Table of Contents
Chapter 1 Review 1
1.1 Exponents 1
1.2 Polynomials 2
1.3 Factoring 3
1.4 Fractions 3
1.5 Radicals 4
1.6 Order of Mathematical Operations 5
1.7 Use of a Pocket Calcular 5
Chapter 2 Equations and Graphs 27
2.1 Equations 27
2.2 Cartesian Coordinate System 28
2.3 Linear Equations and Graphs 28
2.4 Slopes 29
2.5 Intercepts 30
2.6 The Slope-Intercept Form 30
2.7 Determining the Equation of a Straight-Line 32
2.8 Applications of Linear Equations in Business and Economics 33
Chapter 3 Functions 56
3.1 Concepts and Definitions 56
3.2 Graphing Functions 57
3.3 The Algebra of Functions 58
3.4 Applications of Linear Functions for Business and Economics 59
3.5 Solving Quardratic Equations 60
3.6 Facilitating Nonlinear Graphing 60
3.7 Applications of Nonlinear Functions in Business and Economics 61
Chapter 4 System of Equations 89
4.1 Introduction 89
4.2 Graphical Solutions 89
4.3 Supply-and-Demand Analysis 90
4.4 Break-Even Analysis 92
4.5 Elimination and Substitution Methods 93
4.6 Income Determination Models 95
4.7 IS-LM Analysis 96
4.8 Economic and Mathematical Modeling (Optional) 97
4.9 Implicit Functions and Inverse Functions (Optional) 97
Chapter 5 Linear (or Matrix) Algebra 128
5.1 Introduction 128
5.2 Definitions and Terms 128
5.3 Addition and Subtraction of Matrices 129
5.4 Scalar Multiplication 130
5.5 Vector Multiplication 130
5.6 Multiplication of Matrices 130
5.7 Matrix Expression of a System of Linear Equations 132
5.8 Augmented Matrix 133
5.9 Row Operations 134
5.10 Gaussian Method of Solving Linear Equations 134
Chapter 6 Solving Linear Equations with Matrix Algebra 151
6.1 Determinants and Linear Independence 151
6.2 Third-Order Determinants 151
6.3 Cramer's Rule for Solving Linear Equations 152
6.4 Inverse Matrices 154
6.5 Gaussian Method of Finding an Inverse Matrix 155
6.6 Solving Linear Equations with an Inverse Matrix 156
6.7 Business and Economic Applications 157
6.8 Special Determinants 158
Chapter 7 Linear Programming: Using Graphs 177
7.1 Use of Graphs 177
7.2 Maximization Using Graphs 177
7.3 The Extreme-Point Theorem 178
7.4 Minimization Using Graphs 178
7.5 Slack and Surplus Variables 180
7.6 The Basis Theorem 180
Chapter 8 Linear Programming: The Simplex Algorithm and the Dual 197
8.1 The Simplex Algorithm 197
8.2 Maximization 197
8.3 Marginal Value or Shadow Pricing 200
8.4 Minimization 200
8.5 The Dual 200
8.6 Rules of Transformation to Obtain the Dual 201
8.7 The Dual Theorems 202
8.8 Shadow Prices in the Dual 203
8.9 Integer Programming 203
8.10 Zero-One Programming 205
Chapter 9 Differential Calculus: The Derivative and the Rules of Differentiation 219
9.1 Limits 219
9.2 Continuity 220
9.3 The Slope of a Curvilinear Function 221
9.4 The Derivative 223
9.5 Differentiability and Continuity 223
9.6 Derivative Notation 223
9.7 Rules of Differentiation 224
9.8 Higher-Order Derivatives 227
9.9 Implicit Functions 227
Chapter 10 Differential Calculus: Uses of the Derivative 246
10.1 Increasing and Decreasing Functions 246
10.2 Concavity and Convexity 246
10.3 Relative Extrema 246
10.4 Inflection Points 246
10.5 Curve Sketching 248
10.6 Optimization of Functions 249
10.7 The Successive-Derivative Test 251
10.8 Marginal Concepts in Economics 251
10.9 Optimizing Economic Functions for Business 251
10.10 Relationships Among Total, Marginal, and Average Functions 252
Chapter 11 Exponential and Logarithmic Functions 276
11.1 Exponential Functions 276
11.2 Logarithmic Functions 276
11.3 Properties of Exponents and Logarithms 279
11.4 Natural Exponential and Logarithmic Functions 279
11.5 Solving Natural Exponential and Logarithmic Functions 280
11.6 Logarithmic Transformation of Nonlinear Functions 281
11.7 Derivatives of Natural Exponential and Logarithmic Functions 281
11.8 Interest Compounding 282
11.9 Estimating Growth Rates from Data Points 283
Chapter 12 Integral Calculus 304
12.1 Integration 304
12.2 Rules for Indefinite Integrals 304
12.3 Area Under a Curve 306
12.4 The Definite Integral 307
12.5 The Fundamental Theorem of Calculus 307
12.6 Properties of Definite Integrals 308
12.7 Area Between Curves 309
12.8 Integration by Substitution 310
12.9 Integration by Parts 311
12.10 Present Value of a Cash Flow 312
12.11 Consumers' and Producers' Surplus 313
Chapter 13 Calculus of Multivariable Functions 335
13.1 Functions of Several Independent Variables 335
13.2 Partial Derivatives 335
13.3 Rules of Partial Differentiation 336
13.4 Second-Order Partial Derivatives 338
13.5 Optimization of Multivariable Functions 339
13.6 Constrained Optimization with Lagrange Multipliers 341
13.7 Income Detenmnation Multipliers 342
13.8 Optimizing Multivariable Functions in Business and Economics 343
13.9 Constrained Optimization of Multivariable Economic Functions 344
13.10 Constrained Optimization of Cobb-Douglas Production Functions 344
13.11 Implicit and Inverse Function Rules (Optional) 345
Chapter 14 Sequences and Series 376
14.1 Sequences 376
14.2 Representation of Elements 377
14.3 Series and Summations 378
14.4 Property of Summations 380
14.5 Special Formulas of Summations 382
14.6 Economics Applications: Mean and Variance 383
14.7 Infinite Series 384
14.8 Finance Applications: Net Present Value 385
Excel Practice A 401
Excel Practice B 424
Additional Practice Problems 430
Additional Practice Problems: Solutions 483
Index 539
