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More About This Textbook
Overview
Editorial Reviews
Booknews
This text is designed to help students make the transition into calculus. The goals are to present a solid foundation in algebra and trigonometry and their applications to authentic realworld problems, as well as to enable the development of problemsolving skills and critical thinking. Blitzer (MiamiDade Community College) discusses fundamental concepts of algebra; equations, inequalities, and mathematical models; functions and graphs; polynomial and rational, exponential and logarithmic, and trigonometric functions; analytic trigonometry and additional topics; systems of equations and inequalities; matrices and determinants; conic sections and analytic geometry; sequences, induction, and probability; and introduction to calculus. Objectives in each chapter appear in boxed sections, with a color illustration. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
Related Subjects
Read an Excerpt
Preface
Precalculus is designed and written to help students make the transition into calculus. The book has three fundamental goals:
Precalculus is not simply a condensed version of my Algebra and Trigonometry book. Precalculus students are different from algebra and trigonometry students, and this text reflects those differences. Here are a few specific examples:
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 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 Precalculus 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 teaching in a large urban community college is the diversity of who my students; are and what interests them. Realworld data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all updated realworld data to be interesting and intriguing to students. By connecting; precalculus 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 (0130286540); (2865D2). Includes fully worked out. solutions to most of the oddnumbered exercises in the text as well as all exercises in chapter tests and all review exercises.
MathPak Integrated Learning Environment (0130282472); (282465). Contains the College Algebra MathPro 4.0 along with a passcodeprotected Website: specifically designed to accompany this text. This product combines the series' key' supplements into a comprehensive, easytonavigate package. Materials on the Website include but are not limited to: Sectionbysection reading quizzes, SectionbySection Powerpoint downloads, additional chapter projects, Chapter Quizzes and Tests, Student Solutions Manuals presented by chapter (exactly what 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 (0130282405); (2824K6). Sectionbysection 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. (0130109541); (1095D6). A three year NSFfunded project integrates an applied approach to the topics in the Precalculus 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 (0130286567) (2865F7). IRM contains the full solutions to the evennumbered exercises in the text.
TestGenEQ WIN/MAC CD (0130282499) (2824J8). New to Prentice Hall Mathematics is the use of TestGen EQ for our mathematics testing. TestGenEQ is a fully algorithmic, easytouse software program written and based on the section objectives in the text.
Test Item File (0130286761) (2867F5). A hard copy version of materials derived from the TestGenEQ program.
To the Student
I've written this book so that you can learn about the power of algebra and trigonometry and how it relates directly to your life outside the classroom. All concepts are carefully explained, important definitions and procedures are set off in boxes, and workedout examples that present solutions in a stepbystep manner appear in every section. Each example is followed by a similar matched problem, called a Check Point, for you to try so that you can actively participate in the learning process as you read the book. (Answers to all Check Points appear in the back of the book.) Study Tips offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to applying algebra and trigonometry to your life to make your learning experience both interesting and relevant. As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:
It is my hope that that you will enjoy the pages of this book as you empower yourself with the algebra and trigonometry needed to succeed in calculus, your career, and in your life.
Regards,
Bob
Robert Blitzer
Table of Contents
Real Numbers and Algebraic Expressions. Exponents and Scientific Notation. Radicals and Rational Exponents. Polynomials. Factoring Polynomials. Rational Expressions. Solving Linear Equations. Solving Quadratic Equations. Solving Inequalities.
1. Graphs, Functions, and Models.
Graphs and Graphing Utilities. Lines and Slope. Distance and Midpoint Formulas; Circles. Basics of Functions. Graphs of Functions. Transformations of Functions. Combinations of Functions; Composite Functions. Inverse Functions. Modeling with Functions.
2. Polynomial and Rational Functions.
Complex Numbers. Quadratic Functions. Polynomial Functions and their Graphs. Dividing Polynomials: Remainder and Factor Theorems. Zeros of Polynomial Functions. Rational Functions and Their Graphs. Polynomial and Rational Inequalities. Modeling Using Variation.
3. Exponential and Logarithmic Functions.
Exponential Functions. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions.
4. Trigonometric Functions.
Angles and Their Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of other Trigonometric Functions. Inverse Trigonometric Functions. Applications of Trigonometric Functions.
5. Analytic Trigonometry.
Verifying Trigonometric Identities. Sum and Difference Formulas. DoubleAngle and HalfAngle Formulas. Productto Sum and Sumto Product Formulas. Trigonometric Equations.
6. AdditionalTopics 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.
7. 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.
8. Matrices and Determinants.
Matrix Solutions to Linear Systems. Inconsistent and Dependent Systems and Their Applications. Matrix Operations and Their Applications. Multiplicative Inverse of Matrices and Matrix Equations. Determinants and Cramer's Rule.
9. Conic Sections and Analytic Geometry.
The Ellipse. The Hyperbola. The Parabola. Rotation of Axes. Parametric Equations. Conic Sections in Polar Coordinates.
10. Sequences, Induction, and Probability.
Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Counting Principles, Permutations, and Combinations. Probability.
11. Introduction to Calculus.
Finding Limits Using Tables and Graphs. Finding Limits Using Properties of Limits. OneSided Limits; Continuous Functions. Introduction to Derivatives.
Preface
Preface
Precalculus is designed and written to help students make the transition into calculus. The book has three fundamental goals:
Precalculus is not simply a condensed version of my Algebra and Trigonometry book. Precalculus students are different from algebra and trigonometry students, and this text reflects those differences. Here are a few specific examples:
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 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 Precalculus 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 teaching in a large urban community college is the diversity of who my students; are and what interests them. Realworld data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all updated realworld data to be interesting and intriguing to students. By connecting; precalculus 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 (0130286540); (2865D2). Includes fully worked out. solutions to most of the oddnumbered exercises in the text as well as all exercises in chapter tests and all review exercises.
MathPak Integrated Learning Environment (0130282472); (282465). Contains the College Algebra MathPro 4.0 along with a passcodeprotected Website: specifically designed to accompany this text. This product combines the series' key' supplements into a comprehensive, easytonavigate package. Materials on the Website include but are not limited to: Sectionbysection reading quizzes, SectionbySection Powerpoint downloads, additional chapter projects, Chapter Quizzes and Tests, Student Solutions Manuals presented by chapter (exactly what 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 (0130282405); (2824K6). Sectionbysection 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. (0130109541); (1095D6). A three year NSFfunded project integrates an applied approach to the topics in the Precalculus 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 (0130286567) (2865F7). IRM contains the full solutions to the evennumbered exercises in the text.
TestGenEQ WIN/MAC CD (0130282499) (2824J8). New to Prentice Hall Mathematics is the use of TestGen EQ for our mathematics testing. TestGenEQ is a fully algorithmic, easytouse software program written and based on the section objectives in the text.
Test Item File (0130286761) (2867F5). A hard copy version of materials derived from the TestGenEQ program.
To the Student
I've written this book so that you can learn about the power of algebra and trigonometry and how it relates directly to your life outside the classroom. All concepts are carefully explained, important definitions and procedures are set off in boxes, and workedout examples that present solutions in a stepbystep manner appear in every section. Each example is followed by a similar matched problem, called a Check Point, for you to try so that you can actively participate in the learning process as you read the book. (Answers to all Check Points appear in the back of the book.) Study Tips offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to applying algebra and trigonometry to your life to make your learning experience both interesting and relevant. As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:
It is my hope that that you will enjoy the pages of this book as you empower yourself with the algebra and trigonometry needed to succeed in calculus, your career, and in your life.
Regards,
Bob
Robert Blitzer