the Galois group is commutative. An early use of "Abelian" to refer to commutative groups is H. Weber, "Beweis des Satzes, dass jede eigentlich primitive quadratische Form unendlich viele Primzahlen darzustellen f?hig ist,"

60. Ascend Bibliographic Database (BibTeX) For Everybody Tyner and Arthur Westerberg and Karl Westerberg and joseph Zaher}, title Berna ,title = Decomposition of very largescale Newton-raphson based flowsheeting http://www.cs.cmu.edu/~ascend/bibtex/bibdata.html

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