书馨卡帮你省薪
欢迎光临中图网 请 | 注册
> >>
微积分和数学分析引论-(第2卷)(第1册)

微积分和数学分析引论-(第2卷)(第1册)

出版社:世界图书出版公司出版时间:2008-01-01
开本: 32开 页数: 555
读者评分:4.5分2条评论
本类榜单:自然科学销量榜
中 图 价:¥43.5(6.3折) 定价  ¥69.0 登录后可看到会员价
加入购物车 收藏
运费6元,满39元免运费
?新疆、西藏除外
本类五星书更多>
买过本商品的人还买了

微积分和数学分析引论-(第2卷)(第1册) 版权信息

  • ISBN:750629166
  • 条形码:9787506291668 ; 978-7-5062-9166-8
  • 装帧:一般胶版纸
  • 册数:暂无
  • 重量:暂无
  • 所属分类:>>

微积分和数学分析引论-(第2卷)(第1册) 本书特色

《微积分和数学分析引论(第2卷)(第1册)(英文版)》适合于多种学科界的读者,如数学工作者、科学工作者、工程技术人员等。 《微积分和数学分析引论(第2卷)(第1册)(英文版)》为全英文版。

微积分和数学分析引论-(第2卷)(第1册) 内容简介

本书在内容以及形式上有如下三个特点:一是引领读者直达本学科的核心内容;二是注重应用,指导读者灵活运用所掌握的知识;三是突出了直觉思维在数学学习中的作用。作者不掩饰难点以使得该学科貌似简单,而是通过揭示概念之间的内在联系和直观背景努力帮助那些对这门学科真正感兴趣的读者。本书各章均提供了大量的例题和习题,其中一部分有相当的难度,但绝大部分是对内容的补充。另外,本书附有一本专门的习题册,并且给出了习题的提示与解答。本书适合于多种学科界的读者,如数学工作者、科学工作者、工程技术人员等。本书为全英文版。

微积分和数学分析引论-(第2卷)(第1册) 目录

Chapter 1 Functio of Several Variables and Their Derivatives 1.1 Points and Points Sets in the Plane and in Space a. Sequences of points. Convergence b. Sets of points in the plane c. The boundary of a set.Closed and open sets d. Closure as set of limit points e. Points and sets of points in space 1.2 Functio of Several Independent Variables a. Functio and their domai b. The simplest types of functio c. Geometrical representation of functio 1.3 Continuity a. Definition b. The concept of limit of a function of several variables c. The order to which a function vanishes 1.4 The Partial Derivatives of a Function a. Definition. Geometrical representation b. Examples c. Continuity and the existence of partial derivatives d. Change of the order of differentiation, 36 1.5 The Differential of a Function and Its Geometrical Meaning a. The concept of differentiability b. Directional derivatives c. Geometric interpretation of differentiability,The tangent plane d. The total differential of a function e. Application to the calculus of erro 1.6 Functio of Functio (Compound Functio) and the Introduction of New Independent Variables a. Compound functio. The chain rule b. Examples c. Change of independent variables 1.7 The Mean Value Theorem and Taylor's Theorem for Functio of Several Variables a. Preliminary remarks about approximation by polynomials b. The mean value theorem c. Taylor's theorem for several independent variables 1.8 Integrals of a Function Depending on a Parameter a. Examples and definitio b. Continuity and differentiability of an integral with respect to the parameter c. Interchange of integratio. Smoothing of functio 1.9 Differentials and Line Integrals a. Linear differential forms b. Line integrals of linear differential forms c. Dependence of line integrals on endpoints 1.10 The Fundamental Theorem on Integrability of Linear Differential Forms a. Integration of total differentials b. Necessary conditio for line integrals to depend only on the end points c. Iufficiency of the integrability conditio d. Simply connected sets e. The fundamental theorem APPENDIX …… Chapter 2 Vecto, Matrices, Linear Traformatio Chapter 3 Developments and Applicatio of the Differential Calculus Chapter 4 Multiple Integrals Chapter 5 Relatio Between Surface and Volume Integrals Chapter 6 Differential Equatio Chapter 7 Calculus of Variatio Chapter 8 Functio of a Complex Variable List of Biographical Dates Index page 543 of this edition page 545 of this edition
展开全部

微积分和数学分析引论-(第2卷)(第1册) 节选

eface
   Richard Courant's Differential and Integral Calculus, Vols. I and
II, has been tremendously successful in introducing several gener-
ations of mathematicians to higher mathematics. Throughout, those
volumes presented the important lesson that meaningful mathematics
is created from a union of intuitive imagination and deductive reason-
ing. In preparing this revision the authors have endeavored to main-
tain the healthy balance between these two modes of thinking which
characterized the original work. Although Richard Courant did not
live to see the publication of this revision of Volume II, all major
changes had been agreed upon and drafted by the authors before Dr.
Courant's death in January 1972.
   From the outset, the authors realized that Volume II, which deals
with functions of several variables, would have to be revised more
drastically than Volume I. In particular, it seemed desirable to treat
the fundamental theorems on integration in higher dimensions with
the same degree of rigor and generality applied to integration in one
dimension. In addition, there were a number of new concepts and
topics of basic importance, which, in the opinion of the authors, belong
to an introduction to analysis.
   Only minor changes were made in the short chapters (6, 7, and 8)
dealing, respectively, with Differential Equations, Calculus of Vari-
ations, and Functions of a Complex Variable. In the core of the book,
Chapters 1-5, we retained as much as possible the original scheme of
two roughly parallel developments of each subject at different levels:
an informal introduction based on more intuitive arguments together
with a discussion of applications laying the groundwork for the
subsequent rigorous proofs.
    The material from linear algebra contained in the original Chapter
! seemed inadequate as a foundation for the expanded calculus struc-
ture. Thus, this chapter (now Chapter 2) was completely rewritten and
now presents all the required properties of nth order determinants and
matrices, multilinear forms, Gram determinants, and linear manifolds.
                                                                                                       ..
viii Preface
   The new Chapter 1 contains all the fundamental properties of
linear differential forms and their integrals. These prepare the reader
for the introduction to higher-order exterior differential forms added
to Chapter 3. Also found now in Chapter 3 are a new proof of the
implicit function theorem by successive approximations and a discus-
sion of numbers of critical points and of indices of vector fields in two
dimensions.
   Extensive additions were made to the fundamental properties of
multiple integrals in Chapters 4 and 5. Here one is faced with a familiar
difficulty: integrals over a manifold M, defined easily enough by
subdividing M into convenient pieces, must be shown to be inde-
pendent of the particular subdivision. This is resolved by the sys-
tematic use of the family of Jordan measurable sets with its finite
intersection property and of partitions of unity. In order to minimize
topological complications, only manifolds imbedded smoothly into
Euclidean space are considered. The notion of "orientation" of a
manifold is studied in the detail needed for the discussion of integrals
of exterior differential forms and of their additivity properties. On this
basis, proofs are given for the divergence theorem and for Stokes's
theorem in n dimensions. To the section on Fourier integrals in
Chapter 4 there has been added a discussion of Parseval's identity and
of multiple Fourier integrals.
   Invaluable in the preparation of this book was the continued
generous help extended by two friends of the authors, Professors
Albert A. Blank of Carnegie-Mellon University, and Alan Solomon
of the University of the Negev. Almost every page bears the imprint
of their criticisms, corrections, and suggestions. In addition, they
prepared the problems and exercises for this volume.1
   Thanks are due also to our colleagues, Professors K. O. Friedrichs
and Donald Ludwig for constructive and valuable suggestions, and to
John Wiley and Sons and their editorial staff for their continuing
encourgement  and assistance.
FRITZ JOHN
NewYork
September 1973
 1In contrast to Volume I, these have been incorporated completely into the text;
their solutions can be found at the end of the volume.



商品评论(2条)
  • 主题:

    数学经典丛书,科朗执笔

    2019/5/10 13:07:32
    读者:ban***(购买过本书)
  • 主题:书是好书~!

    2卷共三本都买了,是一本相当生动以及精确的书,一本最具启发性和原汁原味的书,你会觉得经典的数学是这样子的。有两卷书污迹很明显,不过也懒得换了

    2011/12/10 16:52:05
    读者:142***(购买过本书)
书友推荐
本类畅销
编辑推荐
返回顶部
中图网
在线客服