微積分和數(shù)學(xué)分析引論

內(nèi)容概要

本書在內(nèi)容以及形式上有如下三個(gè)特點(diǎn)：一是引領(lǐng)讀者直達(dá)本學(xué)科的核心內(nèi)容；二是注重應(yīng)用，指導(dǎo)讀者靈活運(yùn)用所掌握的知識(shí)；三是突出了直覺思維在數(shù)學(xué)學(xué)習(xí)中的作用。作者不掩飾難點(diǎn)以使得該學(xué)科貌似簡單，而是通過揭示概念之間的內(nèi)在聯(lián)系和直觀背景努力幫助那些對(duì)這門學(xué)科真正感興趣的讀者。 　　本書各章均提供了大量的例題和習(xí)題，其中一部分有相當(dāng)?shù)碾y度，但絕大部分是對(duì)內(nèi)容的補(bǔ)充。另外，本書附有一本專門的習(xí)題冊(cè)，并且給出了習(xí)題的提示與解答。 　　本書適合于多種學(xué)科界的讀者，如數(shù)學(xué)工作者、科學(xué)工作者、工程技術(shù)人員等。 　　本書為全英文版。

作者簡介

作者：(美國)庫蘭特

書籍目錄

Chapter 1 Functions 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 Functions of Several Independent Variables　　a. Functions and their domains　　b. The simplest types of functions　　c. Geometrical representation of functions　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 errors　1.6 Functions of Functions (Compound Functions) and the Introduction of New Independent Variables　　a. Compound functions. The chain rule　　b. Examples　　c. Change of independent variables　1.7 The Mean Value Theorem and Taylor's Theorem for Functions 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 definitions　　b. Continuity and differentiability of an integral with respect to the parameter　　c. Interchange of integrations. Smoothing of functions　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 conditions for line integrals to depend only on the end points　　c. Insufficiency of the integrability conditions　　d. Simply connected sets　　e. The fundamental theorem　APPENDIX……Chapter 2 Vectors, Matrices, Linear TransformationsChapter 3 Developments and Applications of the Differential CalculusChapter 4 Multiple IntegralsChapter 5 Relations Between Surface and Volume IntegralsChapter 6 Differential EquationsChapter 7 Calculus of VariationsChapter 8 Functions of a Complex VariableList of Biographical DatesIndexpage 543 of this editionpage 545 of this edition

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　　《微積分和數(shù)學(xué)分析引論(第2卷)(第1冊(cè))(英文版)》適合于多種學(xué)科界的讀者，如數(shù)學(xué)工作者、科學(xué)工作者、工程技術(shù)人員等。　　《微積分和數(shù)學(xué)分析引論(第2卷)(第1冊(cè))(英文版)》為全英文版。

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