New to the Book Co-authors Joel Hass and Chris Heil reconsidered every word, symbol, and piece of art, motivating students to consider the content from different perspectives and compelling a deeper, geometric understanding. Updated graphics emphasize clear visualization and mathematical correctness. New examples and figures have been added throughout all chapters, many based on user feedback. See, for instance, Example 3 in Section 9.1, which helps students overcome a conceptual obstacle. New types of homework exercises , including many geometric in nature, have been added. The new exercises provide different perspectives and approaches to each topic. Short URLs have been added to the historical marginnotes, allowing students to navigate directly to online information.
New annotations within examples (in blue type) guide the student through the problem solution and emphasize that each step in a mathematical argument is rigorously justified. All chapters have been revised for clarity, consistency, conciseness, and comprehension. Detailed content changes Chapter 1 * Clarified explanation of definition of exponential function in 1.4.* Replaced sin-1 notation for the inverse sine function with arcsin as default notation in 1.5, and similarly for other trig functions.* Added new Exercises: 1.1: 59-62, 1.
2: 21-22; 1.3: 64-65, 1.5: 61-64, 79cd; PE: 29-32. Chapter 2 * Added definition of average speed in 2.1.* Updated definition of limits to allow for arbitrary domains. The definition of limits is now consistent with the definition in multivariable domains later in the text and with more general mathematical usage.* Reworded limit and continuity definitions to remove implication symbols and improve comprehension.
* Added new Example 7 in 2.4 to illustrate limits of ratios of trig functions.* Rewrote 2.6 Example 11 to solve the equation by finding a zero, consistent with previous discussion.* Added new Exercises: 2.1: 15-18; 2.2: 3h-k, 4f-I; 2.4: 19-20, 45-46; 2.
5: 69-74; 2.6: 31-32; PE: 57-58; AAE: 35-38. Chapter 3 * Clarified relation of slope and rate of change.* Added new Figure 3.9 using the square root function to illustrate vertical tangent lines.* Added figure of x sin (1> x ) in 3.2 to illustrate how oscillation can lead to non-existence of a derivative of a continuous function.* Revised product rule to make order of factors consistent throughout text, including later dot product and cross product formulas.
* Added new Exercises: 3.2: 36, 43-44; 3.3: 65-66; 3.5: 43-44, 61bc; 3.6: 79-80, 111-113; 3.7: 27-28; 3.8: 97-100; 3.9: 43-46; 3.
10: 47; AAE: 14-15, 26-27. Chapter 4 * Added summary to 4.1.* Added new Example 12 with new Figure 4.35 to give basic and advanced examples of concavity.* Added new Exercises: 4.1: 53-56, 67-70; 4.3: 45-46, 67-68; 4.
4: 107-112; 4.6: 37-42; 4.7: 7-10; 4.8: 115-118; PE: 1-16, 101-102; AAE: 19-20, 38-39. Moved Exercises 4.1: 53-68 to PE. Chapter 5 * Improved discussion in 5.4 and added new Figure 5.
18 to illustrate the Mean Value Theorem.* Added new Exercises: 5.2: 33-36; 5.4: 71-72; 5.6: 47-48; PE: 43-44, 75-76. Chapter 6 * Clarified cylindrical shell method.* Added introductory discussion of mass distribution along a line, with figure, in 6.6.
* Added new Exercises: 6.1: 15; 6.2: 49-50; 6.3: 13-14; 6.5: 1-2; 6.6: 1-6, 21-22; PE: 17-18, 23-24, 37-38. Chapter 7 * Clarified discussion of separable differential equations in 7.2.
* Added new Exercises: 7.1: 61-62, 73; PE: 41-42. Chapter 8 * Updated 8.2 Integration by Parts discussion to emphasize u(x)v(x) dx form rather than u dv . Rewrote Examples 1-3 accordingly.* Removed discussion of tabular integration and associated exercises.* Updated discussion in 8.5 on how to find constants in Partial Fraction method.
* Updated notation in 8.8 to align with standard usage in statistics.* Added new Exercises: 8.1: 41-44; 8.2: 53-56, 72-73; 8.3: 75-76; 8.4: 49-52; 8.5: 51-66, 73-74; 8.
8: 35-38, 77-78; PE: 69-88. Chapter 9 * Clarified the different meaning of a sequence and a series.* Added new Figure 9.9 to illustrate sum of a series as area of a histogram.* Added to 9.3 a discussion on the importance of bounding errors in approximations.* Added new Figure 9.13 illustrating how to use integrals to bound remainder terms of partial sums.
* Rewrote Theorem 10 in 9.4 to bring out similarity to the integral comparison test.* Added new Figure 9.16 to illustrate the differing behaviors of the harmonic and alternating harmonic series.* Renamed the n th term test the " n th term test for divergence" to emphasize that it says nothing about convergence.* Added new Figure 9.19 to illustrate polynomials converging to ln(1 + x ), which illustrates convergence on the half-open interval (-1, 1].* Used red dots and intervals to indicate intervals and points where divergence occurs and blue to indicate convergence throughout Chapter 9.
* Added new Figure 9.21 to show the six different possibilities for an interval of convergence.* Added new Exercises: 9.1: 27-30, 72-77; 9.2: 19-22, 73- 76, 105; 9.3: 11-12, 39-42; 9.4: 55-56; 9.5: 45-46, 65-66; 9.
6: 57-82; 9.7: 61-65; 9.8: 23-24, 39-40; 9.9: 11-12, 37-38; PE: 41-44, 97-102. Chapter 10 * Added new Example 1 and Figure 10.2 in 10.1 to give a straightforward first example of a parametrized curve.* Updated area formulas for polar coordinates to include conditions for positive r and non-overlapping u.
* Added new Example 3 and Figure 10.37 in 10.4 to illustrate intersections of polar curves.* Added new Exercises: 10.1: 19-28; 10.2: 49-50; 10.4: 21-24. Chapter 11 * Added new Figure 11.
13(b) to show the effect of scaling a vector.* Added new Example 7 and Figure 11.26 in 11.3 to illustrate projection of a vector.* Added discussion on general quadric surfaces in 11.6, with new Example 4 and new Figure 11.48 illustrating the description of an ellipsoid not centered at the origin via completing the square.* Added new Exercises: 11.
1: 31-34, 59-60, 73-76; 11.2: 43-44; 11.3: 17-18; 11.4: 51-57; 11.5: 49-52. Chapter 12 * Added sidebars on how to pronounce Greek letters such as kappa, tau, etc.* Added new Exercises: 12.1: 1-4, 27-36; 12.
2: 15-16, 19- 20; 12.4: 27-28; 12.6: 1-2. Chapter 13 * Elaborated on discussion of open and closed regions in 13.1.* Standardized notation for evaluating partial derivatives, gradients, and directional derivatives at a point, throughout the chapter.* Renamed "branch diagrams" as "dependency diagrams" which clarifies that they capture dependence of variables.* Added new Exercises: 13.
2: 51-54; 13.3: 51-54, 59-60, 71-74, 103-104; 13.4: 20-30, 43-46, 57-58; 13.5: 41-44; 13.6: 9-10, 61; 13.7: 61-62. Chapter 14 * Added new Figure 14.21b to illustrate setting up limits of a double integral.
* Added new 14.5 Example 1, modified Examples 2 and 3, and added new Figures 14.31, 14.32, and 14.33 to give basic examples of setting up limits of integration for a triple integral.* Added new material on joint probability distributions as an application of multivariable integration.* Added new Examples 5, 6 and 7 to Section 14.6.
* Added new Exercises: 14.1: 15-16, 27-28; 14.6: 39-44; 14.7: 1-22. Chapter 15 * Added new Figure 15.4 to illustrate a line integral of a function.* Added new Figure 15.17 to illustrate a gradient field.
* Added new Figure 15.19 to illustrate a line integral of a vector field.* Clarified notation for line integrals in 15.2.* Added discussion of the sign of potential energy in 15.3.* Rewrote solution of Example 3 in 15.4 to clarify connection to Green''s Theorem.
* Updated discussion of surface orientation in 15.6 along with Figure 15.52.* Added new Exercises: 15.2: 37-38, 41-46; 15.4: 1-6; 15.6: 49-50; 15.7: 1-6; 15.
8: 1-4. Chapter 16 * Added new Example 3 with Figure 16.3 to illustrate how to construct a slope field.* Added new Exercises: 16.1: 11-14; PE: 17-22, 43-44.Appendices: Rewrote Appendix 8 on complex numbers. Shortened Appendix 2 to focus on issues arising in use of mathematical software and potential pitfalls. Also available with Pearson MyLab Math MyLab(tm) Math 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. A full suite of Interactive Figures have been added to the accompanying MyLab Math course to further support teaching and learning. Enhanced Sample Assignments include just-in-time prerequisite review, help keep skills fresh with distributed practice of key concepts, and provide opportunities to work exercises without learning aids to help students develop confidence in their ability to solve problems independently. New to Pearson MyLab Math: The new edition continues to expand the comprehensive auto-graded exercise options. The pre-existing exercises were carefully reviewed, vetted, and improved using aggregated student usage and performance data over t.