ISBN：978-7-111-27598-5

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ISBN：978-7-111-27598-5

Preface
0 Preliminaries
0.1 Real Numbers.Estimation，and Logic
0.2 Inequalities and Absolute Values
0.3 The Rectangular Coordinate System
0.4 Graphs of Equations
0.5 Functions and Their Graphs
0.6 Operations on Functions
0.7 Trigonometric Functions
0.8 Chapter Review
Review and Preview Problems
1 Limits
1.1 Introduction to Limits
1.2 Rigorous Study of Limits
1.3 Limit Theorems
1.4 Limits Involving Trigonometric Functions
1.5 Limits at Infinity；Infinite Limits
1.6Continuity of Functions
1.7Chapter Review
Review and Preview Problems
2 The Derivative
2.1 Two Problems with One Theme
2.2 The Derivative
2.3 Rules for Finding Derivatives
2.4 Derivatives of Trigonometric Functions
2.5 The Chain Rule
2.6 Higher.Order Derivatives
2.7 Implicit Differentiation
2.8 Related Rates
2.9 Differentials and Approximations
2.10 Chapter Review
Review and Preview Problems
3 Applications of the Derivative
3.1 Maxima and Minima
3.2 Monotonicity and Concavity
3.3 Local Extrema and Extrema on Open Intervals
3.4 Practical Problems
3.5 Graphing Functions Using Calculus
3.6 The Mean Value Theorem for Derivatives
3.7 Solving Equations Numerically
3.8 Antiderivatives
3.9 Introduction to Differential Equations
3.10 Chapter Review
Review and Preview Problems
4 The Deftnite Integral
4.1 Introduction to Area
4.2 The Definite Integral
4.3 The First Fundamental Theorem of Calculus
4.4 The Second Fundamental Theorem of Calculus and the Method of Substitution
4.5 The Mean Value Theorem for Integrals and the Use of Symmetry
4.6 Numerical Integration
4.7 Chapter Review
Review and Preview Problems
5 Applications of the Integral
5.1 The Area of a Plane Region
5.2 volumes of Solids：Slabs.Disks,Wlashers
5.3 Volumes of Solids of Revolution：Shells
5.4 Length of a Plane Curve
5.5 Work and Fluid Force
5.6 Moments and Center of Mass
5.7 Probability and Random Variabtes
5.8 Chapter Review322
Review and Preview Problems
6 Transcendental Functions
6.1 The Natural Logarithm Function
6.2 Inverse Functions and Their Derivatives
6.3 The Natural Exponential Function
6.4 General Exponential and Logarithmic Functions
6.5 Exponential Growth and Decay
6.6 First.Order Linear Differential Equations
6.7 Approximations for Differential Equations
6.8 The Inverse Trigonometric Functions and Their Derivatives
6.9 The Hyperbolic Functions and Their Inverses
6.10 Chapter Review
Review and Preview Problems
7 Techniques of Integration
7.1 Basic Integration Rules
7.2 Integration by Parts
7.3 Some Trigonometric Integrals
7.4 Rationalizing Substitutions
7.5 Integration of Rational Functions Using Partial Fractions
7.6 Strategies for Integration
7.7 Chapter Review
Review and Preview Problems
8 Indeterminate Forms and Improper Integrals
9 Infinite Series
10 Conics and Polar Coordinates
11 Geometry in Space and Vectors
12 Derivatives for Functions of Two or More Variables
13 Multiple Integrals
14 Vector Calculus
AppendixA-1