Calculus

Author: Zhu Laiyi
Publisher:
Publish Date: 2003-01-01
Features: The book introduces the basic content of differentiation and integration in a scientific and systematic way that is easily understandable for students of economics and management. It focuses on the methods of calculus and their applications in economics and management. Compared to previous textbooks, its main features lie in: emphasizing the intuitive introduction of concepts and the connections between different areas of knowledge; emphasizing the cultivation of mathematical thinking and application skills; emphasizing the connection between concepts, methods, and the discipline of economics and management, and adapting to the needs of modern economic, financial, and management development. Each chapter is accompanied by two sets of exercises (a and b) and reference answers, with the b set of exercises designed to meet the needs of readers with higher requirements. This book can be used as a textbook for undergraduate students of economics and management, and is also suitable for postgraduate students preparing for exams.
Chapter 1: Functions
§1.1 Preliminary Knowledge
§1.2 Concept of Function
§1.3 Geometric Characteristics of Functions
§1.4 Inverse Function
§1.5 Composite Function
§1.6 Elementary Functions
§1.7 Establishing Simple Functional Relationships
Exercises 1
Chapter 2: Limits and Continuity
§2.1 Limit of a Sequence
§2.2 Limit of a Function
§2.3 Properties and Rules of Function Limits
§2.4 Infinite Large and Infinite Small Quantities
§2.5 Continuity of Functions
§2.6 Properties of Continuous Functions on Closed Intervals
Exercises 2
Chapter 3: Derivatives and Differentials
§3.1 Concept of Derivative
§3.2 Derivative Operations and Derivative Formulas
§3.3 Derivative Rule for Composite Functions
§3.4 Differentials and Their Calculation
§3.5 Higher-Order Derivatives and Higher-Order Differentials
§3.6 Simple Applications of Derivatives and Differentials in Economics
Exercises 3
Chapter 4: Mean Value Theorems and Applications of Derivatives
§4.1 Mean Value Theorems of Differentiation
§4.2 Taylor's Formula
§4.3 L'H?pital's Rule
§4.4 Monotonicity and Convexity of Functions
§4.5 Extrema and Maximum (Minimum) Values of Functions
§4.6 Graphing Functions
Exercises 4
Chapter 5: Indefinite Integrals
§5.1 Concept of Antiderivative and Indefinite Integral
§5.2 Basic Integration Formulas
§5.3 Substitution Integration
§5.4 Integration by Parts
Exercises 5
Chapter 6: Definite Integrals
§6.1 Concept and Properties of Definite Integrals
§6.2 Fundamental Theorem of Calculus
§6.3 Substitution and Integration by Parts for Definite Integrals
§6.4 Applications of Definite Integrals
§6.5 Preliminary Concepts of Improper Integrals
Exercises 6
Chapter 7: Multivariable Calculus
§7.1 Preliminary Knowledge
§7.2 Concept of Multivariable Functions
§7.3 Directional Derivatives, Partial Derivatives, and Total Differentials
§7.4 Differentiation of Multivariable Composite and Implicit Functions
§7.5 Higher-Order Partial Derivatives and Total Differentials
§7.6 Extrema of Multivariable Functions
Exercises 7
Chapter 8: Infinite Series
§8.1 Concept and Properties of Constant-Term Series
§8.2 Series with Positive Terms
§8.3 Series with Arbitrary Terms
§8.4 Power Series
Exercises 8
Chapter 9: Preliminary Concepts of Differential Equations
§9.1 Basic Concepts of Differential Equations
§9.2 First-Order Differential Equations
§9.3 Second-Order Linear Differential Equations with Constant Coefficients
§9.4 Applications of Differential Equations in Economics
Exercises 9
Chapter 10: Difference Equations
§10.1 Basic Concepts of Difference Equations
§10.2 First-Order Linear Difference Equations with Constant Coefficients
§10.3 Second-Order Linear Difference Equations with Constant Coefficients
§10.4 Simple Applications of Difference Equations in Economics
Exercises 10
Reference Answers to Exercises