作者：候书会，刘白羽编
页数：2册(441页)
出版社：科学出版社
出版日期：2016
ISBN：9787030480453
电子书格式：pdf/epub/txt
内容简介
本书分上、下两册出版, 上册共七章, 着重介绍医院微积分学的基础理论知识, 内容包括函数、极限、函数连续性, 导数、微分及其应用等 ; 下册共六章, 着重介绍多元微分学的基础理论知识, 内容包括无穷级数、向量代数与空间解析几何, 多元函数、极限及其连续性等。
目录
1.1 Some Set Theory Notation for the Study of Calculus
1.1.1 Definition of Set
1.1.2 Descriptions of set
1.1.3 Set Operations
1，1.4 Interval
1.1.5 Neighbourhood
1.2 The Rectangular Coordinate System
1.2.1 Cartesian Coordinates
1.2.2 Distance Formula
1.2.3 The Equation of a Circle
1.3 The Straight Line
1.3.1 The Slope of a Line
1.3.2 The Equation of a Line
1.4 Graphs of Equations
1.4.1 The Graphing Procedure
1.4.2 Symmetry of a Graph
1.4.3 Intercepts
1.4.4 Problems for Chapter 1
Chapter 2 Functions and Limits
2.1 Functions
2.1.1 Definition of Function
2.1.2 Properties of Functions
2.1.3 Operations on Functions
2.1.4 Elementary Functions
2.1.5 Problems for Section 2.1
2.2 Limits
2.2.1 Introduction to Limits
2.2.2 Definition of Limit
2.2.3 Operations on Limits
2.2.4 Limits at Infinity and Infinite Limits
2.2.5 Infinitely Small Quantity (or Infinitesimal)
2.2.6 Problems for Section 2.2
2.3 Continuity of Functions
2.3.1 Definition of Continuity
2.3.2 Continuity under Function Operations
2.3.3 Continuity of Elementary Functions
2.3.4 Intermediate Value Theorem
2.3.5 Problems for Section 2.3
2.4 Chapter Review
2.4.1 Drills
2.4.2 Sample Test Problems
Chapter 3 Differentiation
3.1 Derivatives
3.1.1 Two Problems with One Theme
3.1.2 Definition
3.1.3 Rules for Finding Derivatives
3.1.4 Problems for Section 3.1
3.2 Higher-Order Derivatives
3.2.1 Definition
3.2.2 Sum， Difference and Product Rules
3.2.3 Problems for Section 3.2
3.3 Implicit Differentiation
3.3.1 Guidelines for implicit Differentiation
3.3.2 Related Rates
3.3.3 Problems for Section 3.3
3.4 Differentials and Approximations
3.4.1 Definition of Differential
3.4.2 Differential Rules
……
Chapter 4 Applications of Differentiation
Chapter 5 Indefinite Integrals
Chapter 6 Definite Integrals
Chapter 7 Applications of Integration
Chapter 8 Infinite Series
Chapter 9 Geometry in Space and Vectors
Chapter 10 Derivatives for Functions of Two or More Variables
Chapter 11 Multiple Integrals
Chapter 12 Vector Calculus
Chapter 13 Differential Equations
References
