1. Carle David Tolme Runge (1856-1927) Carle David Tolme Runge (18561927) Carle Runge at MacTutor. Carle Runge at the Mathematics Genealogy Project. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

2. Carle David Tolm Runge Carle David Tolm runge carle David Tolm Runge (August 30 1856 January 3 1927) was a German mathematician, physicist, and spectroscopist. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Carle David Tolme Runge - Definition Of Carle David Tolme Runge In Carle David Tolm Runge (August 30 1856 ndash; January 3 1927) was a German mathematician, physicist, and spectroscopist. His first name is very often http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. Carle David Tolmé Runge - Wikipedia, The Free Encyclopedia (Redirected from Carle David Tolme Runge). Carle David Tolmé Runge (August 30, 1856 – January 3, 1927) was a German mathematician, physicist, http://en.wikipedia.org/wiki/Carle_David_Tolme_Runge

Wikimedia needs your help in the final days of its fund drive. See our fundraising page The Red Cross and other charities also need your help. Carle David Tolm© Runge From Wikipedia, the free encyclopedia. (Redirected from Carle David Tolme Runge Carle David Tolm© Runge August 30 January 3 ) was a German mathematician physicist , and spectroscopist. His first name is very often given as Carl He was co-developer and co- eponym of the Runge-Kutta method , in the field of what is today known as numerical analysis He spent the first few years of his life in Havana , where his father Julius Runge was the Danish consul. The family later moved to Bremen , where his father died early (in In he received his Ph.D. in mathematics at Berlin , where he studied under Karl Weierstrass . In he became a professor in Hanover His interests included mathematics, spectroscopy geodesy and astrophysics . In addition to pure mathematics he did a great deal of experimental work studying spectral lines of various elements, and was very interested in the application of this work to astronomical spectroscopy In he went to G¶ttingen , where he remained until he retired in Runge crater on the Moon is named after him.

5. Runge Biography of Carle Runge (18561927) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

6. Carle David Tolmé Runge - Wikipedia, The Free Encyclopedia Carle David Tolmé Runge He was codeveloper and co-eponym of the Runge-Kutta method, in the field of what is today known as numerical analysis. http://en.wikipedia.org/wiki/Carle_David_Tolmé_Runge

Wikimedia needs your help in the final days of its fund drive. See our fundraising page The Red Cross and other charities also need your help. Carle David Tolm© Runge From Wikipedia, the free encyclopedia. Carle David Tolm© Runge August 30 January 3 ) was a German mathematician physicist , and spectroscopist. His first name is very often given as Carl He was co-developer and co- eponym of the Runge-Kutta method , in the field of what is today known as numerical analysis He spent the first few years of his life in Havana , where his father Julius Runge was the Danish consul. The family later moved to Bremen , where his father died early (in In he received his Ph.D. in mathematics at Berlin , where he studied under Karl Weierstrass . In he became a professor in Hanover His interests included mathematics, spectroscopy geodesy and astrophysics . In addition to pure mathematics he did a great deal of experimental work studying spectral lines of various elements, and was very interested in the application of this work to astronomical spectroscopy In he went to G¶ttingen , where he remained until he retired in Runge crater on the Moon is named after him.

7. Carle David Tolm Runge - Wikipedia, The Free Encyclopedia Carle David Tolm Runge (Redirected from Carl Runge) Categories 1856 births 1927 deaths Mathematicians Physicists http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

8. Runge Carle David Tolm?Runge Runge worked on a procedure for the numerical solution of algebraic equations and later studied the wavelengths of the spectral http://www.sci.hkbu.edu.hk/scilab/math/runge.html

Carle David TolmŽ Runge Aug 30 1856 - Jan 3 1927 Welcome page The World Great Mathematicians Runge worked on a procedure for the numerical solution of algebraic equations and later studied the wavelengths of the spectral lines of elements. At the age of 19, after leaving school, Runge spent 6 months with his mother visiting the cultural centres of Italy. On his return to Germany he enrolled at the University of Munich to study literature. However after 6 weeks of the course he changed to mathematics and physics. Runge attended courses with Max Planck and they became close friends. In 1877 both went to Berlin but Runge turned to pure mathematics after attending Weierstrass' lectures. His doctoral dissertation (1880) dealt with differential geometry. After taking his secondary school teachers examinations he returned to Berlin where he was influenced by Kronecker. Runge then worked on a procedure for the numerical solution of algebraic equations in which the roots were expressed as infinite series of rational functions of the coefficients. Runge published little at that stage but after visiting Mittag-Leffler in Stockholm in September 1884 he produced a large number of papers in Mittag-Leffler's journal "Acta mathematica" (1885).

9. NodeWorks - Encyclopedia Carle David Tolm Runge Carle David Tolm Runge http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. ENGLISH ENCYCLOPAEDIA - Carle David Tolm Runge Carle David Tolm runge carle David Tolm Runge (August 30 1856 January 3 1927) was a German mathematician, physicist, and spectroscopist. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Runge Portraits Portraits of Carle Runge http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. An Alphab Rudnick, Dorthea (1907?), WDB. Runge, Carle David Tolme (1856-1927), Maths Archive. Russell, Bertrand Arthur William (1872-1970), Bjorn's Guide http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Runge-Kutta Methods - Wikipedia, The Free Encyclopedia RungeKutta methods http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. ? ? NonSoloMatematica ? ? Blaise Pascal Blaise Pascal.jpg. Brook Taylor Brook Taylor.jpg. Carl Friedrich Gauss Carl Friedrich Gauss.jpg. Carle runge carle Runge.jpg http://groups.msn.com/NonSoloMatematica/matematici.msnw

var nEditorialCatId = 296; MSN Home My MSN Hotmail Shopping ... Money Web Search: document.write(' Groups Groups Home My Groups Language ... Help ? ? NonSoloMatematica ? ? NonSoloMatematica@groups.msn.com What's New Join Now General Regolamento MSN ... Tools ? Gallery Mathes Choose Another Photo Album View: Grid View List View Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Add Photos Delete Photos Adrien-Marie Legendre Adrien-Marie Legendre.jpg Alan Turing Alan Turing.jpg Albrecht Dürer Albrecht Dürer.jpg Andrei Nikolaevich Kolmogorov Andrei Nikolaevich Kolmogorov.jpg André-Marie Ampère André-Marie Ampère.jpg Augustin-Louis Cauchy Augustin-Louis Cauchy.jpg Bernoulli_Johann.jpg Bertrand Russell Bertrand Russell.jpg Blaise Pascal Blaise Pascal.jpg Brook Taylor Brook Taylor.jpg Carl Friedrich Gauss Carl Friedrich Gauss.jpg Carle Runge Carle Runge.jpg Notice: Microsoft has no responsibility for the content featured in this group. Click here for more info. Try MSN Internet Software for FREE! MSN Home My MSN ... GetNetWise

15. Runge Biography of carle runge (18561927) At the age of 19, after leaving school, carle runge spent 6 months with his mother visiting the cultural centres of http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Runge.html

Born: 30 Aug 1856 in Bremen, Germany Died: Click the picture above to see two larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing At the age of 19, after leaving school, Carle Runge spent 6 months with his mother visiting the cultural centres of Italy. On his return to Germany he enrolled at the University of Munich to study literature. However after 6 weeks of the course he changed to mathematics and physics. Runge attended courses with Max Planck and they became close friends. In 1877 both went to Berlin but Runge turned to pure mathematics after attending Weierstrass 's lectures. His doctoral dissertation (1880) dealt with differential geometry After taking his secondary school teachers examinations he returned to Berlin where he was influenced by Kronecker . Runge then worked on a procedure for the numerical solution of algebraic equations in which the roots were expressed as infinite series of rational functions of the coefficients. Runge published little at that stage but after visiting Mittag-Leffler in Stockholm in September 1884 he produced a large number of papers in Mittag-Leffler 's journal Acta mathematica Runge obtained a chair at Hanover in 1886 and remained there for 18 years. Within a year Runge had moved away from pure mathematics to study the wavelengths of the spectral lines of elements other than hydrogen (J J

16. References For Runge References for the biography of carle runge. I runge, carle runge und sein wissenschaftlickes Werk (G ttingen, 1949). http://www-groups.dcs.st-and.ac.uk/~history/References/Runge.html

References for Carle Runge Version for printing Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: G Richenhagen, Carl Runge (1856-1927): von der reinen Mathematik zur Numerik, Studien zur Wissenschafts-, Sozial- und Bildungsgeschichte der Mathematik (G ttingen, 1985). I Runge, Carle Runge und sein wissenschaftlickes Werk (G ttingen, 1949). Several Articles, in Naturwissenschaften Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR December 1996 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Runge.html

17. The World Great Mathematicians carle David Tolm runge (Aug 30 1856 Jan 3 1927) Born Bremen, Germany. Died Göttingen, Germany. George Gabriel Stokes (Aug 13 1819 - Feb 1 1903) Born Sligo http://www.sci.hkbu.edu.hk/scilab/math/math.html

The World Great Mathematicians Charles Babbage (Dec 26 1792 - Oct 18 1871) Born Teignmouth, England. Died London, England. Augustin Louis Cauchy (Aug 21 1789 - May 23 1857) Born Paris, France. Died Sceaux, France. Albert Einstein (March 14 1879 - April 18 1955) Born Ulm, Germany. Died Princeton, USA. Jean Baptiste Joseph Fourier (March 21 1768 - May 16 1830) Born Auxerre, France. Died Paris, France. Carl Friedrich Gauss David Hilbert Karl Gustav Jacob Jacobi (Dec 10 1804 - Feb 18 1851) Born Potsdam, Germany. Died Berlin, Germany. Pierre-Simon Laplace (March 28 1749 - March 5 1827) Born Beaumont-en-Auge, France. Died Paris, France. Andrei Andreyevich Markov (June 14 1856 - July 20 1922) Born Ryazan, Russia. Died St Petersburg, Russia. Sir Isaac Newton (Jan 4 1643 - March 31 1727) Born Woolsthorpe, England. Died London, England. Blaise Pascal (June 19 1623 - Aug 19 1662) Born Clermont-Ferrand, France. Died Paris, France. Carle David Tolm Runge George Gabriel Stokes (Aug 13 1819 - Feb 1 1903) Born Sligo, Ireland. Died Cambridge, England. Alan Mathison Turing (June 23 1912 - June 7 1954) Born London, England. Died Wilmslow, England.

18. Math Lessons - Carle David Tolmé Runge Math Lessons carle David Tolmé runge. See also. runge s phenomenon; runge s method for diophantine equations . http://www.mathdaily.com/lessons/Carle_David_Tolmé_Runge

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... Physicists Carle David Tolmé Runge Carle David Tolmé Runge August 30 January 3 ) was a German mathematician physicist , and spectroscopist. His first name is very often given as Carl He was co-developer and co- eponym of the Runge-Kutta method , in the field of what is today known as numerical analysis He spent the first few years of his life in Havana , where his father Julius Runge was the Danish consul. The family later moved to Bremen , where his father died early (in In he received his Ph.D. in mathematics at Berlin , where he studied under Karl Weierstrass . In he became a professor in Hanover His interests included mathematics, spectroscopy geodesy and astrophysics . In addition to pure mathematics he did a great deal of experimental work studying spectral lines of various elements, and was very interested in the application of this work to astronomical spectroscopy In he went to , where he remained until he retired in A crater on the Moon is named after him.

19. Math Lessons - Carle David Tolmé Runge Math Lessons carle David Tolmé runge. carle David Tolmé runge. (Redirected from carle David Tolme runge). carle David Tolmé runge (August 30 1856 http://www.mathdaily.com/lessons/Carle_David_Tolme_Runge

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... Physicists Carle David Tolmé Runge (Redirected from Carle David Tolme Runge Carle David Tolmé Runge August 30 January 3 ) was a German mathematician physicist , and spectroscopist. His first name is very often given as Carl He was co-developer and co- eponym of the Runge-Kutta method , in the field of what is today known as numerical analysis He spent the first few years of his life in Havana , where his father Julius Runge was the Danish consul. The family later moved to Bremen , where his father died early (in In he received his Ph.D. in mathematics at Berlin , where he studied under Karl Weierstrass . In he became a professor in Hanover His interests included mathematics, spectroscopy geodesy and astrophysics . In addition to pure mathematics he did a great deal of experimental work studying spectral lines of various elements, and was very interested in the application of this work to astronomical spectroscopy In he went to , where he remained until he retired in A crater on the Moon is named after him.

20. Runge's Phenomenon -- Facts, Info, And Encyclopedia Article more info and facts about carle David Tolmé runge) carle David Tolmé runge when runge found that if you (Click link for more info and facts about http://www.absoluteastronomy.com/encyclopedia/r/ru/runges_phenomenon.htm

var dc_UnitID = 10; var dc_PublisherID = 512; var dc_BackgroundColor1 = 'white'; var dc_BackgroundColor2 = 'white'; var dc_TitleColor = 'blue'; var dc_TextColor = 'black'; var dc_URLColor = 'blue'; var dc_URLVisitedColor = 'green'; var dc_sm_type = 'horizontal'; var dc_Width = 700; var dc_Height = 75; var dc_caption_font_bgColor = 'white'; var dc_caption_font_color = 'blue'; var dc_OutBorder = 'no'; var dc_adprod='TM'; Runge's phenomenon [Categories: Interpolation] In the (Click link for more info and facts about mathematical) mathematical field of (Click link for more info and facts about numerical analysis) numerical analysis Runge's phenomenon is a problem which occurs when using (Click link for more info and facts about polynomial interpolation) polynomial interpolation with polynomials of high degree. It was discovered by (Click link for more info and facts about Carle David Tolmé Runge) Carle David Tolmé Runge when exploring the behaviour of errors when using polynomial interpolation to approximate certain functions. Problem Consider the (A mathematical relation such that each element of one set is associated with at least one element of another set) function Runge found that if you (Click link for more info and facts about interpolate) interpolate this function at equidistant points x i with a (A mathematical expression that is the sum of a number of terms) polynomial Solutions to the problem of Runge's phenomenon The oscillation can be minimized by using (Click link for more info and facts about Chebyshev nodes)

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