Book Preface
Buy Multivariable Calculus 11th edition (378) by Ron Larson for up to 90% off at Textbooks.com. 11.1 Power Series 11.2 Limit of a Power Series 11.3 Taylor Series Chapter Twelve - Integration 12.1 Introduction 12.2 Two Dimensions Chapter Thirteen - More Integration 13.1 Some Applications 13.2 Polar Coordinates 13.3 Three Dimensions Chapter Fourteen - One Dimension Again 14.1 Scalar Line Integrals 14.2 Vector Line Integrals 14.3 Path.
The 11th edition is based on the strengths of the 5th, 6th, and 9th Editions of Thomas' Calculus. New chapter on integration. Integration introduced through finite sums; indefinite integrals follow the Fundamental Theorem. Proofs have been pulled out of the appendix and placed back in the body of the book. Multivariable Calculus - Kindle edition by James Stewart. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks. EBook PHP Free ebook pdf and epub download directory. Multivariable Calculus Pdf. E-Book Review and Description.
Calculus is one of the greatest achievements of the human intellect. Inspired by problems in astronomy, Newton and Leibniz developed the ideas of calculus 300 years ago. Since then, each century has demonstrated the power of calculus to illuminate questions inmathematics, the physical sciences, engineering, and the social and biological sciences.
Calculus has been so successful both because its central theme—change—is pivotal to an analysis of the natural world and because of its extraordinary power to reduce complicated problems to simple procedures. Therein lies the danger in teaching calculus: it is possible to teach the subject as nothing but procedures— thereby losing sight of both the mathematics and of its practical value. This edition of Calculus continues our effort to promote courses in which understanding and computation reinforce each other. It reflects the input of users at research universities, four-year colleges, community colleges, and secondary schools, as well as of professionals in partner disciplines such as engineering and the natural and social sciences. Mathematical Thinking Supported by Theory and Modeling
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The first stage in the development of mathematical thinking is the acquisition of a clear intuitive picture of the central ideas. In the next stage, the student learns to reason with the intuitive ideas in plain English. After this foundation has been laid, there is a choice of direction. All students benefit from both theory and modeling, but the balance may differ for different groups. Some students, such as mathematics majors, may prefer more theory, while others may prefermoremodeling. For instructors wishing to emphasize the connection between calculus and other fields, the text includes:
• A variety of problems from the physical sciences and engineering.
• Examples from the biological sciences and economics.
• Models from the health sciences and of population growth.
• Problems on sustainability.
• Case studies on medicine by David E. Sloane, MD.
Active Learning: Good Problems
As instructors ourselves, we know that interactive classrooms and well-crafted problems promote student learning. Since its inception, the hallmark of our text has been its innovative and engaging problems. These problems probe student understanding in ways often taken for granted. Praised for their creativity and variety, these problems have had influence far beyond the users of our textbook. The Seventh Edition continues this tradition.Under our approach,which we call the “Rule of Four,” ideas are presented graphically, numerically, symbolically, and verbally, thereby encouraging students to deepen their understanding. Graphs and tables in this text are assumed to show all necessary information about the functions they represent, including direction of change, local extrema, and discontinuities.
Problems in this text include:
• Strengthen Your Understanding problems at the end of every section. These problems ask students to reflect on what they have learned by deciding “What is wrong?” with a statement and to “Give an example” of an idea.
• ConcepTests promote active learning in the classroom. These can be used with or without personal response systems (e.g., clickers), and have been shown to dramatically improve student learning. Available in a book or on the web at www.wiley.com/college/hughes-hallett.
• Class Worksheets allow instructors to engage students in individual or group class-work. Samples are available in the Instructor’sManual, and all are on the web at www.wiley.com/college/hughes-hallett.
• Data and Models Many examples and problems throughout the text involve data-driven models. For example, Section 11.7 has a series of problems studying the spread of the chikungunya virus that arrived in the US in 2013. Projects at the end of each chapter of the E-Text (at www.wiley.com/college/hugheshallett) provide opportunities for sustained investigation of real-world situations that can be modeled using calculus.
• Drill Exercises build student skill and confidence.
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We have significantly revised this edition of Thomas’ Calculus to meet the changing needs of today’s instructors and students. The result is a book with more examples, more midlevel exercises, more figures, better conceptual flow, and increased clarity and precision. As with previous editions, this new edition provides a modern introduction to calculus that supports conceptual understanding but retains the essential elements of a traditional course. These enhancements are closely tied to an expanded version for this text of MyMathLab® (discussed further on), providing additional support for students and flexibility for instructors.
Many of our students were exposed to the terminology and computational aspects of calculus during high school. Despite this familiarity, students’ algebra and trigonometry skills often hinder their success in the college calculus sequence. With this text, we have sought to balance the students’ prior experience with calculus with the algebraic skill development they may still need, all without undermining or derailing their confidence. We have taken care to provide enough review material, fully stepped-out solutions, and exercises to support complete understanding for students of all levels.
We encourage students to think beyond memorizing formulas and to generalize concepts as they are introduced. Our hope is that after taking calculus, students will be confident in their problem-solving and reasoning abilities. Mastering a beautiful subject with practical applications to the world is its own reward, but the real gift is the ability to think and generalize. We intend this book to provide support and encouragement for both.
Changes for the Twelfth Edition
CONTENT In preparing this edition we have maintained the basic structure of the Table of Contents from the eleventh edition. Yet we have paid attention to requests by current users and reviewers to postpone the introduction of parametric equations until we present polar coordinates, and to treat 1’H6pital’s Rule after the transcendental functions have been studied. We have made numerous revisions to most of the chapters, detailed as follows.
• Functions We condensed this chapter even more to focus on reviewing function concepts. Prerequisite material covering real numbers, intervals, increments, straight lines, distances, circles, and parabolas is presented in Appendices 1-3.
• Limits To improve the flow of this chapter, we combined the ideas of limits involving infinity and their associations with asymptotes to the graphs of functions, placing them together in the final chapter section.
• Differentiation While we use rates of change and tangents to curves as motivation for studying the limit concept, we now merge the derivative concept into a single chapter. We reorganized and increased the number ofrelated rates examples, and we added new examples and exercises on graphing rational functions.
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• Antiderivatives and Integration We maintain the organization of the eleventh edition in placing antiderivatives as the rmal topic of the chapter covering applications of derivatives. Our focus is on ”recovering a function from its derivative” as the solution to the simplest type offirst-order differential equation. Integrals, as “limits ofRiemann sums,” motivated primarily by the problem of rmding the areas ofgeneral regions with curved boundaries, are a new topic fanning the substance ofChapter 5. After carefully developing the integral concept, we turn our attention to its evaluation and connection to antiderivatives captured in the Fundamental Theorem of Calculus. The ensuing applications then define the various geometric ideas ofarea, volume, lengths ofpaths, and centroids all as limits of Riemann sums giving definite integrals, which can be evaluated by finding an antiderivative ofthe integrand. We return later to the topic of solving more complicated first-order differential equations, after we derme and establish the transcendental functions and their properties.
• Differential Equations Some universities prefer that this subject be treated in a course separate from calculus. Although we do cover solutions to separable differential equations when treating exponential growth and decay applications in the chapter on transcendental functions, we organize the bulk of our material into two chapters (which may be omitted for the calculus sequence). We give an introductory treatment of first-order differential equations in Chapter 9, including a new section on systems and phase planes, with applications to the competitive-hunter and predator-prey models. We present an introduction to second-order differential equations in Chapter 17, which is included in MyMathLab as well as the Thomas’ Calculus Web site, www.pearsonhighered.com/thomas.
• Series We retain the organizational structure and content ofthe eleventh edition for the topics of sequences and series. We have added several new figures and exercises to the various sections, and we revised some of the proofs related to convergence ofpower series in order to improve the accessibility of the material for students. The request stated by one of our users as, “anything you can do to make this material easier for students will be welcomed by our faculty;’ drove our thinking for revisions to this chapter.
• Parametric Equations Several users requested that we move this topic into Chapter II, where we also cover polar coordinates and conic sections. We have done this, realizing that many departments choose to cover these topics at the beginning ofCalculus m, in preparation for their coverage ofvectors and multivariable calculus.
• Vector-Valued Functions We streamlined the topics in this chapter to place more emphasis on the conceptual ideas supporting the later material on partial derivatives, the gradient vector, and line integrals. We condensed the discussions of the Frenet frame and Kepler’s three laws of planetary motion.
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