高等数学

Chapter 1 Preliminaries 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