For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors. This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students’ geometric intuition to introduce fundamental concepts, laying a foundation for the development that follows. The groundbreaking eBook contains over 650 Interactive Figures that can be manipulated to shed light on key concepts.
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1. Functions 2. Limits 3. Derivatives 4. Applications of the Derivative 5. Integration 6. Applications of Integration 7. Integration Techniques 8. Sequences and Infinite Series 9. Power Series 10. Parametric and Polar Curves 11. Vectors and Vector-Valued Functions 12. Functions of Several Variables 13. Multiple Integration 14. Vector Calculus Appendix A. Algebra Review Appendix B. Proofs of Selected Theorems D1. Differential Equations (online) D1.1 Basic Ideas D1.2 Direction Fields and Euler’s Method D1.3 Separable Differential Equations D1.4 Special First-Order Differential Equations D1.5 Modeling with Differential Equations D2. Second-Order Differential Equations (online) D2.1 Basic Ideas D2.2 Linear Homogeneous Equations D2.3 Linear Nonhomogeneous Equations D2.4 Applications D2.5 Complex Forcing Functions
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Reflects how students use a textbook— they generally start with the exercises and flip back to the narrative for help if they need it. Comprehensive exercise sets provide for a variety of student needs and are consistently structured and labeled to facilitate the creation of homework assignments. Review Questions check that students have a general conceptual understanding of the essential ideas from the section.Basic Skills exercises are linked to examples in the section so students get off to a good start with homework.Further Explorations exercises extend students’ abilities beyond the basics.Applications present practical and novel applications and models that use the ideas presented in the section.Additional Exercises challenge students to stretch their understanding by working through abstract exercises and proofs.NEW! 20% more exercises, including more mid-level exercises to enhance the pace of the book and give students more of a computational footing for the exercises that follow.When students flip back to the narrative for help with exercises, they find: Writing that reflects the voice of the instructor.Plentiful examples, each stepped-out in detail. Within examples, the steps are annotated in blue type to help students understand what took place in each step.Figures that are designed to teach rather than simply supplement the narrative. The figures are annotated to lead students through the key ideas, and rendered using the latest software for unmatched clarity and precision.Quick Check exercises punctuate the narrative at key points to test understanding of basic ideas and encourage students to read with pencil in hand. Organisation and presentation facilitates learning of key concepts, skills, and applications. Topics are introduced through concrete examples, geometric arguments, applications, and analogies rather than through abstract arguments. The authors appeal to students’ intuition and geometric instincts to make calculus natural and believable.The 650 Interactive Figures in the eBook provide a resource for instructors to help students visualise concepts where chalk or a marker falls short. The exercises that accompany the figures provide an opportunity for students to manipulate them as part of homework.Sequences and Series, the most challenging content in Calculus 2 for students, has been spread over two chapters to help clarify and pace it more effectively. Chapter 8, Sequences and Infinite Series, begins by providing a big picture with concrete examples of the difference between a sequence and a series followed by studying the properties and limits of sequences in addition to studying special infinite series and convergence tests. This chapter lays the groundwork for analysing the absolute convergence for power series.Chapter 9, Power Series, begins with approximating with polynomials. Power series are introduced as a new way to define functions, building on one series by generating new series using composition, differentiation and integration. Taylor series are then covered and the motivation that precedes the section should make the topic more accessible.The authors chart a clear and uncluttered path through multivariable calculus. They separate cleanly vector-valued functions, functions of several variables, and vector calculus by placing them in separate chapters. This separation avoids common student errors, such as conf
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20% more exercises, including more mid-level exercises to enhance the pace of the book and give students more of a computational footing for the exercises that follow.A thorough, cover-to-cover polishing of the narrative in the second edition makes the presentation of material even more concise and lucid.New topics—several topics that were addressed in Guided Projects in the first edition are now, at the urging of users, included the main text. We now have complete sections with a full complement of exercises on:Newton’s methodSurface area of solids of revolutionHyperbolic functions A new introductory section to the standard chapter on integration techniques.An expanded section on tangent and principal normal vectors for vector curves now includes material on binormal vectors and TNB frames. Online chapters on both first- and second-order differential equations have been added for schools requiring more expansive coverage of the topics. These new chapters can also be produced in printed format. As in the first edition, the second edition contains a single robust survey section on first-order differential equations (section 7.9).More fine-tuning of the content includes:The long introductory section in chapter 3 on derivatives is divided into two more digestible sections.Numerous new applied examples and exercises.Updating of all examples and exercises using real data to the most recent available values.
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Produktdetaljer

ISBN
9781292062310
Publisert
2016-06-17
Utgave
2. utgave
Utgiver
Vendor
Pearson Education Limited
Vekt
2740 gr
Høyde
277 mm
Bredde
216 mm
Dybde
56 mm
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
1320