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ISBN13: 978-0201735109

ISBN10: 0201735105 Edition: 3RD 03

Copyright: 2003

Publisher: Addison-Wesley Longman, Inc.

Published: 2003

International: No

ISBN10: 0201735105 Edition: 3RD 03

Copyright: 2003

Publisher: Addison-Wesley Longman, Inc.

Published: 2003

International: No

This series is the culmination of many years of teaching experience with the graphing calculator. The books were written from the beginning for use with the graphing calculator. Throughout the text, the authors emphasize the power of technology but provide numerous warnings of its limitations: they stress that only through understanding the mathematical concepts can students fully appreciate the power of graphing calculators and use technology appropriately.

Additionally, the authors consistently use the same four-step process when introducing the different classes of functions. This allows students to easily make connections between graphs of functions and their associated equations and inequalities.

**Features :**

- Meaningful Applications of Mathematics. The authors have provided new applied examples and exercises that focus on real-life applications of mathematics. To further motivate the material, each chapter opens with an interesting application that can be solved using the methods introduced in that chapter. Additionally, all applications are titled, and an index of applications can be found in the text.
- Increased Emphasis on Modeling. The authors have included a large number of applications that provide data, often in tabular from. These exercises provide opportunity for the students to construct and analyze mathematical models.
- Reference Chapter on Basic Algebraic Concepts. The reference chapter has been updated, and includes exercises that test each of the concepts, along with answers to the odd exercises.
- Student Projects. Each chapter concludes with a student project that can be used as either an individual or collaborative learning activity. The project provides an opportunity for students to see how the material in the chapter they have just studied can be applied.
- Chapter Summaries. The chapter summaries are provided in a grid format. Section-by-section summaries of important concepts will assist students in reviewing and preparing for examinations.
- Chapter Tests. The authors offer a carefully written test for each chapter. Students can use these to prepare for examinations, and instructors may wish to pattern their classroom tests after them.
- Technology Notes. Notes in the margin provide tips to students on how to use graphing calculators more effectively.
- Cautions and Notes. These warn of common errors and misconceptions.
- For Discussion. This feature offers material for instructors and students to discuss in a classroom setting.
- Relating Concepts Exercises. These groups of exercises tie together different topics, and highlight the connections among various concepts and skills. By working the entire group in sequence, the student can appreciate the relationship among topics that earlier may have seemed unrelated.
- Writing and Conceptual Exercises. In addition to exercises that test concepts and skills, or that present the mathematical concepts in a real-world applied setting, the authors have also included many writing and conceptual exercises. These are aimed at helping students reach a deeper level of understanding of the mathematical ideas being considered, and get them more actively involved in their own learning.

**New To This Edition :**

- Function Capsule. The authors consistently provide a comprehensive visual introduction to each class of function with this feature.
- Analytic and Graphing Calculator Examples. Many examples within the text highlight both analytic and graphical solutions. This feature provides strong support for a multi-representational approach to problem solving and shows students the value of solving analytically and supporting those results graphically.
- Reviewing Basic Concepts. These new sets of exercises can be used for review and to check students' comprehension of the material in the preceding sections.
- What Went Wrong? Using graphing technology to study mathematics opens up a whole new area of error analysis. In anticipation of typical errors, this feature, now with answers, allows students and instructors to discuss such errors.
- Looking Ahead to Calculus. Where appropriate, margin notes provide glimpses of how algebraic topics in the text lead to the concepts of calculus.

Author Bio

**Hornsby, John : University of New Orleans**

Lial, Margaret L. : American River College

Rockswold, Gary : Minnesota State University, Mankato

1. Linear Functions, Equations, and Inequalities.

Real Numbers and Coordinate Systems.

Introduction to Relations and Functions.

Linear Functions.

Equations of Lines and Linear Models.

Linear Equations and Inequalities.

Applications of Linear Functions.

2. Analysis of Graphs of Functions.

Graphs of Basic Functions and Relations; Symmetry.

Vertical and Horizontal Shifts of Graphs.

Stretching, Shrinking, and Reflecting Graphs.

Absolute Value Functions: Graphs, Equations, Inequalities, and Applications.

Piecewise-Defined Functions.

Operations and Composition.

3. Polynomial Functions.

Complex Numbers.

Quadratic Functions and Graphs.

Quadratic Equations and Inequalities.

Further Applications of Quadratic Functions and Models.

Higher Degree Polynomial Functions and Graphs.

Topics in the Theory of Polynomial Functions (I).

Topics in the Theory of Polynomial Functions (II).

Polynomial Equations and Inequalities; Further Applications and Models.

4. Rational, Power, and Root Functions.

Rational Functions and Graphs.

More on Graphs of Rational Functions.

Rational Equations, Inequalities, Applications, and Models.

Functions Defined by Powers and Roots.

Equations, Inequalities, and Applications Involving Root Functions.

5. Inverse, Exponential, and Logarithmic Functions.

Inverse Functions.

Exponential Functions.

Logarithms and Their Properties.

Logarithmic Functions.

Exponential and Logarithmic Equations and Inequalities.

Applications and Modeling with Exponential and Logarithmic Functions.

6. Analytic Geometry.

Circles and Parabolas.

Ellipses and Hyperbolas.

Summary of the Conic Sections.

Parametric Equations.

7. Matrices and Systems of Equations and Inequalities.

Systems of Equations.

Solution of Linear Systems by the Echelon Method.

Solution of Linear Systems by Row Transformations.

Matrix Properties and Operations.

Determinants and Cramer's Rule.

Solution of Linear Systems by Matrix Inverses.

Systems of Inequalities and Linear Programming.

Partial Fractions.

8. Trigonometric Functions and Applications.

Angles and Their Measures.

Right Triangles and Trigonometric Functions.

Evaluating Trigonometric Functions.

Applications of Right Triangles.

The Circular Functions.

Graphs of the Sine and Cosine Functions.

Graphs of the Other Circular Functions.

Harmonic Motion.

9. Trigonometric Identities and Equations.

Identities.

Further Identities.

The Inverse Circular Functions.

Trigonometric Equations and Inequalities.

Further Equations and Inequalities.

10. Applications of Trigonometry; Vectors.

The Law of Sines.

The Law of Cosines and Area Formulas.

Vectors and Their Applications.

Trigonometric (Polar) Form of Complex Numbers.

Powers and Roots of Complex Numbers.

Polar Equations, Graphs, and Applications.

More Parametric Equations.

11. Further Topics in Algebra.

Sequences and Series.

Arithmetic Sequences and Series.

Geometric Sequences and Series.

The Binomial Theorem.

Mathematical Induction.

Counting Theory.

Probability.

R. Reference: Basic Algebraic Concepts and Geometry Formula.

Review of Exponents and Polynomials.

Review of Factoring.

Review of Rational Expressions.

Review of Negative and Rational Exponents.

Review of Radicals.

Review of Geometry Formulas.

Appendix A. Vectors in Space.

Appendix B. Polar Form of Conic Sections.

Appendix C. Rotation of Axes.

John Hornsby, Margaret L. Lial and Gary Rockswold

ISBN13: 978-0201735109ISBN10: 0201735105 Edition: 3RD 03

Copyright: 2003

Publisher: Addison-Wesley Longman, Inc.

Published: 2003

International: No

This series is the culmination of many years of teaching experience with the graphing calculator. The books were written from the beginning for use with the graphing calculator. Throughout the text, the authors emphasize the power of technology but provide numerous warnings of its limitations: they stress that only through understanding the mathematical concepts can students fully appreciate the power of graphing calculators and use technology appropriately.

Additionally, the authors consistently use the same four-step process when introducing the different classes of functions. This allows students to easily make connections between graphs of functions and their associated equations and inequalities.

**Features :**

- Meaningful Applications of Mathematics. The authors have provided new applied examples and exercises that focus on real-life applications of mathematics. To further motivate the material, each chapter opens with an interesting application that can be solved using the methods introduced in that chapter. Additionally, all applications are titled, and an index of applications can be found in the text.
- Increased Emphasis on Modeling. The authors have included a large number of applications that provide data, often in tabular from. These exercises provide opportunity for the students to construct and analyze mathematical models.
- Reference Chapter on Basic Algebraic Concepts. The reference chapter has been updated, and includes exercises that test each of the concepts, along with answers to the odd exercises.
- Student Projects. Each chapter concludes with a student project that can be used as either an individual or collaborative learning activity. The project provides an opportunity for students to see how the material in the chapter they have just studied can be applied.
- Chapter Summaries. The chapter summaries are provided in a grid format. Section-by-section summaries of important concepts will assist students in reviewing and preparing for examinations.
- Chapter Tests. The authors offer a carefully written test for each chapter. Students can use these to prepare for examinations, and instructors may wish to pattern their classroom tests after them.
- Technology Notes. Notes in the margin provide tips to students on how to use graphing calculators more effectively.
- Cautions and Notes. These warn of common errors and misconceptions.
- For Discussion. This feature offers material for instructors and students to discuss in a classroom setting.
- Relating Concepts Exercises. These groups of exercises tie together different topics, and highlight the connections among various concepts and skills. By working the entire group in sequence, the student can appreciate the relationship among topics that earlier may have seemed unrelated.
- Writing and Conceptual Exercises. In addition to exercises that test concepts and skills, or that present the mathematical concepts in a real-world applied setting, the authors have also included many writing and conceptual exercises. These are aimed at helping students reach a deeper level of understanding of the mathematical ideas being considered, and get them more actively involved in their own learning.

**New To This Edition :**

- Function Capsule. The authors consistently provide a comprehensive visual introduction to each class of function with this feature.
- Analytic and Graphing Calculator Examples. Many examples within the text highlight both analytic and graphical solutions. This feature provides strong support for a multi-representational approach to problem solving and shows students the value of solving analytically and supporting those results graphically.
- Reviewing Basic Concepts. These new sets of exercises can be used for review and to check students' comprehension of the material in the preceding sections.
- What Went Wrong? Using graphing technology to study mathematics opens up a whole new area of error analysis. In anticipation of typical errors, this feature, now with answers, allows students and instructors to discuss such errors.
- Looking Ahead to Calculus. Where appropriate, margin notes provide glimpses of how algebraic topics in the text lead to the concepts of calculus.

Author Bio

**Hornsby, John : University of New Orleans**

Lial, Margaret L. : American River College

Rockswold, Gary : Minnesota State University, Mankato

Table of Contents

Real Numbers and Coordinate Systems.

Introduction to Relations and Functions.

Linear Functions.

Equations of Lines and Linear Models.

Linear Equations and Inequalities.

Applications of Linear Functions.

2. Analysis of Graphs of Functions.

Graphs of Basic Functions and Relations; Symmetry.

Vertical and Horizontal Shifts of Graphs.

Stretching, Shrinking, and Reflecting Graphs.

Absolute Value Functions: Graphs, Equations, Inequalities, and Applications.

Piecewise-Defined Functions.

Operations and Composition.

3. Polynomial Functions.

Complex Numbers.

Quadratic Functions and Graphs.

Quadratic Equations and Inequalities.

Further Applications of Quadratic Functions and Models.

Higher Degree Polynomial Functions and Graphs.

Topics in the Theory of Polynomial Functions (I).

Topics in the Theory of Polynomial Functions (II).

Polynomial Equations and Inequalities; Further Applications and Models.

4. Rational, Power, and Root Functions.

Rational Functions and Graphs.

More on Graphs of Rational Functions.

Rational Equations, Inequalities, Applications, and Models.

Functions Defined by Powers and Roots.

Equations, Inequalities, and Applications Involving Root Functions.

5. Inverse, Exponential, and Logarithmic Functions.

Inverse Functions.

Exponential Functions.

Logarithms and Their Properties.

Logarithmic Functions.

Exponential and Logarithmic Equations and Inequalities.

Applications and Modeling with Exponential and Logarithmic Functions.

6. Analytic Geometry.

Circles and Parabolas.

Ellipses and Hyperbolas.

Summary of the Conic Sections.

Parametric Equations.

7. Matrices and Systems of Equations and Inequalities.

Systems of Equations.

Solution of Linear Systems by the Echelon Method.

Solution of Linear Systems by Row Transformations.

Matrix Properties and Operations.

Determinants and Cramer's Rule.

Solution of Linear Systems by Matrix Inverses.

Systems of Inequalities and Linear Programming.

Partial Fractions.

8. Trigonometric Functions and Applications.

Angles and Their Measures.

Right Triangles and Trigonometric Functions.

Evaluating Trigonometric Functions.

Applications of Right Triangles.

The Circular Functions.

Graphs of the Sine and Cosine Functions.

Graphs of the Other Circular Functions.

Harmonic Motion.

9. Trigonometric Identities and Equations.

Identities.

Further Identities.

The Inverse Circular Functions.

Trigonometric Equations and Inequalities.

Further Equations and Inequalities.

10. Applications of Trigonometry; Vectors.

The Law of Sines.

The Law of Cosines and Area Formulas.

Vectors and Their Applications.

Trigonometric (Polar) Form of Complex Numbers.

Powers and Roots of Complex Numbers.

Polar Equations, Graphs, and Applications.

More Parametric Equations.

11. Further Topics in Algebra.

Sequences and Series.

Arithmetic Sequences and Series.

Geometric Sequences and Series.

The Binomial Theorem.

Mathematical Induction.

Counting Theory.

Probability.

R. Reference: Basic Algebraic Concepts and Geometry Formula.

Review of Exponents and Polynomials.

Review of Factoring.

Review of Rational Expressions.

Review of Negative and Rational Exponents.

Review of Radicals.

Review of Geometry Formulas.

Appendix A. Vectors in Space.

Appendix B. Polar Form of Conic Sections.

Appendix C. Rotation of Axes.

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