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Geared toward business and social science majors in a two-semester finite mathematics and applied calculus course, this text equips students with the analytical tools and technological skills they will need in the workplace. Plain language and an easy-to-read style help stress conceptual understanding and reinforce key terms and concepts. At the same time, the incorporation of real-life applications, examples, and data help engage students--even those who have never enjoyed mathematics. Pedagogy throughout the text helps students analyze data from a variety of approaches, including numeric, algebraic, graphical, literal, and technological. A robust supplement package and exciting new technology program provide students with extensive learning and support, so that instructors can spend more time teaching.
Chapter 1
Functions
Linear Functions
Linear Models
Chapter 2
Systems of Two-Variable Linear Equations
Using Matrices to Solve Linear Systems of Equations
Linear System Applications
Chapter 3
Matrix Addition and Scalar Multiplication
Matrix Multiplication and Inverses
Solving Matrix Equations
Leontief Input-Output Models
Chapter 4
Graphing Linear Inequalities
Graphically Solving Linear Programming Problems
The Simplex Method: Solving Standard Maximization Problems
Standard Minimization Problems and the Dual
The Simplex Method: Solving Problems with Mixed Constraints
Chapter 5
Quadratic Function Models
Higher Order Polynomial Function Models
Exponential Models
Logarithmic Models
Choosing a Mathematical Model
Chapter 6
Solving Exponential and Logarithmic Equations
Simple Interest and Compound Interest
Future Value of an Increasing Annuity
Present Value of a Decreasing Annuity
Chapter 7
Sets
Cardinality and the Addition and Multiplication Principles
Permutations and Combinations
Introduction to Probability
Basic Probability Concepts
Chapter 8
Conditional Probability
Bayes' Theorem
Markov Chains
Random Variables and Expected Value
Measures of Central Tendency and Dispersion
Normal Distributions
Chapter 9
Average Rates of Change
Limits and Instantaneous Rates of Change
The Derivative as a Slope: Graphical Method
The Derivative as a Function: Algebraic Method
Interpreting the Derivative
Chapter 10
10.1 Basic Derivative Rules
10.2 Product Rule
10.3 Chain Rule
10.4 Exponential and Logarithmic Rules
10.5 Implicit Differentiation
Chapter 11
11.1 Maxima and Minima
11.2 Applications of Maxima and Minima
11.3 Concavity an the Second Derivative
11.4 Related Rates
Chapter 12
12.1 The Indefinite Integral
12.2 Integration by Substitution
Using Sums to Approximate Area
The Definite Integral
The Fundamental Theorem of Calculus
Chapter 13
Integration by Parts
Area Between Two Curves
The Differential Equations and Applications
The Differential Equations: Limited Growth and Logistic Models
Chapter 14
Multivariable Functions
Partial Derivatives
Multivariable Maxima and Minima
14.4 Constrained Maxima and Minima and Applications
Geared toward business and social science majors in a two-semester finite mathematics and applied calculus course, this text equips students with the analytical tools and technological skills they will need in the workplace. Plain language and an easy-to-read style help stress conceptual understanding and reinforce key terms and concepts. At the same time, the incorporation of real-life applications, examples, and data help engage students--even those who have never enjoyed mathematics. Pedagogy throughout the text helps students analyze data from a variety of approaches, including numeric, algebraic, graphical, literal, and technological. A robust supplement package and exciting new technology program provide students with extensive learning and support, so that instructors can spend more time teaching.
Table of Contents
Chapter 1
Functions
Linear Functions
Linear Models
Chapter 2
Systems of Two-Variable Linear Equations
Using Matrices to Solve Linear Systems of Equations
Linear System Applications
Chapter 3
Matrix Addition and Scalar Multiplication
Matrix Multiplication and Inverses
Solving Matrix Equations
Leontief Input-Output Models
Chapter 4
Graphing Linear Inequalities
Graphically Solving Linear Programming Problems
The Simplex Method: Solving Standard Maximization Problems
Standard Minimization Problems and the Dual
The Simplex Method: Solving Problems with Mixed Constraints
Chapter 5
Quadratic Function Models
Higher Order Polynomial Function Models
Exponential Models
Logarithmic Models
Choosing a Mathematical Model
Chapter 6
Solving Exponential and Logarithmic Equations
Simple Interest and Compound Interest
Future Value of an Increasing Annuity
Present Value of a Decreasing Annuity
Chapter 7
Sets
Cardinality and the Addition and Multiplication Principles
Permutations and Combinations
Introduction to Probability
Basic Probability Concepts
Chapter 8
Conditional Probability
Bayes' Theorem
Markov Chains
Random Variables and Expected Value
Measures of Central Tendency and Dispersion
Normal Distributions
Chapter 9
Average Rates of Change
Limits and Instantaneous Rates of Change
The Derivative as a Slope: Graphical Method
The Derivative as a Function: Algebraic Method
Interpreting the Derivative
Chapter 10
10.1 Basic Derivative Rules
10.2 Product Rule
10.3 Chain Rule
10.4 Exponential and Logarithmic Rules
10.5 Implicit Differentiation
Chapter 11
11.1 Maxima and Minima
11.2 Applications of Maxima and Minima
11.3 Concavity an the Second Derivative
11.4 Related Rates
Chapter 12
12.1 The Indefinite Integral
12.2 Integration by Substitution
Using Sums to Approximate Area
The Definite Integral
The Fundamental Theorem of Calculus
Chapter 13
Integration by Parts
Area Between Two Curves
The Differential Equations and Applications
The Differential Equations: Limited Growth and Logistic Models
Chapter 14
Multivariable Functions
Partial Derivatives
Multivariable Maxima and Minima
14.4 Constrained Maxima and Minima and Applications