【中商原版】常微分方程:定性理论 英文原版 Ordinary Differential Equations Luis Barreira
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商品详情
Ordinary Differential Equations (Graduate Studies in Mathematics)
基本信息
Series:Graduate Studies in Mathematics
Format:Hardback 248 pages
Publisher:American Mathematical Society
Imprint:American Mathematical Society
ISBN:9780821887493
Published:15 Jun 2012
Classifications:Differential calculus & equations
Readership:General (US: Trade)
Weight:620g
Dimensions:259 x 178 x 18 (mm)
页面参数仅供参考,具体以实物为准
书籍简介
这本教科书对常微分方程的定性理论作了全面的介绍。它包括了解的存在性和唯一性的讨论,相位肖像,线性方程,稳定性理论,双曲性和方程在平面。重点主要放在结果和方法上,这些结果和方法允许人们分析解决方案的定性性质,而不需要显式地解方程组。
正文包括许多例子,详细说明了新概念和结果,以及每一章末尾附有练习。这本书也打算作为桥梁,以重要的主题,往往被遗漏在常微分方程的课程。特别对分支理论、中心流形、范式和哈密顿系统作了简要介绍。
This textbook provides a comprehensive introduction to the qualitative theory of ordinary differential equations. It includes a discussion of the existence and uniqueness of solutions, phase portraits, linear equations, stability theory, hyperbolicity and equations in the plane. The emphasis is primarily on results and methods that allow one to analyze qualitative properties of the solutions without solving the equations explicitly.
The text includes numerous examples that illustrate in detail the new concepts and results as well as exercises at the end of each chapter. The book is also intended to serve as a bridge to important topics that are often left out of a course on ordinary differential equations. In particular, it provides brief introductions to bifurcation theory, center manifolds, normal forms and Hamiltonian systems.
作者简介
路易斯·巴雷拉(生于1968年9月25日),葡萄牙数学家,高等理工学院数学系教授。
Luís Barreira (born 25 September 1968) is a Portuguese mathematician and a professor in the department of mathematics of Instituto Superior Técnico.
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