《微積分和數學分析引論（第2卷·第1分冊）》是2018年8月1日世界圖書出版公司出版的著作，作者是[美] Richard、Courant（R.庫朗）、Fritz、John 。
基本介紹
- 中文名：《微積分和數學分析引論（第2卷·第1分冊）》
- 作者：[美] Richard、Courant（R.庫朗）、Fritz、John
- 出版社：世界圖書出版公司
- 出版時間：2018年08月01日
- ISBN：9787519247676
內容簡介,目錄,
內容簡介
本書共分為2卷三冊，內容以及形式上有如下三個特點：一是引導讀者直達本學科的核心內容；二是注重套用，指導讀者靈活運用所掌握的知識；三是突出了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繫和直觀背景努力幫助那些對這門學科真正感興趣的讀者。本書第一章主要圍繞著一元函式展開討論，二、三、四章分別介紹了微積分的基本概念、運算及其在物理和幾何中的套用，隨後講述了泰勒展開式、數值方法、數項級數、函式項級數、三角級數，最後介紹了一些與振動有關的類型簡單的微分方程。本書各章均提供了大量的例題和習題，其中一部分有相當的難度，但絕大部分是對正文內容的補充。
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.Pointsand 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 variable
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.Geometricinterpretation 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, 71
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
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
