[PDF] Further Mathematics For Economic Analysis - Knut Sydsaeter, Peter J. Hammond, Arne Strøm, Atle Seierstad - 1st Edition

Essential Mathematics for Economic Analysis – Knut Sydsaeter – 6th Edition

Descripción

MATEMÁTICAS ESENCIALES PARA EL ANÁLISIS ECONÓMICO es un best-seller mundial que proporciona una extensa introducción a todas las herramientas matemáticas que necesita un economista. Adquiera las habilidades matemáticas clave que necesita para dominar y tener éxito en Economía.

Essential Mathematics for Economic Analysis, sexta edición de Sydsaeter, Hammond, Strøm y Carvajal es un texto de gran éxito a nivel mundial que proporciona una introducción extensa a todos los recursos matemáticos necesarios para estudiar economía en un nivel intermedio. Este libro ha sido aplaudido por cubrir una amplia gama de conocimientos, técnicas y herramientas matemáticas, avanzando desde el cálculo elemental hasta temas más avanzados.

Con una gran cantidad de ejemplos prácticos, preguntas y soluciones integradas, esta última edición le brinda una gran cantidad de oportunidades para aplicarlas en situaciones económicas específicas, ayudándolo a desarrollar habilidades matemáticas clave a medida que avanza su curso. Cuenta con capítulos introductorios para encajar más lógicamente con la enseñanza, ejercicios y sus soluciones completas. Se expone la historia de las ideas matemáticas económicas, así como de los científicos que las desarrollaron.

Autores:

  • Knut Sydsaeter fue profesor emérito de matemáticas en el Departamento de Economía de la Universidad de Oslo, donde enseñó matemáticas a economistas durante más de 45 años.
  • Peter Hammond es actualmente profesor de economía en la Universidad de Warwick, donde se mudó en 2007 después de convertirse en profesor emérito en la Universidad de Stanford. Ha enseñado matemáticas para economistas en ambas universidades, así como en las universidades de Oxford y Essex.
  • Arne Strom es Profesor Asociado Emérito en la Universidad de Oslo y tiene una amplia experiencia en la enseñanza de matemáticas para economistas en el Departamento de Economía allí.
  • Andrés Carvajal es Profesor Asociado en el Departamento de Economía de la Universidad de California.
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  • I PRELIMINARIES

    1 Essentials of Logic and Set Theory
    1.1 Essentials of Set Theory
    1.2 Essentials of Logic
    1.3 Mathematical Proofs
    1.4 Mathematical Induction
    Review Exercises

    2 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 Sign Diagrams
    2.9 Summation Notation
    2.10 Rules for Sums
    2.11 Newton's Binomial Formula
    2.12 Double Sums
    Review Exercises

    3 Solving Equations
    3.1 Solving Equations
    3.2 Equations and Their Parameters
    3.3 Quadratic Equations
    3.4 Some Nonlinear Equations
    3.5 Using Implication Arrows
    3.6 Two Linear Equations in Two Unknowns
    Review Exercises

    4 Functions of One Variable
    4.1 Introduction
    4.2 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
    Review Exercises

    5 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
    Review Exercises

    II SINGLE VARIABLE CALCULUS

    6 Differentiation
    6.1 Slopes of Curves
    6.2 Tangents and Derivatives
    6.3 Increasing and Decreasing Functions
    6.4 Economic Applications
    6.5 A Brief Introduction to Limits
    6.6 Simple Rules for Differentiation
    6.7 Sums, Products, and Quotients
    6.8 The Chain Rule
    6.9 Higher-Order Derivatives
    6.10 Exponential Functions
    6.11 Logarithmic Functions
    Review Exercises

    7 Derivatives in Use
    7.1 Implicit Differentiation
    7.2 Economic Examples
    7.3 The Inverse Function Theorem
    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
    7.11 Infinite Sequences
    7.12 L'Hôpital's Rule
    Review Exercises

    8 Concave and Convex Functions
    8.1 Intuition
    8.2 Definitions
    8.3 General Properties
    8.4 First-Derivative Tests
    8.5 Second-Derivative Tests
    8.6 Inflection Points
    Review Exercises

    9 Optimization
    9.1 Extreme Points
    9.2 Simple Tests for Extreme Points
    9.3 Economic Examples
    9.4 The Extreme and Mean Value Theorems
    9.5 Further Economic Examples
    9.6 Local Extreme Points
    Review Exercises

    10 Integration
    10.1 Indefinite Integrals
    10.2 Area and Definite Integrals
    10.3 Properties of Definite Integrals
    10.4 Economic Applications
    10.5 Integration by Parts
    10.6 Integration by Substitution
    10.7 Improper Integrals
    Review Exercises

    11 Topics in Finance and Dynamics
    11.1 Interest Periods and Effective Rates
    11.2 Continuous Compounding
    11.3 Present Value
    11.4 Geometric Series
    11.5 Total Present Value
    11.6 Mortgage Repayments
    11.7 Internal Rate of Return
    11.8 A Glimpse at Difference Equations
    11.9 Essentials of Differential Equations
    11.10 Separable and Linear Differential Equations
    Review Exercises

    III MULTIVARIABLE ALGEBRA

    12 Matrix Algebra
    12.1 Matrices and Vectors
    12.2 Systems of Linear Equations
    12.3 Matrix Addition
    12.4 Algebra of Vectors
    12.5 Matrix Multiplication
    12.6 Rules for Matrix Multiplication
    12.7 The Transpose
    12.8 Gaussian Elimination
    12.9 Geometric Interpretation of Vectors
    12.10 Lines and Planes
    Review Exercises

    13 Determinants, Inverses, and Quadratic Forms
    13.1 Determinants of Order 2
    13.2 Determinants of Order 3
    13.3 Determinants in General
    13.4 Basic Rules for Determinants
    13.5 Expansion by Cofactors
    13.6 The Inverse of a Matrix
    13.7 A General Formula for the Inverse
    13.8 Cramer's Rule
    13.9 The Leontief Model
    13.10 Eigenvalues and Eigenvectors
    13.11 Diagonalization
    13.12 Quadratic Forms
    Review Exercises

    IV MULTIVARIABLE CALCULUS

    14 Functions of Many Variables
    14.1 Functions of Two Variables
    14.2 Partial Derivatives with Two Variables
    14.3 Geometric Representation
    14.4 Surfaces and Distance
    14.5 Functions of n Variables
    14.6 Partial Derivatives with Many Variables
    14.7 Convex Sets
    14.8 Concave and Convex Functions
    14.9 Economic Applications
    14.10 Partial Elasticities
    Review Exercises

    15 Partial Derivatives in Use
    15.1 A Simple Chain Rule
    15.2 Chain Rules for Many Variables
    15.3 Implicit Differentiation along a Level Curve
    15.4 Level Surfaces
    15.5 Elasticity of Substitution
    15.6 Homogeneous Functions of Two Variables
    15.7 Homogeneous and Homothetic Functions
    15.8 Linear Approximations
    15.9 Differentials
    15.10 Systems of Equations
    15.11 Differentiating Systems of Equations
    Review Exercises

    16 Multiple Integrals
    16.1 Double Integrals Over Finite Rectangles
    16.2 Infinite Rectangles of Integration
    16.3 Discontinuous Integrands and Other Extensions
    16.4 Integration Over Many Variables
    V MULTIVARIABLE OPTIMIZATION
    17 Unconstrained Optimization
    17.1 Two Choice Variables: Necessary Conditions
    17.2 Two Choice Variables: Sufficient Conditions
    17.3 Local Extreme Points
    17.4 Linear Models with Quadratic Objectives
    17.5 The Extreme Value Theorem
    17.6 Functions of More Variables
    17.7 Comparative Statics and the Envelope Theorem
    Review Exercises

    18 Equality Constraints
    18.1 The Lagrange Multiplier Method
    18.2 Interpreting the Lagrange Multiplier
    18.3 Multiple Solution Candidates
    18.4 Why Does the Lagrange Multiplier Method Work?
    18.5 Sufficient Conditions
    18.6 Additional Variables and Constraints
    18.7 Comparative Statics
    Review Exercises
    19 Linear Programming
    19.1 A Graphical Approach
    19.2 Introduction to Duality Theory
    19.3 The Duality Theorem
    19.4 A General Economic Interpretation
    19.5 Complementary Slackness
    Review Exercises

    20 Nonlinear Programming
    20.1 Two Variables and One Constraint
    20.2 Many Variables and Inequality Constraints
    20.3 Nonnegativity Constraints
    Review Exercises

    Appendix
    Geometry
    The Greek Alphabet
    Bibliography
    Solutions to the Exercises
    Index
    Publisher's Acknowledgements
    Back Cover
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