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Schaum's Outline of Mathematical Methods for Business and Economics

Schaum's Outline of Mathematical Methods for Business and Economics

Authors: Edward Dowling

Published: August 2009

eISBN: 9780071702461 0071702466 | ISBN: 9780071635325

Contents

Chapter 1 Review

1.1 Exponents

1.2 Polynomials

1.3 Factoring

1.4 Fractions

1.5 Radicals

1.6 Order of Mathematical Operations

1.7 Use of a Pocket Calculator

Chapter 2 Equations and Graphs

2.1 Equations

2.2 Cartesian Coordinate System

2.3 Linear Equations and Graphs

2.4 Slopes

2.5 Intercepts

2.6 The Slope-Intercept Form

2.7 Determining the Equation of a Straight-Line

2.8 Applications of Linear Equations in Business and Economics

Chapter 3 Functions

3.1 Concepts and Definitions

3.2 Graphing Functions

3.3 The Algebra of Functions

3.4 Applications of Linear Functions for Business and Economics

3.5 Solving Quadratic Equations

3.6 Facilitating Nonlinear Graphing

3.7 Applications of Nonlinear Functions in Business and Economics

Chapter 4 Systems of Equations

4.1 Introduction

4.2 Graphical Solutions

4.3 Supply-and-Demand Analysis

4.4 Break-Even Analysis

4.5 Elimination and Substitution Methods

4.6 Income Determination Models

4.7 IS-LM Analysis

4.8 Economic and Mathematical Modeling (Optional)

4.9 Implicit Functions and Inverse Functions (Optional)

Chapter 5 Linear (or Matrix) Algebra

5.1 Introduction

5.2 Definitions and Terms

5.3 Addition and Subtraction of Matrices

5.4 Scalar Multiplication

5.5 Vector Multiplication

5.6 Multiplication of Matrices

5.7 Matrix Expression of a System of Linear Equations

5.8 Augmented Matrix

5.9 Row Operations

5.10 Gaussian Method of Solving Linear Equations

Chapter 6 Solving Linear Equations with Matrix Algebra

6.1 Determinants and Linear Independence

6.2 Third-Order Determinants

6.3 Cramer's Rule for Solving Linear Equations

6.4 Inverse Matrices

6.5 Gaussian Method of Finding an Inverse Matrix

6.6 Solving Linear Equations with an Inverse Matrix

6.7 Business and Economic Applications

6.8 Special Determinants

Chapter 7 Linear Programming: Using Graphs

7.1 Use of Graphs

7.2 Maximization Using Graphs

7.3 The Extreme-Point Theorem

7.4 Minimization Using Graphs

7.5 Slack and Surplus Variables

7.6 The Basis Theorem

Chapter 8 Linear Programming: The Simplex Algorithm and the Dual

8.1 The Simplex Algorithm

8.2 Maximization

8.3 Marginal Value or Shadow Pricing

8.4 Minimization

8.5 The Dual

8.6 Rules of Transformation to Obtain the Dual

8.7 The Dual Theorems

8.8 Shadow Prices in the Dual

8.9 Integer Programming

8.10 Zero-One Programming

Chapter 9 Differential Calculus: The Derivative and the Rules of Differentiation

9.1 Limits

9.2 Continuity

9.3 The Slope of a Curvilinear Function

9.4 The Derivative

9.5 Differentiability and Continuity

9.6 Derivative Notation

9.7 Rules of Differentiation

9.8 Higher-Order Derivatives

9.9 Implicit Functions

Chapter 10 Differential Calculus: Uses of the Derivative

10.1 Increasing and Decreasing Functions

10.2 Concavity and Convexity

10.3 Relative Extrema

10.4 Inflection Points

10.5 Curve Sketching

10.6 Optimization of Functions

10.7 The Successive-Derivative Test

10.8 Marginal Concepts in Economics

10.9 Optimizing Economic Functions for Business

10.10 Relationship Among Total, Marginal, and Average Functions

Chapter 11 Exponential and Logarithmic Functions

11.1 Exponential Functions

11.2 Logarithmic Functions

11.3 Properties of Exponents and Logarithms

11.4 Natural Exponential and Logarithmic Functions

11.5 Solving Natural Exponential and Logarithmic Functions

11.6 Logarithmic Transformation of Nonlinear Functions

11.7 Derivatives of Natural Exponential and Logarithmic Functions

11.8 Interest Compounding

11.9 Estimating Growth Rates from Data Points

Chapter 12 Integral Calculus

12.1 Integration

12.2 Rules for Indefinite Integrals

12.3 Area under a Curve

12.4 The Definite Integral

12.5 The Fundamental Theorem of Calculus

12.6 Properties of Definite Integrals

12.7 Area between Curves

12.8 Integration by Substitution

12.9 Integration by Parts

12.10 Present Value of a Cash Flow

12.11 Consumers' and Producers' Surplus

Chapter 13 Calculus of Multivariable Functions

13.1 Functions of Several Independent Variables

13.2 Partial Derivatives

13.3 Rules of Partial Differentiation

13.4 Second-Order Partial Derivatives

13.5 Optimization of Multivariable Functions

13.6 Constrained Optimization with Lagrange Multipliers

13.7 Income Determination Multipliers

13.8 Optimizing Multivariable Functions in Business and Economics

13.9 Constrained Optimization of Multivariable Economic Functions

13.10 Constrained Optimization of Cobb-Douglas Production Functions

13.11 Implicit and Inverse Function Rules (Optional)

Index