Algebra and Trigonometry / Edition 4

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Overview

This book presents the traditional content of Precalculus in a manner that answers the age-old question of 'When will I ever use this?' Highlighting truly relevant applications, this book presents the material in an easy to teach from/easy to learn from approach. KEY TOPICS Chapter topics include equations, inequalities, and mathematical models; functions and graphs; polynomial and rational functions; exponential and logarithmic functions; trigonometric functions; analytic trigonometry; systems of equations and inequalities; conic sections and analytic geometry; and sequences, induction, and probability. For individuals studying Precalculus.
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Product Details

  • ISBN-13: 9780321559852
  • Publisher: Pearson
  • Publication date: 12/30/2008
  • Edition description: Older Edition
  • Edition number: 4
  • Pages: 1200
  • Product dimensions: 8.70 (w) x 11.00 (h) x 1.70 (d)

Meet the Author

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob is most energized by teaching mathematics and has taught a variety of mathematics courses at Miami-Dade College for nearly 30 years. He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, and was among the first group of recipients at Miami-Dade College for an endowed chair based on excellence in the classroom. Bob has written Intermediate Algebra for College Students, Introductory Algebra for College Students, Essentials of Intermediate Algebra for College Students, Introductory and Intermediate Algebra for College Students, Essentials of Introductory and Intermediate Algebra for College Students, Algebra for College Students, Thinking Mathematically, College Algebra, Algebra and Trigonometry, Precalculus, and Trigonometry all published by Pearson.

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Read an Excerpt

PREFACE:

Preface

Today's college algebra and trigonometry students are a diverse group. Some are going on into calculus or other math sequences, whereas others will complete their math requirements with this course. This text is designed and written to help both sets of students succeed. The book has three fundamental goals: First, to help students acquire a solid foundation in algebra and trigonometry, preparing them for other college courses such as calculus, business calculus, finite mathematics, and computer science; second, to show students how algebra and trigonometry can model and solve authentic real-world problems; and third, to enable students to develop problem-solving skills, fostering critical thinking within a varied and interesting setting.

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

  • "I cannot follow the explanations."
  • "The applications are not interesting."

I thought about both of these objections in writing every page of this book.

"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in Algebra & Trigonometry have been written to make them extremely accessible. Every section contains a range of simple, intermediate, and challenging examples. Voice balloons allow for specific annotations in examples, further clarifying procedures and concepts.

"The applications are not interesting." One of the things I enjoy most aboutteaching in a large urban community college is the diversity of who my students are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all updated real-world data to be interesting and intriguing to students. By connecting algebra and trigonometry to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.

Student Supplements

Student Solutions Manual (0-13-089785-X); (8978E-0). Includes fully worker out solutions to most of the odd-numbered exercises in the text as well as all exercises in chapter tests and all review exercises.

MathPak Integrated Learning Environment (0-13-089384-6); (8938D-2). Contains the College Algebra MathPro 4.0 along with a passcode-protected Website specifically designed to accompany this text. This product combines the series' key supplements into a comprehensive, easy-to-navigate package. Materials on the Website include but are not limited to: Section-by-section reading quizzes, Section-by-Section Powerpoint downloads, additional chapter projects, Chapter Quizzes and Tests, Student Solutions Manuals presented by chapter (exactly why is in the print version), Chapter Destinations and to interesting math Websites, and Graphing Calculator Manuals for the full line of TI's, Sharp, HP, and Casio Calculators.

Review Videos (0-13-089387-0); (89386-5). Section-by-section videos written by and highlighting Jacquelyn White of St. Leo College. Each segment covers approximately 20 minutes of the key concepts and examples for each section. Each set of videos comes with a permissions letter allowing the school to duplicate for specific campus needs.

Precalculus Investigations/Simundza, et al. (013-010954-1); (1095D-6). A three year NSF-funded project integrates an applied approach to the topics in the Pre; calculus curriculum via applied projects. The investigations reflect the AMATYC and NCTM Standards in both curriculum content and pedagogy.

Companion Website (www.prenhall.com/blitzer). This CW address will lead to the bridge page for all of the Blitzer titles. On the CW sites (which are different than the MathPak sites) are the following: Chapter Quizzes, Chapter Tests, Projects, Graphing Calculator Manual, Destinations, and PowerPoints.

WebCT/Blackboard. Contains all the materials from the MathPak website (i.e., no MathPro) plus testing materials. Can be made available in Blackboard on adoption.

Instructor Supplements

Instructor's Resource Manual (0-13-089784-1); (8978D-3). IRM contains the full solutions to the even-numbered exercises in the text.

TestGen-EQ WIN/MAC CD (0-13-089386-2); (8938F-7). New to Prentice Hall Mathematics is the use of TestGen EQ for our mathematics testing. TestGen-EQI is a fully algorithmic, easy-to-use software program written and based on the section objectives in the text.

Test Item File (0-13-089783-3); (8978C-5). A hard-copy version of materials derived from the TestGen-EQ program.

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Table of Contents

(NOTE: Each chapter concludes with Summary, Review Exercises, and Chapter Test and/or Cumulative Review Exercises.)
P. Prerequisites: Fundamental Concepts of Algebra.

Real Numbers and Algebraic Expressions. Exponents and Scientific Notation. Radicals and Rational Exponents. Polynomials. Factoring Polynomials. Rational Expressions. Complex Numbers. Graphs and Graphing Utilities.

1. Equations, Inequalities, and Mathematical Models.
Linear Equations. Formulas and Applications. Quadratic Equations. Other Types of Equations. Linear Inequalities. Quadratic and Rational Inequalities.

2. Functions and Graphs.
Lines and Slope. Parallel and Perpendicular Lines and Circles. Introduction to Functions. Graphs of Functions. Transformations and Combinations of Functions. Composite and Inverse Functions.

3. Polynomial and Rational Functions.
Quadratic Functions. Polynomial Functions and Their Graphs. Dividing Polynomials: Remainder and Factor Theorems. Zeros of Polynomial Functions. More on Zeros of Polynomial Functions. Rational Functions and Their Graphs. Modeling Using Variation.

4. Exponential and Logarithmic Functions.
Exponential Functions. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions.

5. Trigonometric Functions.
Angles andTheir Measure. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Trigonometric Functions of Real Numbers; Periodic Functions. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications of Trigonometric Functions.

6. Analytic Trigonometry.
Verifying Trigonometric Identities. Sum and Difference Formulas. Double-Angle and Half-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations.

7. Additional Topics in Trigonometry.
The Law of Sines. The Law of Cosines. Polar Coordinates. Graphs of Polar Equations. Complex Numbers in Polar Form; DeMoivre's Theorem. Vectors. The Dot Product.

8. Systems of Equations and Inequalities.
Systems of Linear Equations in Two Variables. Systems of Linear Equations in Three Variables. Partial Fractions. Systems of Nonlinear Equations in Two Variables. Systems of Inequalities. Linear Programming.

9. Matrices and Determinants.
Matrix Solutions to Linear Systems. Inconsistent and Dependent Systems and Their Applications. Matrix Operations and Their Applications. Multiplicative Inverses of Matrices and Matrix Equations. Determinants and Cramer's Rule.

10. Conic Sections and Analytic Geometry.
The Ellipse. The Hyperbola. The Parabola. Rotation of Axes. Parametric Equations. Conic Sections in Polar Coordinates.

11. Sequences, Induction, and Probability.
Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Counting Principles, Permutations, and Combinations. Probability.

Appendix: Where Did That Come From? Selected Proofs.
Answers to Selected Exercises.
Subject Index.
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Preface

Preface

Today's college algebra and trigonometry students are a diverse group. Some are going on into calculus or other math sequences, whereas others will complete their math requirements with this course. This text is designed and written to help both sets of students succeed. The book has three fundamental goals: First, to help students acquire a solid foundation in algebra and trigonometry, preparing them for other college courses such as calculus, business calculus, finite mathematics, and computer science; second, to show students how algebra and trigonometry can model and solve authentic real-world problems; and third, to enable students to develop problem-solving skills, fostering critical thinking within a varied and interesting setting.

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

  • "I cannot follow the explanations."
  • "The applications are not interesting."

I thought about both of these objections in writing every page of this book.

"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in Algebra & Trigonometry have been written to make them extremely accessible. Every section contains a range of simple, intermediate, and challenging examples. Voice balloons allow for specific annotations in examples, further clarifying procedures and concepts.

"The applications are not interesting." One of the things I enjoy most about teachingin a large urban community college is the diversity of who my students are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all updated real-world data to be interesting and intriguing to students. By connecting algebra and trigonometry to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.

Student Supplements

Student Solutions Manual (0-13-089785-X); (8978E-0). Includes fully worker out solutions to most of the odd-numbered exercises in the text as well as all exercises in chapter tests and all review exercises.

MathPak Integrated Learning Environment (0-13-089384-6); (8938D-2). Contains the College Algebra MathPro 4.0 along with a passcode-protected Website specifically designed to accompany this text. This product combines the series' key supplements into a comprehensive, easy-to-navigate package. Materials on the Website include but are not limited to: Section-by-section reading quizzes, Section-by-Section Powerpoint downloads, additional chapter projects, Chapter Quizzes and Tests, Student Solutions Manuals presented by chapter (exactly why is in the print version), Chapter Destinations and to interesting math Websites, and Graphing Calculator Manuals for the full line of TI's, Sharp, HP, and Casio Calculators.

Review Videos (0-13-089387-0); (89386-5). Section-by-section videos written by and highlighting Jacquelyn White of St. Leo College. Each segment covers approximately 20 minutes of the key concepts and examples for each section. Each set of videos comes with a permissions letter allowing the school to duplicate for specific campus needs.

Precalculus Investigations/Simundza, et al. (013-010954-1); (1095D-6). A three year NSF-funded project integrates an applied approach to the topics in the Pre; calculus curriculum via applied projects. The investigations reflect the AMATYC and NCTM Standards in both curriculum content and pedagogy.

Companion Website (www.prenhall.com/blitzer). This CW address will lead to the bridge page for all of the Blitzer titles. On the CW sites (which are different than the MathPak sites) are the following: Chapter Quizzes, Chapter Tests, Projects, Graphing Calculator Manual, Destinations, and PowerPoints.

WebCT/Blackboard. Contains all the materials from the MathPak website (i.e., no MathPro) plus testing materials. Can be made available in Blackboard on adoption.

Instructor Supplements

Instructor's Resource Manual (0-13-089784-1); (8978D-3). IRM contains the full solutions to the even-numbered exercises in the text.

TestGen-EQ WIN/MAC CD (0-13-089386-2); (8938F-7). New to Prentice Hall Mathematics is the use of TestGen EQ for our mathematics testing. TestGen-EQI is a fully algorithmic, easy-to-use software program written and based on the section objectives in the text.

Test Item File (0-13-089783-3); (8978C-5). A hard-copy version of materials derived from the TestGen-EQ program.

Read More Show Less

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