In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greater emphasis.
Many sections now contain more examples and exercises involving applications and real-life data. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
You can share your ebook free to your friends. In an extended project, students will solve a Leontief input-output problem involving a seven-sector model for the U. Chapter 11 Section Mini Project 2 at the end of the section discusses the classic string and T-square construction of the parabola. The use of hyperbolas in determining a location appears in the Section Chapter 12 In Section Two methods for solving certain types of cubic equations are explained and applied in a project for Section This complements the discussion in the text on the history of polynomial equations.
Chapter 13 Section To help students evaluate their progress, each section contains a question Web quiz the quiz results can be e-mailed to the instructor and each chapter contains a chapter test, with the answer to each problem on each test. This CD-ROM also includes MathCue tutorial and answers with step-by-step explanations, a Quiz function that enables students to generate quiz problems keyed to problem types from each section of the book, a Chapter Test that provides many problems keyed to problem types from each chapter, and a Solution Finder that allows students to enter their own basic problems and recieve step-by-step graphing calculator tutorial for precalculus and college algebra, featuring examples, exercises, and video tutorials.
A complete set of answers is printed in the back of the text. PowerPoint lecture slides, combined with all of the instructor supplements in electronic format, are available on this CD-Rom.
The tracking program built into the instructor version of the software enables instructors to carefully monitor student progress. With a personalized study plan, students can focus their time where they need it the most, creating a positive learning environment and paving a pathway to success in their mathematics course. RTF conversion allows instructors to open tests in most word processors, such as Microsoft Word, for further formatting and customization.
Preface xv The iLrn Tutorial interface effectively engages students and helps them learn math concepts faster. ToolBox is ready to use as soon as you log on—or, you can customize its preloaded content by uploading images and other resources, adding Web links, or creating your own practice materials.
Students only have access to student resources on the website. Instructors can enter an access code to reach password-protected Instructor Resources.
Simple to use, iLrn Tutorial allows students to work with real math notation in real time, providing instant analysis and feedback. We are grateful to the following review board participants for their contributions and would like to acknowledge them. The remaining errors are those of the authors.
We can be reached through our editor whose e-mail address is [email protected] Many students and teachers from both colleges and high schools have made constructive suggestions about the text and exercises, and we thank them for that.
We are particularly indebted to Eric Barkan for numerous discussions on the material and his detailed comments on each of the seemingly endless revisions of the applications-oriented projects as well as his help in preparing the manuscript. Special thanks to Ross Rueger who wrote the supplementary manuals and prepared the answer section for the text.
Thanks to Charles Heuer for his careful work in checking the text and the exercise answers for accuracy. It has been a rare pleasure to work with Martha Emry on the production of the text, and we thank her for her patience and extraordinary ability to create order out of chaos and to keep us on track at all times.
Visualizing Data 1. Circles Natural numbers have been used since time immemorial; fractions were employed by the ancient Egyptians as early as B. Richards, Fundamentals Real numbers, equations, graphs—these topics set the stage for our work in precalculus. How much from previous courses should you remember about solving equations?
These are the numbers used in everyday life, in the sciences, in industry, and in business. Certain sets of real numbers are referred to often enough to be given special names. These are summarized in the box that follows. As indicated in Figure 1, the point associated with the number zero is referred to as the origin. The fundamental fact here is that there is a one-to-one correspondence between the set of real numbers and the set of points on the line.
The real number associated with a given point is called the coordinate of the point. It can be proved that a real number is rational if and only if its decimal expansion terminates e. Irrational numbers These are the real numbers that are not rational.
Section A. Lambert — For instance, since p is approximately 3. Similarly, since 12 is approximately 1. It is often convenient to use number lines that show reference points other than the integers used in Figure 2. For instance, Figure 3 a displays a number line with reference points that are multiples of p. In this case it is the integers that we then locate approximately.
For example, in Figure 3 b we show the approximate location of the number 1 on such a line. For ease of reference, we review these and two related symbols in the box on page 3. Roughly speaking, any uninterrupted portion of the number line is referred to as an interval. See Figure 4 a. See Figure 4 b. On a number line, oriented as in Figure 1, 2, or 3, the point a lies to the left of b. On a number line oriented as in Figure 1, 2, or 3, the point b lies to the right of a.
In addition to the Writing Mathematics sections from the previous edition, there are now mini projects or projects at the ends of many sections. These give the students additional opportunities to discuss, explore, learn, and write mathematics, often using real-life data. We are also aware of the limitations of the graphing utility as a sole analysis device. The role of the graphing utility is expanded in this new edition: The existence of the graphing utility is taken for granted and some examples do make use of x Preface xi this technology.
However, just as with the previous edition, this remains a text in which the central focus is on mathematics and its applications. If the instructor chooses, the text can be used without reference to the graphing utility, but a scientific calculator will be required since the text no longer includes logarithmic or trigonometric tables.
Students already familiar with a graphing utility will, at a minimum, need to read the page in Section 1. Overall, the quality and relevance of the graphing utility exercises is vastly improved over the previous edition.
Graphing utility exercises identified by the symbol G are now integrated into the regular exercise sets. As previously mentioned, graphing utility exercises now appear in virtually every exercise set as well as in the text examples. Some of the major changes occur in the following areas. Notes to students at appropriate places remind them to consult one of these appendices if the use of one of these topics seems unclear.
Section 1. Chapter 2 Section 2. Section 2. Sections 2. Chapter 3 Section 3. Functions are introduced at length using algebraic, verbal, tabular, and graphical forms. Functions as models are introduced and used in examples and exercises. Implicit functions are introduced in the section project. In Section 3. Sections 3. Chapter 4 Section 4. There is also a new discussion on the use of spreadsheets in generating scatter plots and regression lines. In Section 4. Also, first and second differences are introduced as a tool for determining whether a set of data points may be generated by a linear or quadratic function.
Section 4. Instructors who require the use of completing the square rather than the vertex formula should find their students well prepared in view of the previous work on that topic in Sections 1.
Chapter 5 Section 5. In Section 5. Historical background motivating the use of the logarithmic scale is provided. The Section 5. These ideas are used to supply insight into the interpretation and use of the exponential growth constant k. Chapter 6 This chapter now includes projects exploring applications of righttriangle trigonometry in astronomy, geometry, and optics with each application placed in a historical context.
The project concluding Section 6. The Section 6. The mini project at the end of Section 6. Chapter 7 We now present both right-triangle and trigonometric identity approaches in the solutions of several examples, encouraging the students to choose whichever method they prefer.
The exercises in this chapter make more extensive use of the graphing utility. Project topics include a basic trigonometric inequality needed in calculus, square waves and other nontrigonometric waveforms, and an introduction to Fourier series. Section 7. Chapter 8 The Section 8.
The derivation leads to a more general formula for combining waveforms. The project at the end of Section 8. The last project in the chapter provides a careful development of the two versions of the inverse secant function most commonly encountered in first-year calculus. Chapter 9 The project at the end of Section 9. The exercises on the dot product, defined using components, in Exercise Set 9. The Section 9.
Some figures have been added and exercise sets rearranged to make the discussion on polar coordinates easier to follow. Chapter 10 In Section The Section Section Students can apply this technology in an extended project on the use of matrices in the study of communication networks. In an extended project, students will solve a Leontief input-output problem involving a seven-sector model for the U. Chapter 11 Section Mini Project 2 at the end of the section discusses the classic string and T-square construction of the parabola.
The use of hyperbolas in determining a location appears in the Section Chapter 12 In Section
0コメント