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Author: Wolfgang Grobner
Publisher: Springer Science & Business Media
ISBN: 146847362X
Category : Science
Languages : en
Pages : 206
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Book Description
Dieses Buch beruht auf 40 lahren intensiven Studiums der Differentialglei chungen, sowohl yom theoretischen als auch yom praktischen Gesichtspunkt aus, eines Studiums, das mit meiner Tatigkeit im Rechen-Institut M. Picones in Rom begann, sodann fortgesetzt wurde in der Gruppe flir Industriemathema tik der Luftfahrt-Forschungsanstalt in Braunschweig, und endlich mit meinen Vorlesungen, hauptsachlich an der Universitat Innsbruck, abgeschlossen wurde. Die Zeit der Weltraumfliige stellte hier neue Aufgaben der Bahnberechnung von Satelliten, deren Bearbeitung theoretisch eine geschlossene Formel zur Losung des n-Korper-Problems, praktisch eine neue Methode zur Berechnung von reguJaren Differentialgleichungssystemen zeitigte, die mit den besten bekannten Losungsmethoden erfolgreich in Konkurrenz treten konnte, was vor aHem meinen Mitarbeitern H. Knapp und G. Wanner zu danken war. Die Vorlesung iiber Differentialgleichungen habe ich seit 1947 in regelmaBi gen Abstanden an der Universitat Innsbruck gehalten, bei jeder Wiederholung neu bearbeitet und durch Seminararbeiten vervollstandigt; auch in meiner flir Physik-Studenten besonders gehaltenen Vorlesung iiber {raquo}Die mathemati schen Methoden der Physik{laquo} habe ich in gekiirzter Form immer die {raquo}Differen tialgleichungen{laquo} eingeschlossen. In der vorliegenden Fassung wurde vor allem das zweite Kapitel iiber Diffe rentialgleichungen mit analytischen Koeffizienten, also speziell der hypergeome trischen, Besselschen und Kummerschen Differentialgleichungen' neu gefaBt und einem neuen Ordnungsprinzip, der {raquo}Invariante{laquo}, unterworfen. Damit ge lingt es, jede vorgelegte Differentialgleichung rasch einzuordnen und auf eine dieser Standardformen zu transformieren. Diese Transformationsformeln wur den neu entwickelt und werden hier zum ersten Mal veroffentlicht. Fiir alle Satze und Entwicklungen werden strenge Beweise geboten; z. B.
Author: Wolfgang Grobner
Publisher: Springer Science & Business Media
ISBN: 146847362X
Category : Science
Languages : en
Pages : 206
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Book Description
Dieses Buch beruht auf 40 lahren intensiven Studiums der Differentialglei chungen, sowohl yom theoretischen als auch yom praktischen Gesichtspunkt aus, eines Studiums, das mit meiner Tatigkeit im Rechen-Institut M. Picones in Rom begann, sodann fortgesetzt wurde in der Gruppe flir Industriemathema tik der Luftfahrt-Forschungsanstalt in Braunschweig, und endlich mit meinen Vorlesungen, hauptsachlich an der Universitat Innsbruck, abgeschlossen wurde. Die Zeit der Weltraumfliige stellte hier neue Aufgaben der Bahnberechnung von Satelliten, deren Bearbeitung theoretisch eine geschlossene Formel zur Losung des n-Korper-Problems, praktisch eine neue Methode zur Berechnung von reguJaren Differentialgleichungssystemen zeitigte, die mit den besten bekannten Losungsmethoden erfolgreich in Konkurrenz treten konnte, was vor aHem meinen Mitarbeitern H. Knapp und G. Wanner zu danken war. Die Vorlesung iiber Differentialgleichungen habe ich seit 1947 in regelmaBi gen Abstanden an der Universitat Innsbruck gehalten, bei jeder Wiederholung neu bearbeitet und durch Seminararbeiten vervollstandigt; auch in meiner flir Physik-Studenten besonders gehaltenen Vorlesung iiber {raquo}Die mathemati schen Methoden der Physik{laquo} habe ich in gekiirzter Form immer die {raquo}Differen tialgleichungen{laquo} eingeschlossen. In der vorliegenden Fassung wurde vor allem das zweite Kapitel iiber Diffe rentialgleichungen mit analytischen Koeffizienten, also speziell der hypergeome trischen, Besselschen und Kummerschen Differentialgleichungen' neu gefaBt und einem neuen Ordnungsprinzip, der {raquo}Invariante{laquo}, unterworfen. Damit ge lingt es, jede vorgelegte Differentialgleichung rasch einzuordnen und auf eine dieser Standardformen zu transformieren. Diese Transformationsformeln wur den neu entwickelt und werden hier zum ersten Mal veroffentlicht. Fiir alle Satze und Entwicklungen werden strenge Beweise geboten; z. B.
Author: Princeton University. Library
Publisher:
ISBN:
Category : Classified catalogs
Languages : en
Pages : 696
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Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 420
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Book Description
The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.
Author: Princeton University. Library
Publisher:
ISBN:
Category : Library catalogs
Languages : en
Pages : 454
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Author: American Mathematical Society, New York
Publisher:
ISBN:
Category :
Languages : en
Pages : 438
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Author: Princeton University. Library
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 124
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Author: Erich Kähler
Publisher: Walter de Gruyter
ISBN: 3110905434
Category : Mathematics
Languages : en
Pages : 984
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Book Description
For most mathematicians and many mathematical physicists the name Erich Kähler is strongly tied to important geometric notions such as Kähler metrics, Kähler manifolds and Kähler groups. They all go back to a paper of 14 pages written in 1932. This, however, is just a small part of Kähler's many outstanding achievements which cover an unusually wide area: From celestial mechanics he got into complex function theory, differential equations, analytic and complex geometry with differential forms, and then into his main topic, i.e. arithmetic geometry where he constructed a system of notions which is a precursor and, in large parts, equivalent to the now used system of Grothendieck and Dieudonné. His principal interest was in finding the unity in the variety of mathematical themes and establishing thus mathematics as a universal language. In this volume Kähler's mathematical papers are collected following a "Tribute to Herrn Erich Kähler" by S. S. Chern, an overview of Kähler's life data by A. Bohm and R. Berndt, and a Survey of his Mathematical Work by the editors. There are also comments and reports on the developments of the main topics of Kähler's work, starting by W. Neumann's paper on the topology of hypersurface singularities, J.-P. Bourguignon's report on Kähler geometry and, among others by Berndt, Bost, Deitmar, Ekeland, Kunz and Krieg, up to A. Nicolai's essay "Supersymmetry, Kähler geometry and Beyond". As Kähler's interest went beyond the realm of mathematics and mathematical physics, any picture of his work would be incomplete without touching his work reaching into other regions. So a short appendix reproduces three of his articles concerning his vision of mathematics as a universal Theme together with an essay by K. Maurin giving an "Approach to the philosophy of Erich Kähler".
Author: Arild Stubhaug
Publisher: Springer Science & Business Media
ISBN: 3662043866
Category : Mathematics
Languages : en
Pages : 556
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Book Description
Sophus Lie (1842-1899) is one of Norways greatest scientific talents. His mathematical works have made him famous around the world no less than Niels Henrik Abel. The terms "Lie groups" and "Lie algebra" are part of the standard mathematical vocabulary. In his comprehensive biography the author Arild Stubhaug introduces us to both the person Sophus Lie and his time. We follow him through: childhood at the vicarage in Nordfjordeid; his youthful years in Moss; education in Christiania; travels in Europe; and learn about his contacts with the leading mathematicians of his time.
Author: A. Ostrowski
Publisher: Springer Science & Business Media
ISBN: 9783764315115
Category : Mathematics
Languages : en
Pages : 732
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Book Description
This publication was made possible through a bequest from my beloved late wife. United together in this present collection are those works by the author which have not previously appeared in book form. The following are excepted: Vorlesungen uber Differential und Integralrechnung (Lectures on Differential and Integral Calculus) Vols 1-3, Birkhauser Verlag, Basel (1965-1968); Aufgabensammlung zur Infinitesimalrechnung (Exercises in Infinitesimal Calculus) Vols 1, 2a, 2b, and 3, Birkhauser Verlag, Basel (1967-1977); two issues from Memorial des Sciences on Conformal Mapping (written together with C. Gattegno), Gauthier-Villars, Paris (1949); Solution of Equations in Euc1idean and Banach Spaces, Academic Press, New York (1973); and Stu dien uber den Schottkyschen Satz (Studies on Schottky's Theorem), Wepf & Co., Basel (1931). Where corrections have had to be implemented in the text of certain papers, references to these are made at the conc1usion of each paper. In the few instances where this system does not, for technical reasons, seem appropriate, an asterisk in the page margin indicates wherever a correction is necessary and this is then given at the end of the paper. (There is one exception: the correc tions to the paper on page 561 are presented on page 722. The works are published in 6 volumes and are arranged under 16 topic headings. Within each heading, the papers are ordered chronologically according to the date of original publication."
Author: Hans Lewy
Publisher: Springer Science & Business Media
ISBN: 9780817635237
Category : Mathematics
Languages : en
Pages : 452
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Book Description
The work of Hans Lewy (1904--1988) has had a profound influence in the direction of applied mathematics and partial differential equations, in particular, from the late 1920s. Two of the particulars are well known. The Courant--Friedrichs--Lewy condition (1928), or CFL condition, was devised to obtain existence and approximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. Lewy's example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regularity theory of elliptic equations and systems, the Monge--Ampère Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and several complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help one understand the essential concepts embedded in an issue, although at a cost in generality. This approach was extremely successful. In this two-volume work, most all of Lewy's papers are presented, in chronological order. They are preceded by several short essays about Lewy himself, prepared by Helen Lewy, Constance Reid, and David Kinderlehrer, and commentaries on his work by Erhard Heinz, Peter Lax, Jean Leray, Richard MacCamy, François Treves, and Louis Nirenberg. Additionally, there are Lewy's own remarks on the occasion of his honorary degree from the University of Bonn.
