Chapter 1  Function

  1.1  Concepts of Functions

  1.2  Some Important Properties of Functions

  1.3  Implicit Functions and Inverse Functions

  1.4  Basic Elementary Functions

  1.5  Composite Functions and Elementary Functions

  1.6  Polar Coordinate System

  1.7  Examples

  Exercises 1

Chapter 2  Limits and Continuity

  2.1  The Limit of a sequence

  2.2  Properties and Operation of Convergent Sequences

  2.3  Existence Discriminances of Sequence Limit

  2.4  The Limit of a Function

  2.5  Properties of Function Limits

  2.6  Infinitesimal and Infinity

  2.7  Continuity

  2.8  Examples

  Exercises 2

Chapter 3  Derivatives

  3.1  Definition of Derivatives

  3.2  Differentiation Rules

  3.3  Higher-Order Derivatives

  3.4  Linearization and Differentials

  3.5  Examples

  Exercises 3

Chapter 4  Applications of Derivatives

  4.1  The Mean Value Theorem

  4.2  L' Hospital' s Rule

  4.3  Taylor Formula

  4.4  Maximum and Minimum Values

  4.5  Curve Sketching

  4.6  Examples

  Exercises 4

Chapter 5  The Indefinite Integral

  5.1  The Antiderivative and the Indefinite Integral

  5.2  Integration by Substitution

  5.3  Integration by Parts

  5.4  The Integration of Several Kinds of Functions

  5.5  Examples

  Exercises 5

Chapter 6  The Definite Integral and Its Applications

  6.1  Concepts and Properties

  6.2  The Fundamental Theorem of Calculus

  6.3  Evaluating the Definite Integral

  6.4  The Improper Integral

  6.5  Applications of Definite Integrals

  6.6  Examples

  Exercises 6

Chapter 7  Differential Equations

  7.1  Basic Concepts of Differential Equations

  7.2  The First-Order Differential Equations

  7.3  Some Order-Reducible Higher-Order Differential Equations

  7.4  Linear Differential Equations of Higher Order

  7.5  The Second-Order Linear Differential Equations with Constant

  Coefficients

  Exercise 7

Appendix

  Ⅰ  Several Fundamental Theorems

  Ⅱ  Superior and Inferior Limits

  Ⅲ  Calculus in Economics