College Algebra and Trigonometry, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Fifth Edition, the authors recognize that students are learning in new ways, and that the classroom is evolving. The Lial team is now offering a new suite of resources to support today’s instructors and students.
New co-author Callie Daniels has experience in all classroom types including traditional, hybrid and online courses, which has driven the new MyMathLab features. For example, MyNotes
provide structure for student note-taking, and Interactive Chapter Summaries
allow students to quiz themselves in interactive examples on key vocabulary, symbols and concepts. Daniels’ experience, coupled with the long-time successful approach of the Lial series, has helped to more tightly integrate the text with online learning than ever before.
R. Review of Basic Concepts
R.2 Real Numbers and Their Properties
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
1.8 Absolute Value Equations and Inequalities
2. Graphs and Functions
2.1 Rectangular Coordinates and Graphs
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
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 and Models of Exponential Growth and Decay
5. Trigonometric Functions
5.2 Trigonometric Functions
5.3 Evaluating Trigonometric Functions
5.4 Solving 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, Cotangent, Secant, and Cosecant
6.6 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 Vectors, Operation, and the Dot Product
8.4 Applications of Vectors
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 Parametic 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
10.4 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
Appendix A. Polar Form of Conic Sections
Appendix B. Rotation of Axes
Appendix C. Geometry Formulas
Solutions to Selected Exercises
Answers to Selected Exercises
Index of Applications
Support for All Classroom Types: a complete suite of instructional materials makes it easier for instructors to prepare for the course, and leads to student success. Updates to MyMathLab® and MathXL® are an integral part of supporting instructors and student success in today’s classroom.
- NEW! MyNotes from new co-author Callie Daniels provide structure for student note taking.
- Interactive chapter summaries allow students to quiz themselves with interactive examples on key vocabulary, symbols, and concepts.
- NEW! Ready-to-Go MyMathLab courses are pre-built MyMathLab courses that make the start-up time building your course quick and easy.
- NEW! Interactive Figures are now available in MyMathLab, enabling users to manipulate figures to bring hard-to-convey math concepts to life.
- Interactive Animations are now tied to Function Boxes.
- The video program is designed to help students study any time, anywhere.
- Quick Reviews cover key definitions and procedures from each section.
- Example Solutions walk students through the detailed solution process for every example in the textbook.
- Author-designated sample homework problems include pencasts for selected problems.
- Additional MathXL coverage of all exercises include Summary Exercises, Relating Concepts Exercises, and Chapter Review exercises.
- Additional MathXL quizzes are assignable as homework. These are based on the text’s mid-chapter quizzes.
- Cumulative assignments follow each chapter test in the homework and test manager, allowing students to synthesize previous material throughout the course. These assignments consist of 30 problems each.
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.
- 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 engaged 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.
- NEW! Animations are available within MyMathLab.
- 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 emphasize 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 memorization.
- 25% of the exercises are new 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 develop problem-solving skills as they compare and contrast ideas, identify and describe patterns, and extend concepts to new situations. These exercises make great collaborative activities for pairs or small groups of students and are available in selected exercise sets.
- Full solutions to selected exercises are included at the back of the text for exercise numbers that are marked with a green square. There are three to five exercises per section and are chosen because they extend the skills and concepts presented in the examples.
- Summary Exercises are mixed review problems that challenge students to reconcile recent topics learned, synthesize concepts and select appropriate solution methods.
- Standard exercise types include writing exercises, optional graphing calculator exercises, multiple-choice, matching, true/false, and completion problems.
Support for Review and Test Preparation: ample opportunities for review are interspersed within chapters and found at the end of chapters.
- Quizzes appear periodically throughout the chapter for students to check their progress. Answers appear in the student answer section at the back of the text. NEW! These are now assignable in MyMathLab.
- Summary Exercises offer mixed review, requiring students to decide which methods covered in the chapter should apply to a particular problem. NEW! These are now assignable in MyMathLab.
- Chapter Reviews and Test Prep conclude every chapter with the following features:
- An extensive Summary, featuring a section-by-section list of Key Terms and New Symbols
- A Quick Review of important concepts, presented alongside corresponding Examples
- A comprehensive set of Review Exercises
- A Chapter Test covering all skills and concepts from the chapter
- A glossary of key terms from throughout the text is provided at the back of the book as an additional student study aid.
Marge Lial has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have 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, but after 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 and for mathematics 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 over 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.
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.