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Overview
PRECALCULUS, Fifth Edition, focuses on teaching the essentials that students need to both fulfill their precalculus requirement and be fully prepared to succeed in calculus. The text presents an integrated review of algebra and trigonometry while covering fundamental calculus concepts, and providing the solid grounding in analysis and graphing that is necessary to make a successful transition to calculus. This streamlined text provides all the mathematics that students need--without bogging them down in review material or overwhelming them with too much, too soon. The authors have purposely kept this book, unlike many available Precalculus books, at a length that can be covered in one term.
- A large number of carefully designed applications that emphasize the importance and relevance of precalculus and calculus have been added to the examples and exercise sets. They cover a wide range of areas, including biology, ecology, medicine, physics, economics, geometry, engineering, archeology, optimization, social science, finance, space science, and mathematics. Highlighted and placed at the ends of sections, the applications can be included or not at the instructor's discretion.
- All exercise sets have been reviewed to ensure that the material covered in the section, and the techniques presented in the examples, are sufficient to permit students to work the problems. As in previous editions, exercises vary in level from routine to those that offer applications and extend the theory presented. Approximately 30% of the routine exercises, purposely similar in design to those in the previous edition, are new.
- Chapter 4, "Trigonometric Functions," now reviews right triangle trigonometry (likely to be most familiar to students) earlier in the chapter so that students feel more comfortable with the subject before they are exposed to the unit circle definition needed for calculus. This approach facilitates an easier transition for students, while still emphasizing the need to give trigonometry a functional approach consistent with the other topics in the text.
- New "Principles of Problem Solving" comments, which highlight key techniques, augment the book's problem-solving focus. The comments--provided when a technique is presented initially and then explicitly used later when needed--are designed to help students develop systematic procedures for setting up and solving routine as well as application problems.
- The authors conducted an exhaustive check of every example, exercise, explanation, and essentially every line of the text, honing as needed to clarify, assure accuracy, and further emphasize the relevance of mathematics--without altering the compact "essentials" presentation.
- The terminology in the text parallels that used in calculus texts, and the examples and exercises are presented in the way students will encounter them in calculus--preparing students for their next course and providing them with a good head start.
- To maintain the text's brevity while allowing instructors greater flexibility in assigning content, the Book Companion Website includes coverage of useful, yet not fundamental, material on such topics as Descartes' Rule of Signs, Rotation of Axes for conic sections, and solving systems of equations.
- The authors weave an algebra and trigonometry review throughout the text to help students see where the gaps in their background must be filled before they take calculus.
- Explanations in the margin alert students to material that applies directly to calculus to help them prioritize their study.
- New concepts are presented using relevant applications, reinforced first with examples and then with the exercises.
- Technology is integrated throughout as a tool to extend knowledge, never as a substitute for the mastery of basic concepts that will be needed in calculus. The authors' primary use of graphing devices is to take a problem further than would be reasonable without this tool. Exercises that require technology are placed at the end of exercise sets where they will not disrupt the sequencing of the other exercises.
- "Calculus Connections" begin each chapter, helping to motivate students' interest in the material by showing them how they'll use what they learn in the chapter when they move on to calculus.
- "Exercises for Calculus" at the end of each chapter provide students with more challenging problems to help them prepare for further study.
- "True and False" questions at the ends of chapters emphasize subtle points in the theory to help students master concepts. The answers to these exercises include examples and counterexamples for cases in which the student is likely to think that a false statement is true, and vice versa.
Chapter 1 Functions.
1.1 Introduction.
1.2 The Real Line.
1.3 The Coordinate Plane.
1.4 Equations and Graphs.
1.5 Using Technology to Graph Functions.
1.6 Functions.
1.7 Linear Functions.
1.8 Quadratic Functions.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 2 New Functions From Old.
2.1 Introduction.
2.2 Other Common Functions.
2.3 Arithmetic Combinations of Functions.
2.4 Composition of Functions.
2.5 Inverse Functions.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 3 Algebraic Functions.
3.1 Introduction.
3.2 Polynomial Functions.
3.3 Finding Factors and Zeros of Polynomials.
3.4 Rational Functions.
3.5 Other Algebraic Functions.
3.6 Complex Roots of Polynomials.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 4 Trigonometric Functions.
4.1 Introduction.
4.2 Measuring Angles.
4.3 Right-Triangle Trigonometry.
4.4 The Sine and Cosine Functions.
4.5 Graphs of the Since and Cosine Functions.
4.6 Other Trigonometric Functions.
4.7 Trigonometric Identities.
4.8 Inverse Trigonometric Functions.
4.9 Additional Trigonometric Applications.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 5 Exponential and Logarithm Functions.
5.1 Introduction.
5.2 The Natural Exponential Function.
5.3 Logarithm Functions.
5.4 Exponential Growth and Decay.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 6 Conic Sections, Polar Coordinates, and Parametric Equations.
6.1 Introduction.
6.2 Parabolas.
6.3 Ellipses.
6.4 Hyperbolas.
6.5 Polar Coordinates.
6.6 Conic Sections in Polar Coordinates.
6.7 Parametric Equations.
Review Exercises.
Exercises for Calculus .
Chapter Test.
1.1 Introduction.
1.2 The Real Line.
1.3 The Coordinate Plane.
1.4 Equations and Graphs.
1.5 Using Technology to Graph Functions.
1.6 Functions.
1.7 Linear Functions.
1.8 Quadratic Functions.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 2 New Functions From Old.
2.1 Introduction.
2.2 Other Common Functions.
2.3 Arithmetic Combinations of Functions.
2.4 Composition of Functions.
2.5 Inverse Functions.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 3 Algebraic Functions.
3.1 Introduction.
3.2 Polynomial Functions.
3.3 Finding Factors and Zeros of Polynomials.
3.4 Rational Functions.
3.5 Other Algebraic Functions.
3.6 Complex Roots of Polynomials.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 4 Trigonometric Functions.
4.1 Introduction.
4.2 Measuring Angles.
4.3 Right-Triangle Trigonometry.
4.4 The Sine and Cosine Functions.
4.5 Graphs of the Since and Cosine Functions.
4.6 Other Trigonometric Functions.
4.7 Trigonometric Identities.
4.8 Inverse Trigonometric Functions.
4.9 Additional Trigonometric Applications.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 5 Exponential and Logarithm Functions.
5.1 Introduction.
5.2 The Natural Exponential Function.
5.3 Logarithm Functions.
5.4 Exponential Growth and Decay.
Review Exercises.
Exercises for Calculus.
Chapter Test.
Chapter 6 Conic Sections, Polar Coordinates, and Parametric Equations.
6.1 Introduction.
6.2 Parabolas.
6.3 Ellipses.
6.4 Hyperbolas.
6.5 Polar Coordinates.
6.6 Conic Sections in Polar Coordinates.
6.7 Parametric Equations.
Review Exercises.
Exercises for Calculus .
Chapter Test.
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- ISBN-10: 1133385036
- ISBN-13: 9781133385035
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- ISBN-13: 9780840068620
- RETAIL $254.95