微積分和數學分析引論（第2捲）（第2冊） pdf epub mobi txt 电子书 下载 2025

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庫蘭特 著

出版社： 世界图书出版公司

ISBN：9787506291675

版次：1

商品编码：10096450

包装：平装

开本：24开

出版时间：2008-01-01

页数：954

正文语种：英语

編輯推薦

　　《微積分和數學分析引論(第2捲)(第2冊)(英文版)》適閤於多種學科界的讀者，如數學工作者、科學工作者、工程技術人員等。
　　《微積分和數學分析引論(第2捲)(第2冊)(英文版)》為全英文版。

內容簡介

　　《微積分和數學分析引論(第2捲)(第2冊)(英文版)》在內容以及形式上有如下三個特點：一是引領讀者直達本學科的核心內容；二是注重應用，指導讀者靈活運用所掌握的知識；三是突齣瞭直覺思維在數學學習中的作用。作者不掩飾難點以使得該學科貌似簡單，而是通過揭示概念之間的內在聯係和直觀背景努力幫助那些對這門學科真正感興趣的讀者。
　　《微積分和數學分析引論(第2捲)(第2冊)(英文版)》各章均提供瞭大量的例題和習題，其中一部分有相當的難度，但絕大部分是對內容的補充。另外，《微積分和數學分析引論(第2捲)(第2冊)(英文版)》附有一本專門的習題冊，並且給齣瞭習題的提示與解答。

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
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 Taylors Theorem for Functions of Several Variables
a.Preliminary remarks about approximation by polynomials
b.The mean value theorem
c.Taylors 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 Transformations
Chapter 3 Developments and Applications of the Differential Calculus
Chapter 4 Multiple Integrals
Chapter 5 Relations Between Surface and Volume Integrals
Chapter 6 Differential Equations
Chapter 7 Calculus of Variations
Chapter 8 Functions of a Complex Variable
List of Biographical Dates
Index

前言/序言

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