# Essential Mathematics for Economic Analysis

Knut Sydsaeter ; Peter Hammond ; Arne Strom ; Andres Carvajal

Essential Mathematics for Economic Analysis, 6th edition by Sydsaeter, Hammond, Strom and Carvajal is a global best-selling text that provides an extensive introduction to all the mathematical tools you need to study economics at intermediate level. Les mer

- Vår pris
- 648,-

(Paperback)
**Fri frakt!**

Leveringstid: Sendes innen 7 virkedager

**648,-**

(Paperback)
**Fri frakt!**

Leveringstid: Sendes innen 7 virkedager

Essential Mathematics for Economic Analysis, 6th edition by Sydsaeter, Hammond, Strom and Carvajal is a global best-selling text that provides an extensive introduction to all the mathematical tools you need to study economics at intermediate level.

This book has been applauded for its scope and covers a broad range of mathematical knowledge, techniques and tools, progressing from elementary calculus to more advanced topics. With a wealth of practice examples, questions and solutions integrated throughout, as well as opportunities to apply them in specific economic situations, this book will help you develop key mathematical skills as your course progresses.

Key features:

- Numerous exercises and worked examples throughout each chapter allow you to practise skills and improve techniques.

- Review exercises at the end of each chapter test your understanding of a topic, allowing you to progress with confidence.

- Solutions to exercises are provided in the book and online, showing you the steps needed to arrive at the correct answer.

Pearson, the world's learning company.

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'Hopital'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 Infinite Intervals of Integration

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 MULTI-VARIABLE 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 MULTI-VARIABLE CALCULUS

14 Multivariable Functions

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 More Variables

14.6 Partial Derivatives with More 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 MULTI-VARIABLE 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

Solutions to the Exercises

Index

Peter Hammond is currently Professor of Economics at the University of Warwick, where he moved in 2007 after becoming an Emeritus Professor at Stanford University. He has taught mathematics for economists at both universities, as well as at the universities of Oxford and Essex.

Arne Strom is Associate Professor Emeritus at the University of Oslo and has extensive experience in teaching mathematics for economists in the Department of Economics there.

Andres Carvajal is an Associate Professor in the Department of Economics at University of California, Davis.