Chapter 1 Function and limit
1.1 Function
1.1.1 Set
1.1.2 Function
1.1.3 Elementary functions
Exercises 1-1
1.2 Limit
1.2.1 Limit of sequence
1.2.2 Limit of function
Exercises 1-2
1.3 Rules of limit operations
1.3.1 Rational operation rules
1.3.2 Operation rule for composite function
Exercises 1-3
1.4 Principle of limit existence and two important limits
1.4.1 Principle of limit existence
1.4.2 Two important limits
Exercises 1-4
1.5 Infinitesimal and infinity
1.5.1 Infinitesimal
1.5.2 Infinity
1.5.3 Comparison of infinitesimal order
Exercises 1-5
1.6 Continuity of function and the properties
1.6.1 Continuity of function and discontinuity
1.6.2 Operations on continuous functions and the continuity of elementary functions
1.6.3 Properties of continuous functions on a closed interval
Exercises 1-6
Summary
Quiz
Exercises
Chapter 2 Derivative and differential
2.1 Definition of derivatives
2.1.1 Cited examples
2.1.2 Definition of derivatives
2.1.3 Geometric interpretation of derivative
2.1.4 Use the unit to explain derivative
2.1.5 Relationship between derivability and continuity
2.1.6 The application of derivative in natural science
Exercises 2-1
2.2 Rules of finding derivatives
2.2.1 Derivative formulas for several fundamental elementary functions
2.2.2 Derivation rules of rational operations
2.2.3 Derivative of inverse functions
2.2.4 Derivation rules of composite functions
Exercises 2-2
2.3 Higher-order derivatives
2.3.1 The concept of higher order derivative
2.3.2 The linear property and Leibniz formula
Exercises 2-3
2.4 Derivation of implicit functions and parametric equations
2.4.1 Derivation of implicit functions
2.4.2 Logarithmic derivation method
2.4.3 Derivation of parametric equations
2.4.4 Derivative of the function expressed by the polar equation
Exercises 2-4
2.5 Differential of the function
2.5.1 Concept of the differential
2.5.2 The necessary and sufficient condition for differential
2.5.3 Geometric meaning of differential
2.5.4 Differential rules of elementary functions
2.5.5 Application of the differential
Exercises 2-5
2.6 The application of derivative in economic analysis
2.6.1 Marginal analysis
2.6.2 Elasticity analysis
Exercises 2-6
Summary
Quiz
Exercises
Chapter 3 The mean value theorem
3.1 Mean value theorems the differential calculus
3.1.1 Format Lemma
3.1.2 Rolle's Theorem
3.1.3 Lagrange's Theorem
3.1.4 Cauehy's Theorem
Exercises 3-1
3.2 Taylor's Theorem
Exercises 3-2
Summary
Quiz
Exercises
Chapter 4 Applications of derivatives
4.1 Indeterminate form limit
4.1.1 The indeterminate form of type 00
4.1.2 The indeterminate form of type ∞∞
4.1.3 Other indeterminate forms
Exercises 4-1
4.2 Monotonicity and local extreme value
4.2.1 Monotonieity of functions
4.2.2 The extreme value of function
4.2.3 Maximum value and minimum value of function
Exercises 4-2
4.3 The convexity, concavity and inflection point of function
Exercises4-3
4.4 Description of the function graph
4.4.1 Asymptote of curve
4.4.2 Description of the function graph
Exercises 4-4
4.5 Curvature
4.5.1 Differentiation of an arc
4.5.2 Calculation formula of curvature
4.5.3 Curvature circle
Exercises 4-5
4.6 Approximation of equation
4.6.1 Bisection method
4.6.2 Tangent method
Exercises 4-6
4.7 The application of extreme value of function in economic management
4.7.1 Demand analysis
4.7.2 Problems of minimum average cost
4.7.3 Problems of minimizing inventory cost
4.7.4 Problems of maximal profit
4.7.5 Problems of maximal revenue
4.7.6 Problems of maximal tax
4.7.7 Problems of compound interest
Exercises4-7
Summary
Quiz
Exercises
Chapter 5 Indefinite integrals
5.1 Indefinite integrals
5.1.1 Antiderivative
5.1.2 The conception of indefinite integral
5.1.3 Table of basic indefinite integrals
5.1.4 Properties of the indefinite integral
Exercises 5-1
5.2 Integration by substitution
5.2.1 Integration by the first substitution (Gather differential together)
5.2.2 Integration by the second substitution
Exercises 5-2
5.3 Integration by parts
Exercises 5-3
5.4 Integration of rational functions
5.4.1 Integration of rational functions
5.4.2 Integration of rational trigonometric functions
5.4.3 Integration of simply irrationa4-functions
Exercises 5-4
5.5 Application of indefinite integral in economy
Exercises 5-5
Summary
Quiz
Exercises
Chapter 6 Definite integrals
6.1 The concept of definite integral
6.1.1 Examples of definite integral problems
6.1.2 The definition of definite integral
Exercises 6-1
6.2 Properties of definite integrals
Exercises 6-2
6.3 Fundamental formula of calculus
6.3.1 The relationship between the displacement and the velocity
6.3.2 A function of upper limit of integral
6.3.3 Newton-Leibnitz formula
Exercises 6-3
6.4 Integration by substitution and parts for definite integrals
6.4.1 Integration by substitution for definite integrals
6.4.2 Integration by parts for definite integrals
Exercises 6-4
6.5 Improper integrals
6.5.1 Improper integrals on an infinite interval
6.5.2 Improper integral of unbounded functions
Exercises 6-5
Summary
Quiz
Exercises
Chapter 7 Applications of definite integral
7.1 The element method of definite integral
7.2 Application of definite integral in geometry
7.2.1 The area of a region
7.2.2 Volume
7.2.3 Arc length of plane curve
Exercises 7-2
7.3 Application of definite integral in economy
7.3.1 Calculate total output if its rate of change is given
7.3.2 Calculate amount function when marginal function is given
7.3.3 Discount problems
Exercises 7-3
Summary
Quiz
Exercises
Answers

本书为全英文教材，主要内容形成以函数、极限、连续、导数、积分、级数、微分方程等为明线，以简单经济函数模型、复利和连续复利、边际、弹性、经济优化模型等为暗线的课程体系，突出微积分的基本方法的理论学习及经济应用。