Essential Mathematics for Economic Analysis – Knut Sydsaeter – 5th Edition

Descripción

En este bestseller mundial se ofrece una amplia introducción a todas las herramientas matemáticas que necesita un economista. El aborda una amplia gama de conceptos matemáticos que son fundamentales para la comprensión y el análisis de cuestiones económicas.

El libro es apreciado por su enfoque en aplicar las matemáticas a problemas económicos y sociales, lo que lo convierte en una herramienta valiosa para estudiantes y profesionales que desean mejorar sus habilidades matemáticas para el análisis económico. Es especialmente útil para aquellos que estudian economía, finanzas, ciencias sociales y áreas relacionadas.

Novedades de esta edición:
– Los capítulos introductorios se han reestructurado para que se ajusten más lógicamente a la enseñanza.
– Se han introducido varios nuevos, así como soluciones más completas a los ya existentes.
– Se ha añadido más cobertura de la de las matemáticas y económicas, así como de los científicos que las desarrollaron.
– Nuevo ejemplo basado en la reforma de la fiscalidad de la vivienda en el Reino Unido de 2014 que ilustra cómo una función discontinua puede tener importantes consecuencias económicas.

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  • Chapter 01: Essentials of Logic and Set Theory
    1.1. Essentials of set theory
    1.2. Some aspects of logic
    1.3. Mathematical proofs
    1.4. Mathematical induction

    Chapter 02: Algebra
    2.1. The real numbers
    2.2. Integer powers
    2.3. Rules of algebra
    2.4. Fractions
    2.5. Fractional powers
    2.6. Inequalities
    2.7. Intervals and absolute values
    2.8. Summation
    2.9. Rules for sums
    2. 10. Newton’s binomial formula
    2. 11. Double sums

    Chapter 03: Solving Equations
    3.1. Solving equations
    3.2. Equations and their parameters
    3.3. Quadratic equations
    3.4. Nonlinear equations
    3.5. Using implication arrows
    3.6. Two linear equations in two unknowns

    Chapter 04: Functions of One Variable
    4.1. Introduction
    4.2. Basic definitions
    4.3. Graphs of functions
    4.4. Linear functions
    4.5. Linear models
    4.6. Quadratic functions
    4.7. Polynomials
    4.8. Power functions
    4.9. Exponential functions
    4. 10. Logarithmic functions

    Chapter 05: Properties of Functions
    5.1. Shifting graphs
    5.2. New functions from old
    5.3. Inverse functions
    5.4. Graphs of equations
    5.5. Distance in the plane
    5.6. General functions

    Chapter 06: Differentiation
    6.1. Slopes of curves
    6.2. Tangents and derivatives
    6.3. Increasing and decreasing functions
    6.4. Rates of change
    6.5. A dash of limits
    6.6. Simple rules for differentiation
    6.7. Sums, products and quotients
    6.8. The Chapter ain Rule
    6.9. Higher-order derivatives
    6. 10. Exponential functions
    6. 11. Logarithmic functions

    Chapter 07: Derivatives in Use
    7.1. Implicit differentiation
    7.2. Economic examples
    7.3. Differentiating the inverse
    7.4. Linear approximations
    7.5. Polynomial approximations
    7.6. Taylor's formula
    7.7. Elasticities
    7.8. Continuity
    7.9. More on limits
    7. 10. The intermediate value theorem and Newton’s method
    7. 11. Infinite sequences
    7. 12. L'Hôpital's Rule

    Chapter 08: Single-Variable Optimization
    8.1. Extreme points
    8.2. Simple tests for extreme points
    8.3. Economic examples
    8.4. The Extreme Value Theorem
    8.5. Further economic examples
    8.6. Local extreme points
    8.7. Inflection points

    Chapter 09: Integration
    9.1. Indefinite integrals
    9.2. Area and definite integrals
    9.3. Properties of definite integrals
    9.4. Economic applications
    9.5. Integration by parts
    9.6. Integration by substitution
    9.7. Infinite intervals of integration
    9.8. A glimpse at differential equations
    9.9. Separable and linear differential equations

    Chapter 10: Topics in Financial Mathematics
    10.1. Interest periods and effective rates
    10.2. Continuous compounding
    10.3. Present value
    10.4. Geometric series
    10.5. Total present value
    10.6. Mortgage repayments
    10.7. Internal rate of return
    10.8. A glimpse at difference equations

    Chapter 11: Functions of Many Variables
    11.1. Functions of two variables
    11.2. Partial derivatives with two variables
    11.3. Geometric representation
    11.4. Surfaces and distance
    11.5. Functions of more variables
    11.6. Partial derivatives with more variables
    11.7. Economic applications
    11.8. Partial elasticities

    Chapter 12: Tools for Comparative Statics
    12.1. A simple chain rule
    12.2. Chain rules for many variables
    12.3. Implicit differentiation along a level curve
    12.4. More general cases
    12.5. Elasticity of substitution
    12.6. Homogeneous functions of two variables
    12.7. Homogeneous and homothetic functions
    12.8. Linear approximations
    12.9. Differentials
    12. 10. Systems of equations
    12. 11. Differentiating systems of equations

    Chapter 13: Multivariable Optimization
    13.1. Two variables: necessary conditions
    13.2. Two variables: sufficient conditions
    13.3. Local extreme points
    13.4. Linear models with quadratic objectives
    13.5. The Extreme Value Theorem
    13.6. The general case
    13.7. Comparative statics and the envelope theorem

    Chapter 14: Constrained Optimization
    14.1. The Lagrange Multiplier Method
    14.2. Interpreting the Lagrange multiplier
    14.3. Multiple solution candidates
    14.4. Why the Lagrange method works
    14.5. Sufficient conditions
    14.6. Additional variables and constraints
    14.7. Comparative statics
    14.8. Nonlinear programming: a simple case
    14.9. Multiple inequality constraints
    14. 10. Nonnegativity constraints

    Chapter 15: Matrix and Vector Algebra
    15.1. Systems of linear equations
    15.2. Matrices and matrix operations
    15.3. Matrix multiplication
    15.4. Rules for matrix multiplication
    15.5. The transpose
    15.6. Gaussian elimination
    15.7. Vectors
    15.8. Geometric interpretation of vectors
    15.9. Lines and planes

    Chapter 16: Determinants and Inverse Matrices
    16.1. Determinants of order 2
    16.2. Determinants of order 3
    16.3. Determinants in general
    16.4. Basic rules for determinants
    16.5. Expansion by cofactors
    16.6. The inverse of a matrix
    16.7. A general formula for the inverse
    16.8. Cramer's Rule
    16.9. The Leontief Model

    Chapter 17: Linear Programming
    17.1. A graphical approach
    17.2. Introduction to Duality Theory
    17.3. The Duality Theorem
    17.4. A general economic interpretation
    17.5. Complementary slackness
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