Intuitive introductions present ideas through concrete examples, figures, applications, or analogies. The authors appeal to students’ intuition and geometric instincts to make calculus natural and believable.
Figures are designed to help today’s visually oriented learners. They are:
Conceived to convey important ideas and facilitate learning in new ways.
Annotated to lead students through the key ideas in the figure.
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 a pencil in hand.
Comprehensive exercise sets provide for a variety of student needs and are consistently labeled to enable the creation of homework assignments by inspection.
Review Questions check that students have a general and conceptual understanding of the essential ideas from the section.
Basic Skills exercises are linked to examples in the text 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.
Calculus 1–Section 2.1, The Idea of Limits, provides an intuitive introduction to limits by using two ideas that are featured throughout the semester–slopes of tangent lines and instantaneous velocity. Then the section culminates with a visual summary of the concept in preparation for generalizing the idea of a limit.
Calculus 2–Sequences and Series is the most challenging content in Calculus 2 for students, and the authors have spread the content 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 analyzing 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.
Calculus 3–The clear structure of the Multivariable content makes the material easier for students to follow.
Chapter 11 considers functions with one independent variable and several dependent variables; these are vector-valued functions.
Chapter 12 considers functions with several independent variables and one dependent variable; these are functions of several variables.
Once vector-valued functions and functions of several variables are covered, they are combined in Chapter 13 to get vector-valued functions of several variables, or more simply vector fields.
Guided Projects are available for each chapter, giving step-by-step instruction for carrying out extended calculations (e.g., finding the arc length of an ellipse), deriving physical models (e.g., Kepler’s Laws), or exploring related topics (e.g., numerical integration).
The Instructor’s Resource Guide and Test Bank provides a wealth of instructional resources including Guided Projects, Lecture Support Notes with Key Concepts, Quick Quizzes for each section in the text, Chapter Reviews, Chapter Test Banks, Tips and Help for Interactive Figures, and Student Study Cards.
Interactive Figures included in the ebook enable you and your students to manipulate the figures to bring to life hard-to-convey concepts.
All images used under license from Shutterstock and Getty Images.
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