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.

Topological Methods in Hydrodynamics (Applied Mathematical Sciences, 125)

Arnold, Vladimir I.

Khesin, Boris A.

Reference

Springer

Science & Math

Mathematics

Topological Methods in Hydrodynamics (Applied Mathematical Sciences)

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,&nbsp;&nbsp; combinatorics of Bernoulli, Euler and Springer numbers,&nbsp;&nbsp; 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&nbsp; 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&nbsp; 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.

VLADIMIR I. ARNOLD―Collected Works: Dynamics, Combinatorics, and Invariants of Knots, Curves, and Wave Fronts 1992–1995 (Vladimir I. Arnold - Collected Works, 6)

The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

Mathematical Aspects of Classical and Celestial Mechanics (Encyclopaedia of Mathematical Sciences, 3)

Kozlov, Valery V.

Neishtadt, Anatoly I.

Yesterday and Long Ago

This is a charming collection of essays on life and science, by one of the leading mathematicians of our day. Vladimir Igorevich Arnold is renowned for his achievements in mathematics, and nearly as famous for his informal teaching style, and for the clarity and accessibility of his writing. The chapter headings convey Arnold’s humor and restless imagination. A few examples: My first recollections; The combinatorics of Plutarch; The topology of surfaces according to Alexander of Macedon; Catching a pike in Cambridge. Yesterday and Long Ago offers a rare opportunity to appreciate the life and work of one of the world’s outstanding living mathematicians.

Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEW

Ordinary Differential Equations (Universitext)

Choice Outstanding Title! (January 2006) This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. 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.

Lectures on Partial Differential Equations (Universitext)

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.

Vorlesungen über partielle Differentialgleichungen (Springer-Lehrbuch) (German Edition)

Foreign Language Study & Reference

See the best price to sell, buy, or rent books by Arnold, Vladimir I.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Arnold, Vladimir I.

See the best price to sell, buy, or rent books by Arnold, Vladimir I.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Topological Methods in Hydrodynamics (Applied Mathematical Sciences, 125)

Topological Methods in Hydrodynamics (Applied Mathematical Sciences, 125)

Topological Methods in Hydrodynamics (Applied Mathematical Sciences, 125)

Topological Methods in Hydrodynamics (Applied Mathematical Sciences)

VLADIMIR I. ARNOLD―Collected Works: Dynamics, Combinatorics, and Invariants of Knots, Curves, and Wave Fronts 1992–1995 (Vladimir I. Arnold - Collected Works, 6)

Mathematical Aspects of Classical and Celestial Mechanics (Encyclopaedia of Mathematical Sciences, 3)

Yesterday and Long Ago

Ordinary Differential Equations (Universitext)

Lectures on Partial Differential Equations (Universitext)

Vorlesungen über partielle Differentialgleichungen (Springer-Lehrbuch) (German Edition)