Economic Mathematics Lecture
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Book Introduction
Economic Mathematics Lectures Return to the Third Edition
Six years after the first edition was published in 2011 and the second edition in 2017, the third edition of 『Economic Mathematics Lectures』 has been published.
This time, we have especially reinforced the sections on functions (chapters 1-3), definite integrals (chapters 11), matrices (chapters 13-15), and total differentiation and implicit function theorem (chapters 17-18).
Practice problems have also been revised and supplemented based on the 2nd edition.
This book is suitable for beginners who are concerned about "what and how to study in economic mathematics," and serves as a guide for studying advanced economic mathematics.
You will be able to build a solid foundation in economic mathematics by learning through friendly explanations and real-life examples that feel like you are attending a lecture.
Six years after the first edition was published in 2011 and the second edition in 2017, the third edition of 『Economic Mathematics Lectures』 has been published.
This time, we have especially reinforced the sections on functions (chapters 1-3), definite integrals (chapters 11), matrices (chapters 13-15), and total differentiation and implicit function theorem (chapters 17-18).
Practice problems have also been revised and supplemented based on the 2nd edition.
This book is suitable for beginners who are concerned about "what and how to study in economic mathematics," and serves as a guide for studying advanced economic mathematics.
You will be able to build a solid foundation in economic mathematics by learning through friendly explanations and real-life examples that feel like you are attending a lecture.
- You can preview some of the book's contents.
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index
Introduction: Mathematics and Economic Models
0.1 Mathematical representation of social science hypotheses
0.2 Economic Model
Key Concepts and Terms
summation
Food for thought
PART 01 Function
CHAPTER 01 Function Basics
1.1 Definition of functions
1.2 Graph of a function
1.3 Properties of functions
Key Concepts and Terms
summation
Practice problems
CHAPTER 02 Exponential Functions
2.1 Exponential functions
2.2 Numbers and natural exponential functions
2.3 Applications
Key Concepts and Terms
summation
Practice problems
CHAPTER 03 Logarithmic Functions
3.1 Basic properties and graphs of logarithmic functions
3.2 Useful properties of logarithmic functions
3.3 Natural logarithm function
3.4 Applications
Key Concepts and Terms
summation
Practice problems
PART 02 Differentiation
CHAPTER 04 Concept of Differentiation
4.1 Marginal or instantaneous rate of change: Differential coefficient
4.2 Derivatives and Differentiation
4.3 Second derivative
4.4 Finding the shape of a function's graph using first-order and second-order derivatives
Key Concepts and Terms
summation
Practice problems
CHAPTER 05 Rules of Differentiation: Differentiation of Polynomial Functions
5.1 Constant product and differentiation
5.2 Addition and differentiation between functions
5.3 Multiplication and differentiation between functions
5.4 Differentiation of monomials
Key Concepts and Terms
summation
Practice problems
CHAPTER 06 Rules of Differentiation: Differentiation of Composite Functions, Exponential Functions, and Logarithmic Functions
6.1 Differentiability
6.2 Differentiation of composite functions
6.3 Differentiation of exponential and logarithmic functions
6.4 Differentiation Rules for Monomials: Power Rule Final Edition
6.5 Derivatives of Fractional Functions
Key Concepts and Terms
summation
Practice problems
CHAPTER 07 Applications of Differentiation
7.1 The concept of 'limit'
7.2 Elasticity
7.3 Percentage change in multiplied value
7.4 Differential Calculations and Approximations
Key Concepts and Terms
summation
Practice problems
CHAPTER 08 Optimization of Single-Variable Functions: (1) First-Order Conditions
8.1 The Concept of Optimization and Its Economic Implications
8.2 One-order conditions: Necessary conditions for optimization
8.3 Application: Profit Maximization for Businesses
Key Concepts and Terms
summation
Practice problems
CHAPTER 09 Optimization of Single-Variable Functions: (2) Second-Order Conditions
9.1 Otherworldly conditions: sufficient conditions
9.2 Convexity and concaveness of functions
9.3 Application: Profit Maximization in Monopoly
Key Concepts and Terms
summation
Practice problems
PART 03 INTEGRATION
CHAPTER 10 INTEGRAL: (1) INDEFINITE INTEGRAL
10.1 Concept of indefinite integral
10.2 Basic Rules for Indefinite Integers
10.3 Basic Rules of Integration (3) Integration by Parts
10.4 Basic Rules of Integration (7) Substitution Integral
Key Concepts and Terms
summation
Practice problems
CHAPTER 11 INTEGRAL: (2) DEFINITE INTEGRAL
11.1 Definite Integrals: Area Under a Graph
11.2 Fundamental Theorem of Calculus: The Relationship Between Definite and Indefinite Integrators
11.3 Indefinite integrals, definite integrals, and differentiation
Key Concepts and Terms
summation
Practice problems
CHAPTER 12 INTEGRATION: (3) APPLICATIONS
12.1 Consumer Surplus
12.2 Gini coefficient
12.3 Probability and Integration
Key Concepts and Terms
summation
Practice problems
PART 04 Matrix
CHAPTER 13: Fundamentals of Matrix Algebra
13.1 Scalars, Vectors, and Matrices
13.2 Operations on Vectors and Matrices: Addition and Subtraction
13.3 Operations on Vectors and Matrices: Various Multiplications
Key Concepts and Terms
summation
Practice problems
CHAPTER 14 Inverse and Determinant
14.1 Identity matrix and inverse matrix
14.2 Inverse of a (2×2) matrix
14.3 Determinant of an (n×n) matrix
14.4 Inverse of an (n×n) matrix
Key Concepts and Terms
summation
Practice problems
CHAPTER 15 Solving and Applying Systems of Equations
15.1 Systems of linear equations
15.2 Three methods for solving systems of linear equations
15.3 Example: Three-Way First-Degree System of Equations
15.4 Application: Macroeconomic Models
Key Concepts and Terms
summation
Practice problems
PART 05 Multivariable Functions and Differentiation
CHAPTER 16 PARTIAL DIFFERENTIATION
16.1 Partial derivatives
16.2 Graphs of multivariable functions
16.3 Economics and Partial Differentiation
Key Concepts and Terms
summation
Practice problems
CHAPTER 17 Total Differentiation: Differentiation of Multivariable Composite Functions
17.1 Single-variable composite functions with multiple parameters
17.2 Multivariate composite functions with multiple parameters
17.3 Total Differentiation
17.4 Application of Total Differentiation: Keynesian Macroeconomic Models
17.5 Total amount
Key Concepts and Terms
summation
Practice problems
CHAPTER 18 Implicit Function Theorem and Comparative Statics Analysis
18.1 Implicit functions
18.2 Implicit differentiation when there is only one equation
18.3 Application: Marginal Rate of Substitution for Indifference Curves, Marginal Rate of Technical Substitution for Isoquants
18.4 Implicit differentiation when there are two equations
18.5 Application: The IS-LM Model
Key Concepts and Terms
summation
Practice problems
CHAPTER 19 Homogeneous Functions
19.1 Definition of a homogeneous function
19.2 Economics and Homogeneous Functions
19.3 Properties of homogeneous functions (1) Euler's theorem
19.4 Properties of homogeneous functions (2) Partial derivatives of homogeneous functions
19.5 Properties of Homogeneous Functions (3)
Key Concepts and Terms
summation
Practice problems
PART 06 Optimization
CHAPTER 20 Optimization of Multivariable Functions Without Constraints
20.1 Optimization of two-variable functions
20.2 Hessian matrix
20.3 Optimization of multivariable functions
Key Concepts and Terms
summation
Practice problems
CHAPTER 21 Optimization under Equality Constraints: (1) Introduction
21.1 Mathematical Example (1): Linear Constraints
21.2 Consumer Utility Maximization Problem
21.3 Consumer Utility Maximization: When There Are Two Goods
21.4 Consumer Utility Maximization: The Case of Three Goods
21.5 Mathematical Example (2): Nonlinear Constraints
Key Concepts and Terms
summation
Practice problems
CHAPTER 22 Optimization under Equality Constraints: (2) Lagrangian Method
22.1 How to use the Lagrange method
22.2 Proof of the Lagrange method
22.3 Interpreting the Lagrange Multiplier in Consumer Utility Maximization Problems
Key Concepts and Terms
summation
Practice problems
CHAPTER 23 Optimization under Equality Constraints: (3) Extensions and Applications
23.1 Extension of the Lagrange method (1) Minimization problem
23.2 Minimal Problems Under Constraints: Producer Cost Minimization (Long Run)
23.3 Extension of the Lagrange method (2) Multiple constraints
23.4 Optimization Problems with Multiple Constraints: Minimizing Producer Costs (Short-Run)
Key Concepts and Terms
summation
Practice problems
PART 07 Advanced Economic Mathematics Topics
CHAPTER 24 Optimization under Inequality Constraints
24.1 Concepts and Terminology Related to Real Estate Restrictions
24.2 Upper and lower constraints on selection variables
24.3 General Inequality Constraints
Key Concepts and Terms
summation
Practice problems
CHAPTER 25: DIFFERENCE EQUATIONS AND DYNAMIC ANALYSIS
25.1 Dynamic Model: Mathematical Representation of Time
25.2 Types and Key Concepts of Difference Equations
25.3 Solution and stability of differential equation models
25.4 Trademark
25.5 Differential Equations
Key Concepts and Terms
summation
Practice problems
CHAPTER 25A APPENDIX
25A.1 Solution of linear second-order difference equations
25A.2 Linear first-order differential equations
CHAPTER 26 Linear Independence: Foundations of Linear Algebra
26.1 Understanding Vectors Geometrically
26.2 Geometric Meaning of Vector Algebra: Addition, Subtraction, and Scalar Multiplication
26.3 Generation of vectors and linear independence
26.4 Basis, Dimensions, and Coordinates of Space
Key Concepts and Terms
summation
Practice problems
CHAPTER 26A APPENDIX: GEOMETRIC MEANING OF THE VECTOR DORT PRODUCT
26A.1 Cosine
26A.2 Geometric interpretation of the inner product
26A.3 Economic Interpretation of the Geometric Meaning of the Inner Product
Search
0.1 Mathematical representation of social science hypotheses
0.2 Economic Model
Key Concepts and Terms
summation
Food for thought
PART 01 Function
CHAPTER 01 Function Basics
1.1 Definition of functions
1.2 Graph of a function
1.3 Properties of functions
Key Concepts and Terms
summation
Practice problems
CHAPTER 02 Exponential Functions
2.1 Exponential functions
2.2 Numbers and natural exponential functions
2.3 Applications
Key Concepts and Terms
summation
Practice problems
CHAPTER 03 Logarithmic Functions
3.1 Basic properties and graphs of logarithmic functions
3.2 Useful properties of logarithmic functions
3.3 Natural logarithm function
3.4 Applications
Key Concepts and Terms
summation
Practice problems
PART 02 Differentiation
CHAPTER 04 Concept of Differentiation
4.1 Marginal or instantaneous rate of change: Differential coefficient
4.2 Derivatives and Differentiation
4.3 Second derivative
4.4 Finding the shape of a function's graph using first-order and second-order derivatives
Key Concepts and Terms
summation
Practice problems
CHAPTER 05 Rules of Differentiation: Differentiation of Polynomial Functions
5.1 Constant product and differentiation
5.2 Addition and differentiation between functions
5.3 Multiplication and differentiation between functions
5.4 Differentiation of monomials
Key Concepts and Terms
summation
Practice problems
CHAPTER 06 Rules of Differentiation: Differentiation of Composite Functions, Exponential Functions, and Logarithmic Functions
6.1 Differentiability
6.2 Differentiation of composite functions
6.3 Differentiation of exponential and logarithmic functions
6.4 Differentiation Rules for Monomials: Power Rule Final Edition
6.5 Derivatives of Fractional Functions
Key Concepts and Terms
summation
Practice problems
CHAPTER 07 Applications of Differentiation
7.1 The concept of 'limit'
7.2 Elasticity
7.3 Percentage change in multiplied value
7.4 Differential Calculations and Approximations
Key Concepts and Terms
summation
Practice problems
CHAPTER 08 Optimization of Single-Variable Functions: (1) First-Order Conditions
8.1 The Concept of Optimization and Its Economic Implications
8.2 One-order conditions: Necessary conditions for optimization
8.3 Application: Profit Maximization for Businesses
Key Concepts and Terms
summation
Practice problems
CHAPTER 09 Optimization of Single-Variable Functions: (2) Second-Order Conditions
9.1 Otherworldly conditions: sufficient conditions
9.2 Convexity and concaveness of functions
9.3 Application: Profit Maximization in Monopoly
Key Concepts and Terms
summation
Practice problems
PART 03 INTEGRATION
CHAPTER 10 INTEGRAL: (1) INDEFINITE INTEGRAL
10.1 Concept of indefinite integral
10.2 Basic Rules for Indefinite Integers
10.3 Basic Rules of Integration (3) Integration by Parts
10.4 Basic Rules of Integration (7) Substitution Integral
Key Concepts and Terms
summation
Practice problems
CHAPTER 11 INTEGRAL: (2) DEFINITE INTEGRAL
11.1 Definite Integrals: Area Under a Graph
11.2 Fundamental Theorem of Calculus: The Relationship Between Definite and Indefinite Integrators
11.3 Indefinite integrals, definite integrals, and differentiation
Key Concepts and Terms
summation
Practice problems
CHAPTER 12 INTEGRATION: (3) APPLICATIONS
12.1 Consumer Surplus
12.2 Gini coefficient
12.3 Probability and Integration
Key Concepts and Terms
summation
Practice problems
PART 04 Matrix
CHAPTER 13: Fundamentals of Matrix Algebra
13.1 Scalars, Vectors, and Matrices
13.2 Operations on Vectors and Matrices: Addition and Subtraction
13.3 Operations on Vectors and Matrices: Various Multiplications
Key Concepts and Terms
summation
Practice problems
CHAPTER 14 Inverse and Determinant
14.1 Identity matrix and inverse matrix
14.2 Inverse of a (2×2) matrix
14.3 Determinant of an (n×n) matrix
14.4 Inverse of an (n×n) matrix
Key Concepts and Terms
summation
Practice problems
CHAPTER 15 Solving and Applying Systems of Equations
15.1 Systems of linear equations
15.2 Three methods for solving systems of linear equations
15.3 Example: Three-Way First-Degree System of Equations
15.4 Application: Macroeconomic Models
Key Concepts and Terms
summation
Practice problems
PART 05 Multivariable Functions and Differentiation
CHAPTER 16 PARTIAL DIFFERENTIATION
16.1 Partial derivatives
16.2 Graphs of multivariable functions
16.3 Economics and Partial Differentiation
Key Concepts and Terms
summation
Practice problems
CHAPTER 17 Total Differentiation: Differentiation of Multivariable Composite Functions
17.1 Single-variable composite functions with multiple parameters
17.2 Multivariate composite functions with multiple parameters
17.3 Total Differentiation
17.4 Application of Total Differentiation: Keynesian Macroeconomic Models
17.5 Total amount
Key Concepts and Terms
summation
Practice problems
CHAPTER 18 Implicit Function Theorem and Comparative Statics Analysis
18.1 Implicit functions
18.2 Implicit differentiation when there is only one equation
18.3 Application: Marginal Rate of Substitution for Indifference Curves, Marginal Rate of Technical Substitution for Isoquants
18.4 Implicit differentiation when there are two equations
18.5 Application: The IS-LM Model
Key Concepts and Terms
summation
Practice problems
CHAPTER 19 Homogeneous Functions
19.1 Definition of a homogeneous function
19.2 Economics and Homogeneous Functions
19.3 Properties of homogeneous functions (1) Euler's theorem
19.4 Properties of homogeneous functions (2) Partial derivatives of homogeneous functions
19.5 Properties of Homogeneous Functions (3)
Key Concepts and Terms
summation
Practice problems
PART 06 Optimization
CHAPTER 20 Optimization of Multivariable Functions Without Constraints
20.1 Optimization of two-variable functions
20.2 Hessian matrix
20.3 Optimization of multivariable functions
Key Concepts and Terms
summation
Practice problems
CHAPTER 21 Optimization under Equality Constraints: (1) Introduction
21.1 Mathematical Example (1): Linear Constraints
21.2 Consumer Utility Maximization Problem
21.3 Consumer Utility Maximization: When There Are Two Goods
21.4 Consumer Utility Maximization: The Case of Three Goods
21.5 Mathematical Example (2): Nonlinear Constraints
Key Concepts and Terms
summation
Practice problems
CHAPTER 22 Optimization under Equality Constraints: (2) Lagrangian Method
22.1 How to use the Lagrange method
22.2 Proof of the Lagrange method
22.3 Interpreting the Lagrange Multiplier in Consumer Utility Maximization Problems
Key Concepts and Terms
summation
Practice problems
CHAPTER 23 Optimization under Equality Constraints: (3) Extensions and Applications
23.1 Extension of the Lagrange method (1) Minimization problem
23.2 Minimal Problems Under Constraints: Producer Cost Minimization (Long Run)
23.3 Extension of the Lagrange method (2) Multiple constraints
23.4 Optimization Problems with Multiple Constraints: Minimizing Producer Costs (Short-Run)
Key Concepts and Terms
summation
Practice problems
PART 07 Advanced Economic Mathematics Topics
CHAPTER 24 Optimization under Inequality Constraints
24.1 Concepts and Terminology Related to Real Estate Restrictions
24.2 Upper and lower constraints on selection variables
24.3 General Inequality Constraints
Key Concepts and Terms
summation
Practice problems
CHAPTER 25: DIFFERENCE EQUATIONS AND DYNAMIC ANALYSIS
25.1 Dynamic Model: Mathematical Representation of Time
25.2 Types and Key Concepts of Difference Equations
25.3 Solution and stability of differential equation models
25.4 Trademark
25.5 Differential Equations
Key Concepts and Terms
summation
Practice problems
CHAPTER 25A APPENDIX
25A.1 Solution of linear second-order difference equations
25A.2 Linear first-order differential equations
CHAPTER 26 Linear Independence: Foundations of Linear Algebra
26.1 Understanding Vectors Geometrically
26.2 Geometric Meaning of Vector Algebra: Addition, Subtraction, and Scalar Multiplication
26.3 Generation of vectors and linear independence
26.4 Basis, Dimensions, and Coordinates of Space
Key Concepts and Terms
summation
Practice problems
CHAPTER 26A APPENDIX: GEOMETRIC MEANING OF THE VECTOR DORT PRODUCT
26A.1 Cosine
26A.2 Geometric interpretation of the inner product
26A.3 Economic Interpretation of the Geometric Meaning of the Inner Product
Search
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GOODS SPECIFICS
- Date of issue: February 28, 2023
- Page count, weight, size: 464 pages | 188*257*30mm
- ISBN13: 9791156646525
- ISBN10: 1156646529
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