GEWÖHNLICHE DIFFERENTIALGLEICHUNGEN (SPRINGERLEHRBUCH) von Vladimir Arnold TOP

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Gut: Buch, das gelesen wurde, sich aber in einem guten Zustand befindet. Der Einband weist nur sehr ...
Book Title
Ordinary Differential Equations (Springer Textbook)
Item Height
0.77 inches
ISBN-10
3540548130
ISBN
9783540548133
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
Springer
ISBN-10
3540548130
ISBN-13
9783540548133
eBay Product ID (ePID)
4432204

Product Key Features

Number of Pages
IV, 338 Pages
Language
English
Publication Name
Ordinary Differential Equations
Publication Year
1992
Subject
Differential Equations / General, Physics / Mathematical & Computational, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics, Science
Author
V. I. Arnold
Series
Springer Textbook Ser.
Format
Trade Paperback

Dimensions

Item Weight
16.6 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
Reviews
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 ... . The new edition is highly recommended as a general reference for the essential theory of ordinary differential equations and as a textbook for an introductory course for serious undergraduate or graduate students. ... In the US system, it is an excellent text for an introductory graduate course." (Carmen Chicone, SIAM Review, Vol. 49 (2), 2007) "Vladimir Arnold's is a master, not just of the technical realm of differential equations but of pedagogy and exposition as well. ... The writing throughout is crisp and clear. ... Arnold's says that the book is based on a year-long sequence of lectures for second-year mathematics majors in Moscow. In the U.S., this material is probably most appropriate for advanced undergraduates or first-year graduate students." (William J. Satzer, MathDL, August, 2007)
Number of Volumes
1 vol.
Illustrated
Yes
Original Language
Russian
Synopsis
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)., 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, Few books on ODEs have the elegant geometric insight of this one, which puts a clear emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. In many instances, the author employs physical reasoning as shorthand for much longer formal mathematical reasoning., 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)."
LC Classification Number
QA299.6-433QC19.2-2

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