(Ebook) Essential Mathematics for Economic Analysis 4th Edition by Knut Sydsaeter ISBN 0273760688 9780273760689

(Ebook) Essential Mathematics for Economic Analysis 4th Edition by Knut Sydsaeter ISBN 0273760688 9780273760689

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ISBN 10: 0273760688 
ISBN 13: 9780273760689
Author: Knut Sydsaeter

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This text provides an invaluable introduction to the mathematical tools that undergraduate economists need. The coverage is comprehensive, ranging from elementary algebra to more advanced material, whilst focusing on all the core topics that are usually taught in undergraduate courses on mathematics for economists.

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(Ebook) Essential Mathematics for Economic Analysis 4th Table of contents:

Part I: Preliminaries

• Chapter 1: Essentials of Logic and Set Theory

  • Essentials of Set Theory

  • Essentials of Logic

  • Mathematical Proofs

  • Mathematical Induction

• Chapter 2: Algebra

  • The Real Numbers

  • Integer Powers

  • Rules of Algebra

  • Fractions

  • Fractional Powers

  • Inequalities

  • Intervals and Absolute Values

  • Sign Diagrams

  • Summation Notation

  • Rules for Sums

  • Newton's Binomial Formula

  • Double Sums

• Chapter 3: Solving Equations

  • Solving Equations

  • Equations and Their Parameters

  • Quadratic Equations

  • Some Nonlinear Equations

  • Using Implication Arrows

  • Two Linear Equations in Two Unknowns

• Chapter 4: Functions of One Variable

  • Introduction

  • Definitions

  • Graphs of Functions

  • Linear Functions

  • Linear Models

  • Quadratic Functions

  • Polynomials

  • Power Functions

  • Exponential Functions

  • Logarithmic Functions

• Chapter 5: Properties of Functions

  • Shifting Graphs

  • New Functions from Old

  • Inverse Functions

  • Graphs of Equations

  • Distance in the Plane

  • General Functions

Part II: Single Variable Calculus

• Chapter 6: Differentiation

  • Slopes of Curves

  • Tangents and Derivatives

  • Increasing and Decreasing Functions

  • Economic Applications

  • A Brief Introduction to Limits

  • Simple Rules for Differentiation

  • Sums, Products, and Quotients

  • The Chain Rule

  • Higher-Order Derivatives

  • Exponential Functions

  • Logarithmic Functions

• Chapter 7: Derivatives in Use

  • Implicit Differentiation

  • Economic Examples

  • The Inverse Function Theorem

  • Linear Approximations

  • Polynomial Approximations

  • Taylor's Formula

  • Elasticities

  • Continuity

  • More on Limits

  • The Intermediate Value Theorem

  • Infinite Sequences

  • L'Hôpital's Rule

• Chapter 8: Concave and Convex Functions

  • Intuition

  • Definitions

  • General Properties

  • First-Derivative Tests

  • Second-Derivative Tests

  • Inflection Points

• Chapter 9: Optimization

  • Extreme Points

  • Simple Tests for Extreme Points

  • Economic Examples

  • The Extreme and Mean Value Theorems

  • Further Economic Examples

  • Local Extreme Points

• Chapter 10: Integration

  • Indefinite Integrals

  • Area and Definite Integrals

  • Properties of Definite Integrals

  • Economic Applications

  • Integration by Parts

  • Integration by Substitution

  • Improper Integrals

• Chapter 11: Topics in Finance and Dynamics

  • Interest Periods and Effective Rates

  • Continuous Compounding

  • Present Value

  • Geometric Series

  • Total Present Value

  • Mortgage Repayments

  • Internal Rate of Return

  • A Glimpse at Difference Equations

  • Essentials of Differential Equations

  • Separable and Linear Differential Equations

Part III: Multivariable Algebra

• Chapter 12: Matrix Algebra

  • Matrices and Vectors

  • Systems of Linear Equations

  • Matrix Addition

  • Algebra of Vectors

  • Matrix Multiplication

  • Rules for Matrix Multiplication

  • The Transpose

  • Gaussian Elimination

  • Geometric Interpretation of Vectors

  • Lines and Planes

• Chapter 13: Determinants, Inverses, and Quadratic Forms

   

  • Determinants of Order 2

     

  • Determinants of Order 3

     

  • Determinants in General

     

  • Basic Rules for Determinants

     

  • Expansion by Cofactors

     

  • The Inverse of a Matrix

     

  • A General Formula for the Inverse

     

  • Cramer's Rule

     

  • The Leontief Model

     

  • Eigenvalues and Eigenvectors

  • Diagonalization

  • Quadratic Forms

Part IV: Multivariable Calculus

• Chapter 14: Functions of Many Variables

  • Functions of Two Variables

  • Partial Derivatives with Two Variables

  • Geometric Representation

  • Surfaces and Distance

  • Functions of More Variables

  • Partial Derivatives with More Variables

  • Economic Applications

  • Partial Elasticities

• Chapter 15: Tools for Comparative Statics

  • A Simple Chain Rule

  • Chain Rules for Many Variables

  • Implicit Differentiation along a Level Curve

  • More General Cases

• Chapter 16: Multivariable Optimization

  • Economic Motivation

  • Local Extreme Points

  • Partial Derivatives and Differentiability

  • The Hessian Matrix and the Second-Derivative Test

  • Concave and Convex Functions of Several Variables

  • Optimization with Equality Constraints (Lagrange Multipliers)

  • Economic Applications of Constrained Optimization

  • Homogeneous Functions

• Chapter 17: Constrained Optimization (More Advanced Topics)

  • Nonlinear Programming and Kuhn-Tucker Conditions

  • Envelope Theorem

  • Linear Programming (brief introduction)

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Tags: Knut Sydsaeter, Essential, Mathematics