Essential Mathematics for Economic Analysis

Höfundar: Knut Sydsaeter; Peter Hammond; Arne Strom; Andrés Carvajal (Útgáfa: 7)
Essential Mathematics for Economic Analysis

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"This new edition of the classic introductory textbook on the essential mathematics needed by any serious student of modern economics adds relevance to its well-known rigorous approach. This is a tour de force in clarity and rigour. " - Dr. Giancarlo Ianulardo, Senior Lecturer in Economics, University of Exeter Business School "Students and teachers of mathematics for economic analysis will welcome a new edition of this outstanding book, which describes the methods and their applications with exemplary clarity and accuracy, and a deep understanding of students’ needs.

" - Ralph Bailey, Associate Professor in Economics, University of Birmingham Gain the core mathematical skills you need to master and succeed in economics. Essential Mathematics for Economic Analysis, 7th edition by Sydsaeter, Hammond, Strøm, and Carvajal is a global best-selling text providing an extensive introduction to all the mathematical resources you need to study economics at an intermediate level.

Applauded for its scope, the book covers a broad range of mathematical knowledge, techniques and tools, progressing from elementary calculus to more advanced topics. With a wealth of practice examples and questions throughout, as well as opportunities to apply them in specific economic contexts, this book will help you develop key mathematical skills and see the relevance of these in real world applications.

Key features: Numerous exercises and worked examples throughout each chapter allow you to practice skills and improve techniques. Review exercises at the end of each chapter test your understanding of a topic, allowing you to progress with confidence. Online Solutions to exercises are provided in the book and online, showing you the steps needed to arrive at the correct answer. Accurate visual representation of calculations and graphs Pair this text with MyLab® Math MyLab is the teaching and learning platform available to support this title.

By combining trusted author content with digital tools and a flexible learning experience, MyLab Math personalises learning and assessment to help improve results. MyLab Math is not included with this title. If you would like to purchase both the physical textbook and MyLab (which also comes with the eBook), search for: 9781292487977 Essential Mathematics for Economic Analysis + MyLab Math (Package) which consists of: Print textbook eTextbook MyLab Math.

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Útgefandi
Pearson International Content
ISBN
9781292755779
Print ISBN
9781292755755
Format
ePub
Útgáfa
7
Höfundar
Knut Sydsaeter; Peter Hammond; Arne Strom; Andrés Carvajal
Tungumál
English
Útgefið
2026-08-10
Prent takmörkun á líftíma
100
Prent takmörkun
2
Afritunar takmörkun
2

Kaflar

  • Cover Page
  • Title
  • Copyright
  • Contents
  • Preface
  • 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, Differences, Products, and Quotients
  • 6.8 The Chain Rule
  • 6.9 Higher 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 Essentials of 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
  • 14.5 Functions of Multiple 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 Double Integrals Over General Domains
  • 16.4 Integrals of Radial Functions
  • 16.5 Integration by Substitution
  • 16.6 Extensions
  • Review Exercises
  • 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 MethodWork?
  • 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
  • Bibliography
  • Index