Vladimir I. Arnold – författare
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44 produkter
44 produkter
E-bok
PDF, Engelska, 20082 207 kr
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Inbunden, Engelska, 1998
1 723 kr
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The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Del 125 - Applied Mathematical Sciences
Topological Methods in Hydrodynamics
Inbunden, Engelska, 2021
1 401 kr
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First published in 1998 this unique monograph treats topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view.It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. This book, now accepted as one of the main references in the field, is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry. The updated second edition also contains a survey of recent developments in this now-flourishing field of topological and geometric hydrodynamics.
E-bok
PDF, Engelska, 20211 672 kr
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First published in 1998 this unique monograph treats topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view.
It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. This book, now accepted as one of the main references in the field, is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry. The updated second edition also contains a survey of recent developments in this now-flourishing field of topological and geometric hydrodynamics.
Del 125 - Applied Mathematical Sciences
Topological Methods in Hydrodynamics
Häftad, Engelska, 2022
1 201 kr
Skickas inom 5-8 vardagar
First published in 1998 this unique monograph treats topological, group-theoretic, and geometric problems of ideal hydrodynamics and magneto-hydrodynamics from a unified point of view.It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. This book, now accepted as one of the main references in the field, is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry. The updated second edition also contains a survey of recent developments in this now-flourishing field of topological and geometric hydrodynamics.
Inbunden, Engelska, 2023
1 830 kr
Skickas inom 5-8 vardagar
This volume 6 of the Collected Works comprises 27 papers by V.I.Arnold, one of the most outstanding mathematicians of all times, written in 1991 to 1995. During this period Arnold's interests covered Vassiliev’s theory of invariants and knots, invariants and bifurcations of plane curves, combinatorics of Bernoulli, Euler and Springer numbers, geometry of wave fronts, the Berry phase and quantum Hall effect.The articles include a list of problems in dynamical systems, a discussion of the problem of (in)solvability of equations, papers on symplectic geometry of caustics and contact geometry of wave fronts, comments on problems of A.D.Sakharov, as well as a rather unusual paper on projective topology. The interested reader will certainly enjoy Arnold’s 1994 paper on mathematical problems in physics with the opening by-now famous phrase “Mathematics is the name for those domains of theoretical physics that are temporarily unfashionable.”The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science. The volume also includes translations of two interviews given by Arnold to the French and Spanish media. One can see how worried he was about the fate of Russian and world mathematics and science in general.
Häftad, Engelska, 2024
1 830 kr
Skickas inom 10-15 vardagar
This volume 6 of the Collected Works comprises 27 papers by V.I.Arnold, one of the most outstanding mathematicians of all times, written in 1991 to 1995. During this period Arnold's interests covered Vassiliev’s theory of invariants and knots, invariants and bifurcations of plane curves, combinatorics of Bernoulli, Euler and Springer numbers, geometry of wave fronts, the Berry phase and quantum Hall effect.The articles include a list of problems in dynamical systems, a discussion of the problem of (in)solvability of equations, papers on symplectic geometry of caustics and contact geometry of wave fronts, comments on problems of A.D.Sakharov, as well as a rather unusual paper on projective topology. The interested reader will certainly enjoy Arnold’s 1994 paper on mathematical problems in physics with the opening by-now famous phrase “Mathematics is the name for those domains of theoretical physics that are temporarily unfashionable.”The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science. The volume also includes translations of two interviews given by Arnold to the French and Spanish media. One can see how worried he was about the fate of Russian and world mathematics and science in general.
Inbunden, Engelska, 2025
2 152 kr
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This volume 5 of the Collected Works includes papers written by V.I. Arnold, one of the most outstanding mathematicians of all times, during the period from 1986 to 1991. Arnold’s work during this period covers symplectic topology, contact geometry and wave propagation, quasicrystals, dynamics of intersections, bifurcations, and catastrophe theory.He was seriously concerned with decaying mathematical education in Russia and worldwide — one can see this in several articles translated for this volume. Of particular interest are the sets of problems which Arnold collected under the name “Mathematical Trivium” — in his opinion, any math or physics university graduate should be able to solve any problem from that list. The reader will also enjoy perusing several interviews with Arnold, as well as his remarkable warm memories about Ya.B. Zeldovich and his teacher A.N. Kolmogorov. One of Arnold’s papers on catastrophe theory translated for this volume also contains a beautiful translation of E.A. Baratynsky’s poem made by A.B. Givental.The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science.
Häftad, Engelska, 2026
3 042 kr
Kommande
This volume 5 of the Collected Works includes papers written by V.I. Arnold, one of the most outstanding mathematicians of all times, during the period from 1986 to 1991. Arnold’s work during this period covers symplectic topology, contact geometry and wave propagation, quasicrystals, dynamics of intersections, bifurcations, and catastrophe theory.He was seriously concerned with decaying mathematical education in Russia and worldwide — one can see this in several articles translated for this volume. Of particular interest are the sets of problems which Arnold collected under the name “Mathematical Trivium” — in his opinion, any math or physics university graduate should be able to solve any problem from that list. The reader will also enjoy perusing several interviews with Arnold, as well as his remarkable warm memories about Ya.B. Zeldovich and his teacher A.N. Kolmogorov. One of Arnold’s papers on catastrophe theory translated for this volume also contains a beautiful translation of E.A. Baratynsky’s poem made by A.B. Givental.The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science.
Inbunden, Engelska, 2025
2 367 kr
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This volume 7 of the “Collected Works" includes papers written by V.I. Arnold, one of the most outstanding mathematicians of all times, during the period from 1996 to 1999. At that time Arnold was focusing on the description of various spaces of curves, higher-dimensional continued fractions, pseudoperiodic topology, and unifying ideas related to symplectization, complexification and mathematical trinities in topology and mathematics in general. The “Arnoldfest" conference celebrating 60th anniversary of V.Arnold took place at the Fields Institute and University of Toronto, Canada, in 1997, and Arnold's lectures at that conference are included in this volume. In the 1990s Arnold got increasingly concerned with the decay of science and math education in many Western countries, and his publications fighting “the victorious march of the antiscientific revolution" (as he phrased it in one of his papers) are collected in this volume as well. Some of Arnold's writings stimulated others to write supplements with more detail, and the volume also includes the notes of A.M.Vershik, J.K.Moser, and B.A.Khesin. Finally, a glimpse of Arnold's personality can also be appreciated in a little gem, his short article devoted to resolving the mystery of the origin of the epigraph to “Eugene Onegin" by A.S. Pushkin, a famous XIXth century Russian poet. The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science. This volume completes the seven-volume project of “Collected Works of Vladimir Arnold", the first volume of which was published in 2009. Arnold's publications in the 2000s were also abundant, he turned to new topics, wrote several books, he gave numerous lectures, both research and educational. But what has already been published in these seven volumes is a treasure trove, an ocean of ideas, methods, and results, and this is now before the reader to explore. Happy voyage!
Häftad, Engelska, 2026
3 278 kr
Kommande
This volume 7 of the “Collected Works" includes papers written by V.I. Arnold, one of the most outstanding mathematicians of all times, during the period from 1996 to 1999. At that time Arnold was focusing on the description of various spaces of curves, higher-dimensional continued fractions, pseudoperiodic topology, and unifying ideas related to symplectization, complexification and mathematical trinities in topology and mathematics in general. The “Arnoldfest" conference celebrating 60th anniversary of V.Arnold took place at the Fields Institute and University of Toronto, Canada, in 1997, and Arnold's lectures at that conference are included in this volume. In the 1990s Arnold got increasingly concerned with the decay of science and math education in many Western countries, and his publications fighting “the victorious march of the antiscientific revolution" (as he phrased it in one of his papers) are collected in this volume as well. Some of Arnold's writings stimulated others to write supplements with more detail, and the volume also includes the notes of A.M.Vershik, J.K.Moser, and B.A.Khesin. Finally, a glimpse of Arnold's personality can also be appreciated in a little gem, his short article devoted to resolving the mystery of the origin of the epigraph to “Eugene Onegin" by A.S. Pushkin, a famous XIXth century Russian poet. The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science. This volume completes the seven-volume project of “Collected Works of Vladimir Arnold", the first volume of which was published in 2009. Arnold's publications in the 2000s were also abundant, he turned to new topics, wrote several books, he gave numerous lectures, both research and educational. But what has already been published in these seven volumes is a treasure trove, an ocean of ideas, methods, and results, and this is now before the reader to explore. Happy voyage!
E-bok
PDF, Engelska, 20121 258 kr
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In July 1996, a conference was organized by the editors of this volume at the Mathematische Forschungsinstitut Oberwolfach to honour Egbert Brieskorn on the occasion of his 60th birthday. Most of the mathematicians invited to the conference have been influenced in one way or another by Brieskorn''s work in singularity theory. It was the first time that so many people from the Russian school could be present at a conference in singularity theory outside Russia. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory''s relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn''s own interests. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory''s relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrates the breadth of Brieskorn''s own interests.
E-bok
PDF, Engelska, 20121 258 kr
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Translated from the Russian by E.J.F. Primrose "Remarkable little book." -SIAM REVIEW V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century. Some of Huygens'' and Newton''s ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics. The book provides present-day generalizations of Newton''s theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings.
Del 162 - Progress in Mathematics
Singularities
The Brieskorn Anniversary Volume
Häftad, Engelska, 2012
972 kr
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In July 1996, a conference was organized by the editors of this volume at the Mathematische Forschungsinstitut Oberwolfach to honour Egbert Brieskorn on the occasion of his 60th birthday. Most of the mathematicians invited to the conference have been influenced in one way or another by Brieskorn's work in singularity theory. It was the first time that so many people from the Russian school could be present at a conference in singularity theory outside Russia. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn's own interests. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrates the breadth of Brieskorn's own interests.
Inbunden, Engelska, 2004
1 723 kr
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Arnold's Problems contains mathematical problems brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books. The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (especially of physics), i.e. an experimental science. Many of these problems are still at the frontier of research today and are still open, and even those that are mainly solved keep stimulating new research, appearing every year in journals all over the world. The second part of the book is a collection of commentaries, mostly by Arnold's former students, on the current progress in the problems' solutions (featuring a bibliography inspired by them). This book will be of great interest to researchers and graduate students in mathematics and mathematical physics.
Häftad, Engelska, 2004
1 439 kr
Skickas inom 5-8 vardagar
Arnold's Problems contains mathematical problems brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books. The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (especially of physics), i.e. an experimental science. Many of these problems are still at the frontier of research today and are still open, and even those that are mainly solved keep stimulating new research, appearing every year in journals all over the world. The second part of the book is a collection of commentaries, mostly by Arnold's former students, on the current progress in the problems' solutions (featuring a bibliography inspired by them). This book will be of great interest to researchers and graduate students in mathematics and mathematical physics.
Del 3 - Encyclopaedia of Mathematical Sciences
Mathematical Aspects of Classical and Celestial Mechanics
Inbunden, Engelska, 2006
2 367 kr
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In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.
Inbunden, Engelska, 2006
386 kr
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History is not what we were wearing, It is how we had been utterly ruined. B.Pasternak.“Spektorsky” In the spring of 1999 the police found me lying unconscious with a broken forehead next to my bike in the outskirts of Paris, and delivered me to a hospital. It took a few weeks for French doctors to bring me to consciousness. But I did not recognize my son and said about my wife: “this woman says that she is my wife”. A doctor asked me how many years we had been married. I answered correctly, “twenty four”, and the doctor wrote down: “arithmetical abilities are preserved”. Later, French doctors told me that with such a trauma any Frenchman would succumb immediately. But then they added: “Russians are very tough so you should live several months more”. In a Western textbook I had read regarding effects of poisons: “as for alcohol the lethal dose for Russians is several times higher”. Perhaps the same applies to traumas.
Häftad, Engelska, 2006
999 kr
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The first two chapters of this book have been thoroughly revised and sig nificantly expanded. Sections have been added on elementary methods of in tegration (on homogeneous and inhomogeneous first-order linear equations and on homogeneous and quasi-homogeneous equations), on first-order linear and quasi-linear partial differential equations, on equations not solved for the derivative, and on Sturm's theorems on the zeros of second-order linear equa tions. Thus the new edition contains all the questions of the current syllabus in the theory of ordinary differential equations. In discussing special devices for integration the author has tried through out to lay bare the geometric essence of the methods being studied and to show how these methods work in applications, especially in mechanics. Thus to solve an inhomogeneous linear equation we introduce the delta-function and calculate the retarded Green's function; quasi-homogeneous equations lead to the theory of similarity and the law of universal gravitation, while the theorem on differentiability of the solution with respect to the initial conditions leads to the study of the relative motion of celestial bodies in neighboring orbits. The author has permitted himself to include some historical digressions in this preface. Differential equations were invented by Newton (1642-1727).
E-bok
PDF, Tyska, 2006253 kr
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Nach seinem bekannten und viel verwendeten Buch über gewöhnliche Differentialgleichungen widmet sich der berühmte Mathematiker Vladimir Arnold nun den partiellen Differentialgleichungen in einem neuen Lehrbuch. In seiner unnachahmlich eleganten Art führt er über einen geometrischen, anschaulichen Weg in das Thema ein, und ermöglicht den Lesern so ein vertieftes Verständnis der Natur der partiellen Differentialgleichungen. Für Studierende der Mathematik und Physik ist dieses Buch ein Muss.
Wie alle Bücher Vladimir Arnolds ist dieses Buch voller geometrischer Erkenntnisse. Arnold illustriert jeden Grundsatz mit einer Abbildung. Das Buch behandelt die elementarsten Teile des Fachgebiets and beschränkt sich hauptsächlich auf das Cauchy-Problem und das Neumann-Problems für die klassischen Lineargleichungen der mathematischen Physik, insbesondere auf die Laplace-Gleichung und die Wellengleichung, wobei die Wärmeleitungsgleichung und die Korteweg-de-Vries-Gleichung aber ebenfalls diskutiert werden. Die physikalische Intuition wird besonders hervorgehoben. Eine große Anzahl von Problemen ist übers ganze Buch verteilt, und ein ganzer Satz von Aufgaben findet sich am Ende.
Was dieses Buch so einzigartig macht, ist das besondere Talent Arnolds, ein Thema aus einer neuen, frischen Perspektive zu beleuchten. Er lüftet gerne den Schleier der Verallgemeinerung, der so viele mathematische Texte umgibt, und enthüllt die im wesentlichen einfachen, intuitiven Ideen, die dem Thema zugrunde liegen. Das kann er besser als jeder andere mathematische Autor.
Häftad, Engelska, 2003
758 kr
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Choice Outstanding Title! (January 2006)Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's equation and the wave equation, although the heat equation and the Korteweg-de Vries equation are also discussed. Physical intuition is emphasized. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging!What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.
Häftad, Tyska, 2004
258 kr
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Nach seinem bekannten und viel verwendeten Buch über gewöhnliche Differentialgleichungen widmet sich der berühmte Mathematiker Vladimir Arnold nun den partiellen Differentialgleichungen in einem neuen Lehrbuch. In seiner unnachahmlich eleganten Art führt er über einen geometrischen, anschaulichen Weg in das Thema ein, und ermöglicht den Lesern so ein vertieftes Verständnis der Natur der partiellen Differentialgleichungen. Für Studierende der Mathematik und Physik ist dieses Buch ein Muss.Wie alle Bücher Vladimir Arnolds ist dieses Buch voller geometrischer Erkenntnisse. Arnold illustriert jeden Grundsatz mit einer Abbildung. Das Buch behandelt die elementarsten Teile des Fachgebiets and beschränkt sich hauptsächlich auf das Cauchy-Problem und das Neumann-Problems für die klassischen Lineargleichungen der mathematischen Physik, insbesondere auf die Laplace-Gleichung und die Wellengleichung, wobei die Wärmeleitungsgleichung und die Korteweg-de-Vries-Gleichung aber ebenfalls diskutiert werden. Die physikalische Intuition wird besonders hervorgehoben. Eine große Anzahl von Problemen ist übers ganze Buch verteilt, und ein ganzer Satz von Aufgaben findet sich am Ende. Was dieses Buch so einzigartig macht, ist das besondere Talent Arnolds, ein Thema aus einer neuen, frischen Perspektive zu beleuchten. Er lüftet gerne den Schleier der Verallgemeinerung, der so viele mathematische Texte umgibt, und enthüllt die im wesentlichen einfachen, intuitiven Ideen, die dem Thema zugrunde liegen. Das kann er besser als jeder andere mathematische Autor.
E-bok
PDF, Engelska, 20073 157 kr
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In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.
Häftad, Engelska, 1992
865 kr
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This well-known booklet, now in its third, expanded edition, provides an informal survey of applications of singularity theory in a wide range of areas. Although the first few chapters touch briefly (and critically) on theThom-Zeeman catastrophe theory, most of the book is concerned with more recent and less controversial aspects, covering such topics as: bifurcations and stability loss, wavefront propagation, the distribution of matter in the universe, optimization and control problems, visible contours,bypassing an obstacle, symplectic and contact geometry, complex singularities, and the surprising connections between singularities and widely disparate mathematical objects such as regular polyhedra and reflection groups. Readers familiar with the previous editions will find much that is new. Results have been brought up to date, and among the new or expanded topics discussed are delayed loss of stability, cascades of period doublings and triplings, shock waves, implicit differential equationsand folded singularities, interior scattering, and more. Three new sections give an overview of the history of singularity theory and its applications from Leonardo da Vinci to modern times, a discussion of perestroika in terms of the theory of metamorphoses, and a list of 93 problems touching on most of the subject matter in the book. The text is enhanced by fifteen new drawings (there are now 87 in all) and improvements to old ones. The already extensive literature list has been updated and expanded. As a result, the book has been enlarged by almost a third. Arnol'd's goal with this edition remains the same: to explain the essence of the results and applications to readers having a minimal mathematical background. All that he asks, is that the reader have an inquiring mind.
Häftad, Tyska, 2001
408 kr
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Newton entwickeltealle elementaren Funktionen (rationale Funktionen, Wurzelfunktionen, trigonometrische Funktionen, Exponentialfunktion und Logarithmus) in"Taylorreihen". Diese und die von ihm erstellte Liste von Stammfunktionen (die fast unverändert in moderne Lehrbücher der Analysis übernommen wurde) ermöglichten ihm nach seinen eigenen Worten, "in einer halben Viertelstunde" die Flächen beliebiger Figuren zu vergleichen. Newton zeigte, daß die Koeffizienten seiner Reihen proportional zu den sukzessiven Ableitungen der Funktion sind, doch ging er darauf nicht weiter ein, da er zu Recht meinte, daß die Rechnungen in der Analysis bequemer auszuführen sind, wenn man nicht mit höheren Ableitungen arbeitet, sondern die ersten Glieder der Reihenentwicklung ausrechnet. Für Newton diente der Zusammenhang zwischen den Koeffizienten der Reihe und den Ableitungen eher dazu, die Ableitungen zu berechnen als die Reihe aufzustellen. Eine von Newtons wichtigsten Leistungen war seine Theorie des Sonnensy stems, die in den "Mathematischen Prinzipien der Naturlehre" ("Principia") ohne Verwendung der mathematischen Analysis dargestellt ist. Allgemein wird angenommen, daß Newton das allgemeine Gravitationsgesetz mit Hilfe seiner Analysis entdeckt habe. Tatsächlich hat Newton (1680) lediglich bewiesen, daß die Bahnkurven in einem Anziehungsfeld Ellipsen sind, wenn die Anziehungskraft invers proportional zum Abstandsquadrat ist: Auf das Gesetz selbst wurde Newton von Hooke (1635-1703) hingewiesen (vgl. § 8) und es scheint, daß es noch von weiteren Forschern vermutet wurde.
Del 1 - Vladimir I. Arnold - Collected Works
Vladimir I. Arnold - Collected Works
Representations of Functions, Celestial Mechanics, and KAM Theory 1957-1965
Inbunden, Engelska, 2009
2 325 kr
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Vladimir Igorevich Arnold is one of the most influential mathematicians of our time. V. I. Arnold launched several mathematical domains (such as modern geometric mechanics, symplectic topology, and topological fluid dynamics) and contributed, in a fundamental way, to the foundations and methods in many subjects, from ordinary differential equations and celestial mechanics to singularity theory and real algebraic geometry. Even a quick look at a partial list of notions named after Arnold already gives an overview of the variety of such theories and domains: KAM (Kolmogorov-Arnold-Moser) theory, The Arnold conjectures in symplectic topology, The Hilbert-Arnold problem for the number of zeros of abelian integrals, Arnold's inequality, comparison, and complexification method in real algebraic geometry, Arnold-Kolmogorov solution of Hilbert's 13th problem, Arnold's spectral sequence in singularity theory, Arnold diffusion, The Euler-Poincare-Arnold equations for geodesics on Lie groups, Arnold's stability criterion in hydrodynamics, ABC (Arnold-Beltrami-Childress) ?ows in ?uid dynamics, The Arnold-Korkina dynamo, Arnold's cat map, The Arnold-Liouville theorem in integrable systems, Arnold's continued fractions, Arnold's interpretation of the Maslov index, Arnold's relation in cohomology of braid groups, Arnold tongues in bifurcation theory, The Jordan-Arnold normal forms for families of matrices, The Arnold invariants of plane curves.Arnold wrote some 700 papers, and many books, including 10 university textbooks. He is known for his lucid writing style, which combines mathematical rigour with physical and geometric intuition. Arnold's books on Ordinarydifferentialequations and Mathematical methodsofclassicalmechanics became mathematical bestsellers and integral parts of the mathematical education of students throughout the world.
E-bok
PDF, Engelska, 20093 054 kr
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Del 3 - Encyclopaedia of Mathematical Sciences
Mathematical Aspects of Classical and Celestial Mechanics
Häftad, Engelska, 2010
2 367 kr
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In this book we describe the basic principles, problems, and methods of cl- sical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth ?rst and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.
Häftad, Engelska, 2010
381 kr
Skickas inom 10-15 vardagar
History is not what we were wearing, It is how we had been utterly ruined. B.Pasternak.“Spektorsky” In the spring of 1999 the police found me lying unconscious with a broken forehead next to my bike in the outskirts of Paris, and delivered me to a hospital. It took a few weeks for French doctors to bring me to consciousness. But I did not recognize my son and said about my wife: “this woman says that she is my wife”. A doctor asked me how many years we had been married. I answered correctly, “twenty four”, and the doctor wrote down: “arithmetical abilities are preserved”. Later, French doctors told me that with such a trauma any Frenchman would succumb immediately. But then they added: “Russians are very tough so you should live several months more”. In a Western textbook I had read regarding effects of poisons: “as for alcohol the lethal dose for Russians is several times higher”. Perhaps the same applies to traumas.
Häftad, Engelska, 2012
2 367 kr
Skickas inom 10-15 vardagar
Vladimir Igorevich Arnold is one of the most influential mathematicians of our time. V. I. Arnold launched several mathematical domains (such as modern geometric mechanics, symplectic topology, and topological fluid dynamics) and contributed, in a fundamental way, to the foundations and methods in many subjects, from ordinary differential equations and celestial mechanics to singularity theory and real algebraic geometry. Even a quick look at a partial list of notions named after Arnold already gives an overview of the variety of such theories and domains: KAM (Kolmogorov-Arnold-Moser) theory, The Arnold conjectures in symplectic topology, The Hilbert-Arnold problem for the number of zeros of abelian integrals, Arnold's inequality, comparison, and complexification method in real algebraic geometry, Arnold-Kolmogorov solution of Hilbert's 13th problem, Arnold's spectral sequence in singularity theory, Arnold diffusion, The Euler-Poincare-Arnold equations for geodesics on Lie groups, Arnold's stability criterion in hydrodynamics, ABC (Arnold-Beltrami-Childress) ?ows in ?uid dynamics, The Arnold-Korkina dynamo, Arnold's cat map, The Arnold-Liouville theorem in integrable systems, Arnold's continued fractions, Arnold's interpretation of the Maslov index, Arnold's relation in cohomology of braid groups, Arnold tongues in bifurcation theory, The Jordan-Arnold normal forms for families of matrices, The Arnold invariants of plane curves.Arnold wrote some 700 papers, and many books, including 10 university textbooks. He is known for his lucid writing style, which combines mathematical rigour with physical and geometric intuition. Arnold's books on Ordinarydifferentialequations and Mathematical methodsofclassicalmechanics became mathematical bestsellers and integral parts of the mathematical education of students throughout the world.