Design changes Illustrative examples have been set up side by side with selected definitions and procedural boxes so students can make a clearer connection between the steps of a procedure and the example. Since these examples are placed next to the procedure they illustrate, they do not have descriptive titles. They follow the numbering sequence of all examples, and are indicated with a beside the example. Content has been reformatted so that figures in definitions appear immediately next to the text that describes them, enabling clearer comparisons between different definitions. A step-wise solving framework has been introduced for solving word problems, especially those in the earlier chapters. The end of examples has been made more obvious by enclosing examples within lines. Named rules Throughout the text, individual rules pertaining to a set have been given names so that they can be more easily referred to. For instance, the rules of exponents include the product rule, quotient rule, power of a power rule , and negative exponent rule .
Similarly, the rules for differentiation include the constant rule, general power rule, product rule, and quotient rule . Increased breadth of applications The text features many new applications in the examples and exercises. Here is a sampling of the contexts for these new applications: Indigenous culture (Sections 2.4, 2.6, and 21.3) Height of One World Trade Center (Section 4.4) Multimedia messaging by Canadians (Section 5.1) Hydronium ion concentration of a solution (Section 7.
3) Circadian rhythm in plants (Section 10.3) Phase angle for current/voltage lead and lag (Section 10.3) Bezier curve roof design (Section 15.3) Social networks usage (Section 22.1) Video game system market share (Section 22.1) Glacier Skywalk shape and area (Sections 21.4 and 26.2) Graphing utilities The use of technology in this edition follows a flexible approach.
Instead of focusing attention on the use of a specific graphing calculator, the text encourages students to solve problems using any graphing utility (such as graphing calculators, computer algebra systems, spreadsheet programs, or statistical software). Exercises More than 950 exercises are new or have been updated for this edition. MyLab Math Hundreds of new assignable algorithmic exercises are available to help instructors address the homework needs of students. Rounding This edition returns to the round half up rule for rounding measured values. Select content updates Revisions to content in the eleventh edition were informed by the extensive reviews of the tenth edition. Examples of these include: In Section 1.2, visual illustrations of the fundamental operations of algebra were introduced with side-by-side illustrations of the literal rule, a numerical example,and an algebraic example. In Section 1.
3, explanations of units and unit systems were completely redone, putting greater focus on practical reasons for use. In response to reviewer feedback, the section on rectangular coordinates has been moved to the beginning of the chapter, before the introduction to functions, which is now Section 3.2. The beginning of Chapter 5 has been reorganized so that systems of equations has a strong introduction in Section 5.2. The prerequisite material needed for systems of equations (linear equations and graphs of linear functions) has been consolidated into Section 5.1. In Section 6.
3, factoring of trinomials is done more methodically using tables of factors and sums and then grouping rather than by trial and error. In Chapter 7, the square root property is explicitly stated and illustrated. In Chapter 8, the unit circle definition of the trigonometric functions has been added. In Chapter 9, more emphasis had been given to solving equilibrium problems, including those that have more than one unknown. In Chapter 10, an example was added to show how the phase angle can be interpreted, and how it is different from the phase shift. In Chapter 16, the terminology row echelon form is used. Also, the approach for solving systems of equations is to focus on operations on matrices rather than on operations with equations. In Chapter 23, the terminology direct substitution has been introduced in the context of limits.
In Chapter 30, the proof of the Fourier coefficients has been moved online. Functional Use of Colour The text continues to use colour effectively for didactical purposes. New to this edition is the use of colour within equations to emphasize an important step in a procedure. For example, students can identify visually how one expression is replaced by another equivalent one when both expressions are written in the same colour.