Former Library book. Shows some signs of wear, and may have some markings on the inside. Bookseller Inventory #
Synopsis: Although there is no lack of other books on this subject, even with the same title, the appearance of this new one is fully justified on at least two grounds: its approach makes full use of modern mathematical concepts and terminology of considerable sophistication and abstraction, going well beyond the traditional presentation of the subject; and, at the same time, the resulting enhancement of mathematical abstractness is counterbalanced by a constant appeal to geometrical and physical considerations, presented in the main text and in numerous problems and exercises.
In terms of mathematical approach, the text is dominated by two central ideas: the theorem on rectifiability of a vector field (which is equivalent to the usual theorems on existence, uniqueness, and differentiability of solutions) and the theory of one-parameter groups of linear transformations (equivalent to the theory of linear autonomous systems). The book also develops whole congeries of fundamental concepts—like phase space and phase flows, smooth manifolds and tangent bundles, vector fields and one-parameter groups of diffeomorphisms—that remain in the shadows in the traditional coordinate-based approach. All of these concepts are presented in some detail, but without assuming any background on the part of the reader beyond the scope of the standard elementary courses on analysis and linear algebra.
In terms of concrete applications, the book introduces the pendulum equation at the very beginning, and the efficacy of various concepts and methods introduced throughout is subsequently tested by applying them to this example. Thus, the section on first integrals leads to the law of conservation of energy; the theorem on differentiation with respect to a parameter finds application in the "method of small parameters"; and the theory of linear equations with periodic coefficients merges naturally with the study of parametric resonance. This geometrical and physical specificity is made still more vivid through the inclusion of 259 line drawings and 260 exercises in which other examples are taken up.
From the Back Cover: From the reviews: "... This book is an excellent text for a course whose goal is a mathematical treatment of differential equations and the related physical systems." L'Enseignment Mathematique "... Arnold's book is unique as a sophisticated but accessible introduction to the modern theory, and we should be grateful that it exists in a convenient language." Mathematical Association of America Monthly
Title: Ordinary Differential Equations
Publisher: The MIT Press
Publication Date: 1973
Book Condition: Good
Book Description Dec 15, 1973. Book Condition: gebraucht; gut. ohne Schutzumschlag, textsauber und gepflegt, leicht angedunkelt altersbedingt. Bookseller Inventory # 202-3-15
Book Description The MIT Press 1973-12-15, 1973. Hardcover. Book Condition: good. First Edition, First Printing. 0262010372. Bookseller Inventory # 688736
Book Description The MIT Press, 1973. Hardcover. Book Condition: Used: Good. Bookseller Inventory # SONG0262010372
Book Description The MIT Press, 1973. Hardcover. Book Condition: Very Good. Great condition with minimal wear, aging, or shelf wear. Bookseller Inventory # P020262010372
Book Description The MIT Press. Hardcover. Book Condition: New. 0262010372 New. Looks like an interesting title, learn more! We provide domestic tracking upon request. We provide personalized customer service and want you to have a great experience purchasing from us. 100% satisfaction guaranteed and thank you for your consideration. Bookseller Inventory # S-0262010372
Book Description The MIT Press, 1973. Hardcover. Book Condition: Like New. Almost new condition. Bookseller Inventory # P010262010372
Book Description The MIT Press, 1973. Hardcover. Book Condition: New. Never used!. Bookseller Inventory # P110262010372
Book Description The MIT Press, 1973. Hardcover. Book Condition: Good. 0. Ships with Tracking Number! INTERNATIONAL WORLDWIDE Shipping available. May not contain Access Codes or Supplements. Buy with confidence, excellent customer service!. Bookseller Inventory # 0262010372