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by Margaret Lial, Raymond Greenwell and Nathan Ritchey

Edition: 7TH 05Copyright: 2005

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

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Widely known for incorporating interesting, relevant, and realistic applications, this text offers many real applications citing current data sources. There are a wide variety of opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts. MyMathLab, a complete online course, will be available with this text. For the first time, a comprehensive series of lectures on video will be available.

**Features **

- Section Opening Questions are thought-provoking questions which are revisited again and answered within the section.
- Variety of Applications--using real data from current sources, applied exercises are grouped by subject and highlighted for easy identification; Extended Applications appear at the end of most chapters.
- Excel Spreadsheets are included in examples and exercises as appropriate, allowing students to work problems that closely relate to real-life and business situations.
- Optional Graphing Calculator Integration. Graphing calculator discussions and TI-83/84 Plus screens are used in many examples.
- Cautions/Notes warn students of common errors/misconceptions and/or offer additional useful information.
- Margin Reviews provide immediate review, or refer students to appropriate review sections as needed.
- Exercise Sets. Includes exercises from Japan's university entrance exam showing how math is used in a variety of areas and around the globe. In addition, there are exercises that require writing and conceptualization in order to promote critical thinking, deeper understanding, and to integrate concepts and skills. Connection Exercises, denoted with an icon, integrate topics/concepts from different sections.
- Chapter R, Algebra Reference begins the text allowing students to brush up on their algebra skills.

**New To This Edition**

- The Chapter on Logic (Ch. 6) has been re-organized to help the material flow better and to emphasize helping students create logical proofs.
- New directions for Group Projects have been added to the Extended Applications to provide an opportunity for cooperative learning.
- MyMathLab is now available with this text. Providing a complete, online course that is customizable by instructors, this Web-based software includes a wide variety of resources from dynamic multimedia to course management tools. With MyMathLab, instructors can help increase student comprehension and success.
- Lecture-style videos are now available with this text. Offered on VHS cassettes, CD and online within MyMathLab, these videos provide students with additional help on key topics as taught by a mathematics instructor.

**R. Algebra Reference. **

Polynomials.

Factoring.

Rational Expressions.

Equations.

Inequalities.

Exponents.

Radicals.

**1. Linear Functions. **

Slopes and Equations of Lines.

Linear Functions and Applications.

The Least Squares Line.

**2. Systems of Linear Equations and Matrices. **

Solution of Linear Systems by the Echelon Method.

Solution of Linear Systems by the Gauss-Jordan Method.

Addition and Subtraction of Matrices.

Multiplication of Matrices.

Matrix Inverses.

Input-Output Models.

**3. Linear Programming: The Graphical Method. **

Graphing Linear Inequalities.

Solving Linear Programming Problems Graphically.

Applications of Linear Programming.

**4. Linear Programming: The Simplex Method. **

Slack Variables and the Pivot.

Maximization Problems.

Minimization Problems; Duality.

Nonstandard Problems.

**5. Mathematics of Finance. **

Simple and Compound Interest.

Future Value of an Annuity.

Present Value of an Annuity; Amortization.

**6. Logic. **

Statements.

Truth Tables and Equivalent Statements.

The Conditional and Circuits.

More on the Conditional.

Analyzing Arguments and Proofs.

Analyzing Arguments with Quantifiers.

**7. Sets and Probability. **

Sets.

Applications of Venn Diagrams.

Introduction to Probability.

Basic Concepts of Probability.

Conditional Probability; Independent Events.

Bayes' Theorem.

**8. Counting Principles; Further Probability Topics. **

The Multiplication Principle; Permutations.

Combinations.

Probability Applications of Counting Principles.

Binomial Probability.

Probability Distributions; Expected Value.

**9. Statistics. **

Frequency Distributions; Measures of Central Tendency.

Measures of Variation.

The Normal Distribution.

Normal Approximation to the Binomial Distribution.

**10. Nonlinear Functions. **

Properties of Functions.

Quadratic Functions; Translation and Reflection.

Polynomial and Rational Functions.

Exponential Functions.

Logarithmic Functions.

Applications: Growth and Decay; Mathematics of Finance.

**11. The Derivative. **

Limits.

Continuity.

Rates of Change.

Definition of the Derivative.

Graphical Differentiation.

**12. Calculating the Derivative. **

Techniques for Finding Derivatives.

Derivatives of Products and Quotients.

The Chain Rule.

Derivatives of Exponential Functions.

Derivatives of Logarithmic Functions.

**13. Graphs and the Derivative. **

Increasing and Decreasing Functions.

Relative Extrema.

Higher Derivatives, Concavity, and the Second Derivative Test.

Curve Sketching.

**14. Applications of the Derivative. **

Absolute Extrema.

Applications of Extrema.

Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand.

Implicit Differentiation.

Related Rates.

Differentials: Linear Approximation.

**15. Integration. **

Antiderivatives.

Substitution.

Area and the Definite Integral.

The Fundamental Theorem of Calculus.

The Area Between Two Curves.

Numerical Integration.

**16. Further Techniques and Applications of Integration. **

Integration by Parts.

Volume and Average Value.

Continuous Money Flow.

Improper Integrals.

Solutions of Elementary and Separable Differential Equations.

**17. Multivariable Calculus. **

Functions of Several Variables.

Partial Derivatives.

Maxima and Minima.

Lagrange Multipliers.

Total Differentials and Approximations.

Double Integrals.

**18. Probability and Calculus. **

Continuous Probability Models.

Expected Value and Variance of Continuous Random Variables.

Special Probability Density Functions.

**Tables. **

Table 1: Formulas from Geometry.

Table 2: Area Under a Normal Curve.

Table 3: Integrals.

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Summary

Widely known for incorporating interesting, relevant, and realistic applications, this text offers many real applications citing current data sources. There are a wide variety of opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts. MyMathLab, a complete online course, will be available with this text. For the first time, a comprehensive series of lectures on video will be available.

**Features **

- Section Opening Questions are thought-provoking questions which are revisited again and answered within the section.
- Variety of Applications--using real data from current sources, applied exercises are grouped by subject and highlighted for easy identification; Extended Applications appear at the end of most chapters.
- Excel Spreadsheets are included in examples and exercises as appropriate, allowing students to work problems that closely relate to real-life and business situations.
- Optional Graphing Calculator Integration. Graphing calculator discussions and TI-83/84 Plus screens are used in many examples.
- Cautions/Notes warn students of common errors/misconceptions and/or offer additional useful information.
- Margin Reviews provide immediate review, or refer students to appropriate review sections as needed.
- Exercise Sets. Includes exercises from Japan's university entrance exam showing how math is used in a variety of areas and around the globe. In addition, there are exercises that require writing and conceptualization in order to promote critical thinking, deeper understanding, and to integrate concepts and skills. Connection Exercises, denoted with an icon, integrate topics/concepts from different sections.
- Chapter R, Algebra Reference begins the text allowing students to brush up on their algebra skills.

**New To This Edition**

- The Chapter on Logic (Ch. 6) has been re-organized to help the material flow better and to emphasize helping students create logical proofs.
- New directions for Group Projects have been added to the Extended Applications to provide an opportunity for cooperative learning.
- MyMathLab is now available with this text. Providing a complete, online course that is customizable by instructors, this Web-based software includes a wide variety of resources from dynamic multimedia to course management tools. With MyMathLab, instructors can help increase student comprehension and success.
- Lecture-style videos are now available with this text. Offered on VHS cassettes, CD and online within MyMathLab, these videos provide students with additional help on key topics as taught by a mathematics instructor.

Table of Contents

**R. Algebra Reference. **

Polynomials.

Factoring.

Rational Expressions.

Equations.

Inequalities.

Exponents.

Radicals.

**1. Linear Functions. **

Slopes and Equations of Lines.

Linear Functions and Applications.

The Least Squares Line.

**2. Systems of Linear Equations and Matrices. **

Solution of Linear Systems by the Echelon Method.

Solution of Linear Systems by the Gauss-Jordan Method.

Addition and Subtraction of Matrices.

Multiplication of Matrices.

Matrix Inverses.

Input-Output Models.

**3. Linear Programming: The Graphical Method. **

Graphing Linear Inequalities.

Solving Linear Programming Problems Graphically.

Applications of Linear Programming.

**4. Linear Programming: The Simplex Method. **

Slack Variables and the Pivot.

Maximization Problems.

Minimization Problems; Duality.

Nonstandard Problems.

**5. Mathematics of Finance. **

Simple and Compound Interest.

Future Value of an Annuity.

Present Value of an Annuity; Amortization.

**6. Logic. **

Statements.

Truth Tables and Equivalent Statements.

The Conditional and Circuits.

More on the Conditional.

Analyzing Arguments and Proofs.

Analyzing Arguments with Quantifiers.

**7. Sets and Probability. **

Sets.

Applications of Venn Diagrams.

Introduction to Probability.

Basic Concepts of Probability.

Conditional Probability; Independent Events.

Bayes' Theorem.

**8. Counting Principles; Further Probability Topics. **

The Multiplication Principle; Permutations.

Combinations.

Probability Applications of Counting Principles.

Binomial Probability.

Probability Distributions; Expected Value.

**9. Statistics. **

Frequency Distributions; Measures of Central Tendency.

Measures of Variation.

The Normal Distribution.

Normal Approximation to the Binomial Distribution.

**10. Nonlinear Functions. **

Properties of Functions.

Quadratic Functions; Translation and Reflection.

Polynomial and Rational Functions.

Exponential Functions.

Logarithmic Functions.

Applications: Growth and Decay; Mathematics of Finance.

**11. The Derivative. **

Limits.

Continuity.

Rates of Change.

Definition of the Derivative.

Graphical Differentiation.

**12. Calculating the Derivative. **

Techniques for Finding Derivatives.

Derivatives of Products and Quotients.

The Chain Rule.

Derivatives of Exponential Functions.

Derivatives of Logarithmic Functions.

**13. Graphs and the Derivative. **

Increasing and Decreasing Functions.

Relative Extrema.

Higher Derivatives, Concavity, and the Second Derivative Test.

Curve Sketching.

**14. Applications of the Derivative. **

Absolute Extrema.

Applications of Extrema.

Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand.

Implicit Differentiation.

Related Rates.

Differentials: Linear Approximation.

**15. Integration. **

Antiderivatives.

Substitution.

Area and the Definite Integral.

The Fundamental Theorem of Calculus.

The Area Between Two Curves.

Numerical Integration.

**16. Further Techniques and Applications of Integration. **

Integration by Parts.

Volume and Average Value.

Continuous Money Flow.

Improper Integrals.

Solutions of Elementary and Separable Differential Equations.

**17. Multivariable Calculus. **

Functions of Several Variables.

Partial Derivatives.

Maxima and Minima.

Lagrange Multipliers.

Total Differentials and Approximations.

Double Integrals.

**18. Probability and Calculus. **

Continuous Probability Models.

Expected Value and Variance of Continuous Random Variables.

Special Probability Density Functions.

**Tables. **

Table 1: Formulas from Geometry.

Table 2: Area Under a Normal Curve.

Table 3: Integrals.

Publisher Info

Publisher: Addison-Wesley Longman, Inc.

Published: 2005

International: No

Published: 2005

International: No

Widely known for incorporating interesting, relevant, and realistic applications, this text offers many real applications citing current data sources. There are a wide variety of opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts. MyMathLab, a complete online course, will be available with this text. For the first time, a comprehensive series of lectures on video will be available.

**Features **

- Section Opening Questions are thought-provoking questions which are revisited again and answered within the section.
- Variety of Applications--using real data from current sources, applied exercises are grouped by subject and highlighted for easy identification; Extended Applications appear at the end of most chapters.
- Excel Spreadsheets are included in examples and exercises as appropriate, allowing students to work problems that closely relate to real-life and business situations.
- Optional Graphing Calculator Integration. Graphing calculator discussions and TI-83/84 Plus screens are used in many examples.
- Cautions/Notes warn students of common errors/misconceptions and/or offer additional useful information.
- Margin Reviews provide immediate review, or refer students to appropriate review sections as needed.
- Exercise Sets. Includes exercises from Japan's university entrance exam showing how math is used in a variety of areas and around the globe. In addition, there are exercises that require writing and conceptualization in order to promote critical thinking, deeper understanding, and to integrate concepts and skills. Connection Exercises, denoted with an icon, integrate topics/concepts from different sections.
- Chapter R, Algebra Reference begins the text allowing students to brush up on their algebra skills.

**New To This Edition**

- The Chapter on Logic (Ch. 6) has been re-organized to help the material flow better and to emphasize helping students create logical proofs.
- New directions for Group Projects have been added to the Extended Applications to provide an opportunity for cooperative learning.
- MyMathLab is now available with this text. Providing a complete, online course that is customizable by instructors, this Web-based software includes a wide variety of resources from dynamic multimedia to course management tools. With MyMathLab, instructors can help increase student comprehension and success.
- Lecture-style videos are now available with this text. Offered on VHS cassettes, CD and online within MyMathLab, these videos provide students with additional help on key topics as taught by a mathematics instructor.

**R. Algebra Reference. **

Polynomials.

Factoring.

Rational Expressions.

Equations.

Inequalities.

Exponents.

Radicals.

**1. Linear Functions. **

Slopes and Equations of Lines.

Linear Functions and Applications.

The Least Squares Line.

**2. Systems of Linear Equations and Matrices. **

Solution of Linear Systems by the Echelon Method.

Solution of Linear Systems by the Gauss-Jordan Method.

Addition and Subtraction of Matrices.

Multiplication of Matrices.

Matrix Inverses.

Input-Output Models.

**3. Linear Programming: The Graphical Method. **

Graphing Linear Inequalities.

Solving Linear Programming Problems Graphically.

Applications of Linear Programming.

**4. Linear Programming: The Simplex Method. **

Slack Variables and the Pivot.

Maximization Problems.

Minimization Problems; Duality.

Nonstandard Problems.

**5. Mathematics of Finance. **

Simple and Compound Interest.

Future Value of an Annuity.

Present Value of an Annuity; Amortization.

**6. Logic. **

Statements.

Truth Tables and Equivalent Statements.

The Conditional and Circuits.

More on the Conditional.

Analyzing Arguments and Proofs.

Analyzing Arguments with Quantifiers.

**7. Sets and Probability. **

Sets.

Applications of Venn Diagrams.

Introduction to Probability.

Basic Concepts of Probability.

Conditional Probability; Independent Events.

Bayes' Theorem.

**8. Counting Principles; Further Probability Topics. **

The Multiplication Principle; Permutations.

Combinations.

Probability Applications of Counting Principles.

Binomial Probability.

Probability Distributions; Expected Value.

**9. Statistics. **

Frequency Distributions; Measures of Central Tendency.

Measures of Variation.

The Normal Distribution.

Normal Approximation to the Binomial Distribution.

**10. Nonlinear Functions. **

Properties of Functions.

Quadratic Functions; Translation and Reflection.

Polynomial and Rational Functions.

Exponential Functions.

Logarithmic Functions.

Applications: Growth and Decay; Mathematics of Finance.

**11. The Derivative. **

Limits.

Continuity.

Rates of Change.

Definition of the Derivative.

Graphical Differentiation.

**12. Calculating the Derivative. **

Techniques for Finding Derivatives.

Derivatives of Products and Quotients.

The Chain Rule.

Derivatives of Exponential Functions.

Derivatives of Logarithmic Functions.

**13. Graphs and the Derivative. **

Increasing and Decreasing Functions.

Relative Extrema.

Higher Derivatives, Concavity, and the Second Derivative Test.

Curve Sketching.

**14. Applications of the Derivative. **

Absolute Extrema.

Applications of Extrema.

Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand.

Implicit Differentiation.

Related Rates.

Differentials: Linear Approximation.

**15. Integration. **

Antiderivatives.

Substitution.

Area and the Definite Integral.

The Fundamental Theorem of Calculus.

The Area Between Two Curves.

Numerical Integration.

**16. Further Techniques and Applications of Integration. **

Integration by Parts.

Volume and Average Value.

Continuous Money Flow.

Improper Integrals.

Solutions of Elementary and Separable Differential Equations.

**17. Multivariable Calculus. **

Functions of Several Variables.

Partial Derivatives.

Maxima and Minima.

Lagrange Multipliers.

Total Differentials and Approximations.

Double Integrals.

**18. Probability and Calculus. **

Continuous Probability Models.

Expected Value and Variance of Continuous Random Variables.

Special Probability Density Functions.

**Tables. **

Table 1: Formulas from Geometry.

Table 2: Area Under a Normal Curve.

Table 3: Integrals.