Precalculus

Description

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Her desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor’s and Master’s degrees from California State University at Sacramento, was most recently affiliated with American River College. An avid reader and traveler, Marge’s travel experiences often find their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology. Trips to various digs and ruin sites produced some fascinating problems for her textbooks, involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, and now after more than twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching andmathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John’s personal life is busy, as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John’s other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

David Schneider has taught mathematics at universities for more than 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland—College Park. His hobbies include travel, dancing, bicycling, and hiking.

Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks on an athletic scholarship, playing both basketball and tennis. While there, she earned a Bachelor’s degree in Secondary Mathematics Education as well as the NAIA Academic All-American Award. She has two Master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri—Rolla, the second in Adult Education from the University of Missouri—St. Louis. Her hobbies include watching her sons play sports, riding horses, fishing, shooting photographs, and playing guitar. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding.

About the Book

 

Support for Learning Concepts: a systematic approach is used to present each topic, and is designed to actively engage students in the learning process. As a result, students develop both the conceptual understanding and the analytical skills necessary for success.

• NEW! Concept Preview Exercises now begin each homework section to ensure students’ understanding of vocabulary and basic concepts, especially for hybrid, online, and flipped courses.
• Pointers in the examples provide on-the-spot reminders and warnings about common pitfalls. Examples now offer additional side comments where appropriate in the step-by-step solutions, and there are more section references to previously covered material.
• Now Try exercises conclude every example with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set. Students are able to immediately apply and reinforce the concepts and skills presented in the examples, while actively engaging in the learning process.
• Real-life applications in the examples and exercises draw from fields such as business, pop-culture, sports, life sciences, and environmental studies to show the relevance of algebra to daily life.
• Functions are introduced in Chapter 2 and are a unifying theme throughout the text.
• Function boxes offer a comprehensive, visual introduction to each class of function and also serve as an excellent resource for student reference and review throughout the course. Each function box includes a table of values alongside traditional and calculator graphs, as well as the domain, range, and other specific information about the function.
• Graphing calculator coverage is optional and may be omitted without loss of continuity. The authors stress that these devices can be useful as an aid to understanding, but that students must master the underlying mathematical concepts first.
• • Graphing calculator solutions are included for selected examples, as appropriate.
  • Graphing calculator notes and exercises are marked with an icon for easy identification and flexibility.
• Cautions and Notes boxes throughout the text give students warnings of common errors and emphasise important ideas.
• Looking Ahead to Calculus offers glimpses of how the algebraic topics currently being studied are used in calculus. These notes can be found in the margins of the text in key places.
• Connections boxes provide connections to the real world or to other mathematical concepts, historical backgrounds, and thought-provoking questions for writing, class discussion, or group work.
• Chapter Openers provide a motivating application topic that is tied to the chapter content, plus a list of sections and any quizzes or summary exercises in the chapter.

Support for Practicing Concepts: the variety of exercise types promotes understanding of the concepts and reduces the opportunity for rote memorisation.

• Nearly 1,000 of the exercises are new or modified in this edition.
• Quizzes allow students to periodically check their understanding of the material covered. At least one quiz now appears in each chapter, where appropriate.
• Connecting Graphs with Equations problems, by request, provide students with opportunities to write equations for given graphs.
• Concept Check exercises focus on mathematical thinking and conceptual understanding.
• Relating Concepts Exercises help students tie together topics and d

New and Updated Features

• NEW! Concept Preview Exercises now begin each homework section to ensure students’ understanding of vocabulary and basic concepts, especially for hybrid, online, and flipped courses. These are also assignable in MyMathLab and also available in Learning Catalytics.
• Nearly 1,000 of the exercises are new or modified in this edition.

 

 

Content Updates

• In Chapter R, more detail has been added to set-builder notation, illustrations of the rules for exponents have been provided, and many exercises have been updated to better match section examples.
• Several new and updated applications have been inserted into the Chapter 1exercise sets. New objectives have been added to Section 1.4, outlining the four methods for solving a quadratic equation, along with guidance suggesting when each method may be used efficiently.
• Chapters 2 and 3 contain numerous new and updated applications and exercises, as well as many updated calculator screenshots that are now provided in color. In response to reviewer suggestions, the discussion on increasing, decreasing, and constant functions in Section 2.3 has been written to apply to open intervals of the domain. Also, as a response to reviewers, intercepts of graphs are now defined as coordinates rather than a single number. This notation continues throughout the text.
• In Chapter 4, greater emphasis is given to the concept of exponential and logarithmic functions as inverses, there is a new table providing descriptions of the additional properties of exponents, and additional exercises requiring graphing logarithmic functions with translations have been included. There are also many new and updated real-life applications of exponential and logarithmic functions.
• In Chapter 5, special attention has been given to finding partial fraction decompositions in Section 5.4 and to linear programming in Section 5.6. Examples have been rewritten to promote student understanding of these very difficult topics.
• In Chapter 6, greater emphasis is given to analyzing the specific aspects of conic sections—such as finding the equation of the axis of symmetry of a parabola, finding the coordinates of the foci of ellipses and hyperbolas, and finding the equations of the asymptotes of hyperbolas.
• Throughout Chapter 7, examples have been carefully updated to ensure that students are able to understand each step of the solutions. Special consideration was given to mathematical induction in Section 7.5 by providing numerous additional side comments for the steps of examples in this difficult section.
• For visual learners, numbered Figure and Example references within the text are set using the same typeface as the figure and hold print for the example. This makes it easier for the students to identify and connect them. The authors  also have increased use of “drop down” style when appropriate, to distinguish between simplifying expressions and solving equations, and have added many more explanatory side comments.
• Enhancing the already well-respected exercises, nearly 1,000 are new or modified, and hundreds present updated real-life data. In addition, the MyMathLab course has expanded coverage of all exercise types appearing in the exercise sets, as well as the mid-chapter Quizzes and Summary Exercises.

 Also available with MyMathLab

MyMathLab^® is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

 

The authors have developed specific content in MyMathLab to give students the practice they need to develop a conceptual understanding of College Algebra and the analytical skills necessary for success in mathematics. The MyMathLab features described here support College Algebra students in a variety of classroom formats (traditional, hybrid and online).

• NEW! Concept Preview Exercises now begin each homework section to ensure students’ understanding of vocabulary and basic concepts, especially for hybrid, online, and flipped courses. These are assignable in MyMathLab and also available in Learning Catalytics.
• NEW! MyMathLab with Integrated Review is a new course option that includes additional review resources (skill-check quizzes, personalized homework, review worksheets, and videos) at the beginning of each chapter in the College Algebra course.
• NEW! Guided Visualizations bring mathematical concepts to life. These animated figures help students visualize the concepts through directed explorations and purposeful manipulation. Guided Visualizations are assignable in MyMathLab and encourage active learning, critical thinking, and conceptual learning.

 

R. Review of Basic Concepts

R-1 Sets

R-2 Real Numbers and Their Properties

R-3 Polynomials

R-4 Factoring Polynomials

R-5 Rational Expressions

R-6 Rational Exponents

R-7 Radical Expressions

1. Equations and Inequalities

1-1 Linear Equations

1-2 Applications and Modeling with Linear Equations

1-3 Complex Numbers

1-4 Quadratic Equations

1-5 Applications and Modeling with Quadratic Equations

1-6 Other Types of Equations and Applications

1-7 Inequalities

1-8 Absolute Value Equations and Inequalities

2. Graphs and Functions

2-1 Rectangular Coordinates and Graphs

2-2 Circles

2-3 Functions

2-4 Linear Functions

2-5 Equations of Lines and Linear Models

2-6 Graphs of Basic Functions

2-7 Graphing Techniques

2-8 Function Operations and Composition

3. Polynomial and Rational Functions

3-1 Quadratic Functions and Models

3-2 Synthetic Division

3-3 Zeros of Polynomial Functions

3-4 Polynomial Functions: Graphs, Applications, and Models

3-5 Rational Functions: Graphs, Applications, and Models

3-6 Variation

4. Inverse, Exponential, and Logarithmic Functions

4-1 Inverse Functions

4-2 Exponential Functions

4-3 Logarithmic Functions

4-4 Evaluating Logarithms and the Change-of-Base Theorem

4-5 Exponential and Logarithmic Equations

4-6 Applications of Models of Exponential Growth and Decay

5. Trigonometric Functions

5-1 Angles

5-2 Trigonometric Functions

5-3 Trigonometric Function Values and Angle Measures

5-4 Solutions and Applications of Right Triangles

6. The Circular Functions and Their Graphs

6-1 Radian Measure

6-2 The Unit Circle and Circular Functions

6-3 Graphs of the Sine and Cosine Functions

6-4 Translations of the Graphs of the Sine and Cosine Functions

6-5 Graphs of the Tangent and Cotangent Functions

6-6 Graphs of the Secant and Cosecant Functions

6-7 Harmonic Motion

7. Trigonometric Identities and Equations

7-1 Fundamental Identities

7-2 Verifying Trigonometric Identities

7-3 Sum and Difference Identities

7-4 Double-Angle and Half-Angle Identities

7-5 Inverse Circular Functions

7-6 Trigonometric Equations

7-7 Equations Involving Inverse Trigonometric Functions

8. Applications of Trigonometry

8-1 The Law of Sines

8-2 The Law of Cosines

8-3 Geometrically Defined Vectors and Applications

8-4 Algebraically Defined Vectors and the Dot Product

8-5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients

8-6 De Moivre’s Theorem; Powers and Roots of Complex Numbers

8-7 Polar Equations and Graphs

8-8 Parametric Equations, Graphs, and Applications

9. Systems and Matrices

9-1 Systems of Linear Equations

9-2 Matrix Solution of Linear Systems

9-3 Determinant Solution of Linear Systems

9-4 Partial Fractions

9-5 Nonlinear Systems of Equations

9-6 Systems of Inequalities and Linear Programming

9-7 Properties of Matrices

9-8 Matrix Inverses

10. Analytic Geometry

10-1 Parabolas

10-2 Ellipses

10-3 Hyperbolas

10-4 Summary of the Conic Sections

11. Further Topics in Algebra

11-1 Sequences and Series

11-2 Arithmetic Sequences and Series

11-3 Geometric Sequences and Series

11-4 The Binomial Theorem

11-5 Mathematical Induction

11-6 Counting Theory

11-7 Basics of Probability

Appendices

For courses in precalculus.

 

Steadfast Support for your Evolving Course

The College Algebra series, by Lial, Hornsby, Schneider, and Daniels, combines the experience of master teachers to help students develop both the conceptual understanding and the analytical skills necessary for success in mathematics. With this latest edition, the authors respond to the challenges of new student expectations and new classroom models. The Lial team is now offering a new suite of resources to support today’s instructors and students.

 

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

 

The authors have developed specific content in MyMathLab to give students the practice they need to develop a conceptual understanding of College Algebra and the analytical skills necessary for success in mathematics. The MyMathLab features support College Algebra students in a variety of classroom formats (traditional, hybrid, and online).

 

For courses in precalculus.
Steadfast Support for your Evolving Course

The College Algebra series, by Lial, Hornsby, Schneider, and Daniels, combines the experience of master teachers to help students develop both the conceptual understanding and the analytical skills necessary for success in mathematics. With this latest edition, the authors respond to the challenges of new student expectations and new classroom models. The Lial team is now offering a new suite of resources to support today’s instructors and students.

Note: You are purchasing a standalone product; MyMathLab does not come packaged with this content. Students, if interested in purchasing this title with MyMathLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

If you would like to purchase both the physical text and MyMathLab, search for:

0134309049 / 9780134309040 Precalculus plus MyMathLab Student Access Kit

Package consists of:

013421742X / 9780134217420 Precalculus

0321431308 / 9780321431301 MyMathLab — Glue-in Access Card

0321654064 / 9780321654069 MyMathLab Inside Star Sticker

Additional information

Dimensions	1.70 × 8.50 × 11.00 in
Imprint	Pearson
Format	gen
ISBN-13	09780134217420
ISBN-10	013421742X
Author	Callie J. Daniels, David I. Schneider, John Hornsby, Margaret L. Lial
Subjects	mathematics, higher education, Precalculus