Calculus and Its Applications, 10/e (IE-Paperback)

Marvin L. Bittinger , David J. Ellenbogen , Scott Surgent

  • 出版商: Prentice Hall
  • 出版日期: 2011-01-15
  • 售價: $1,050
  • 貴賓價: 9.8$1,029
  • 語言: 英文
  • 頁數: 696
  • ISBN: 0321766989
  • ISBN-13: 9780321766984
  • 相關分類: 微積分 Calculus

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Calculus and Its Applications, Tenth Edition, remains a best-selling text because of its accessible presentation that anticipates student needs. The writing style is ideal for today's students, providing intuitive explanations that work with the carefully crafted artwork to help them visualize new calculus concepts. Additionally, the text's numerous and up-to-date applications from business, economics, life sciences, and social sciences help motivate students. Algebra diagnostic and review material is available for those who need to strengthen basic skills. Every aspect of this revision is designed to motivate and help students to more readily understand and apply the mathematics.


Chapter 1

Chapter 1 contains 10 new examples designed to reinforce the main concepts and applications of limits, continuity, derivatives and the Chain Rule. Some of these examples serve as a bridge between concepts. In Section 1.5, the authors have added an expanded demonstration of the power rule of differentiation. While not a complete proof, it ties together skills students developed in earlier sections in taking the derivative of a positive-integer power. To see a general demonstration of this fact may help convince some students the derivative form is not a “lucky accident.” A new example is included in 1.5 in which the derivative can be used as a means to demonstrate behaviors of a function. While we do more of this in Chapter 2, it is valuable to introduce an easy example early, so that students have some familiarity of the derivative as an analytical tool, as opposed to a formula to be memorized. In Section 1.6, more detail is shown for the steps in the product and quotient rules. Finally, in Section 1.8, a new example continues the discussion from section 1.7 in which we “hint” at the change in value of a derivative and the concept of concavity, although the specific term is not yet introduced until Chapter 2.


Chapter 2

Sections 2.1 and 2.2 are refreshed by adding clarification to key themes and a discussion of optimization from both an algebraic and a calculus approach. A new example in Section 2.2 is added to tie together the discussion in earlier examples. In Section 2.3, a new example is included that asks the student to “build” a function based on some given facts about its behavior. This provides an opportunity to see if the student understands the concepts as opposed to memorizing steps. Section 2.6 has significant new material on using differentials as a means for approximation in real-world settings and greatly expands on what was presented in the 9th Edition.


Chapter 3

This chapter reflects the tone of the rest of the book with new features, applications and updates of data in examples and exercises. New applications include the exponential growth in the value of the Forever stamp, of Facebook membership, of costs of attending a 4-year college or university, the number of subscribers to Sirius XM radio, growth in net sales of Green Mountain Coffee Roasters, actuarial applications, and resale of antique Batman and Superman comic books. There are also new examples of exponential decay in the number of farms in the U.S., in the number of cases of tuberculosis, and in the magnitude of earthquakes in Haiti and Chile.


Chapter 4

This chapter has seen some significant rearrangement of the presentation of integration. It starts with general antidifferentiation in 4.1. We feel this is a good way to segue from differential to integral calculus. Students at this stage may not know “why” they are taking antiderivatives yet, but they can at least draw upon their skills of differentiation to learn the process of antidifferentiation. At the end of Section 4.1, a new Technology Connection is included that introduces area under a curve. Although area under curves is not formally discussed until 4.2, we feel that by introducing it now, and walking the students through the process, they may be able to make a connection that antidifferentiation has something to do with area. That way, when they start in on 4.2, they have some basic skills of antidifferentiation and some idea of its significance. In Section 4.2, we concentrate on the geometry behind integration: Riemann Sums and the development of the definite integral. Many basic examples are given with the intent to show more cases where area under a curve “makes sense”. Finally in 4.3, we bring the two processes together with the Fundamental Theorem of Calculus. New examples are given throughout the remainder of Chapter 4 to show some of the concepts in a different light. For example, in Section 4.5, we include a new example that shows an extension of the usual u-du method of substitution. This concept can be extended to integration by parts (Section 4.6), with the idea to show students that sometimes, there may be more than one way to work an antiderivative. Many of these concepts are further discussed in these sections' synthesis section of the homework. Finally, the Extended Technology Connection for Ch 4 is new, detailing the Lorenz Functions and Gini Coefficients in discussing distribution of wealth (or resources) in a society.


Chapter 5

Chapter 5 begins with the discussion of consumer and producer surplus, which has been rewritten and the graphs re-rendered to illustrate some of the concepts more clearly. Section 5.2 has been entirely rewritten. Reviewers made several suggestions that brought clarity to this section. We especially want to thank Bruce Thomas of Kennesaw State University for his extensive help. Section 5.5 includes a significant amount of new material on percentiles, including three new examples. And, Section 5.6 now includes a new example illustrating the use of volumes by rotation is included. Finally, a brief discussion of solving general first-ordered linear differential equations is now included in the synthesis section of 5.7.


Chapter 6

Many new examples have been added to Chapter 6. One of the new examples in Section 6.1 shows how tables are used in real-life as a means to express a multivariable concept (payment on an amortized loan). Later, a more formal discussion and an example on domains of a two-variable function is included. Section 6.4 presents a new Technology Connection discussing a method to find solutions to two-variable linear systems using matrices. Although systems is not covered formally in this text, the need to solve such a system is central to the topic presented in 6.4, Regression. This allows the student to handle this one aspect of the long process of regression quicker. In section 6.5, a more formal discussion of constrained optimization on a closed and bounded region allows us to include the Extreme Value Theorem, and extend the ideas of path constraints already presented in this section. Finally, in Section 6.6, an extra example illustrating the use of a double integral is presented