• Most of the pre-calculus material in the previous edition Chapter 0 has been moved to Appendices, and the remaining Chapter 0 material is merged into Chapter 1.
• Some prose in other areas of the text has been tightened to enhance clarity and student understanding.
• New applied exercises have been added to the book and some existing applied exercises have been updated.
Flexibility This edition has a built-in flexibility that is designed to serve a broad spectrum of calculus philosophies-from traditional to "reform." Technology can be emphasized or not, and the order of many topics can be permuted freely to accommodate each instructor's specific needs.
Rigor The challenge of writing a good calculus book is to strike the right balance between rigor and clarity. Our goal is to present precise mathematics to the fullest extent possible in an introductory treatment. Where clarity and rigor conflict, we choose clarity; however, we believe it to be important that the student understand the difference between a careful proof and an informal argument, so we have informed the reader when the arguments being presented are informal or motivational. Theory involving e-o arguments appears in separate sections so that they can be covered or not, as preferred by the instructor.
Rule of Four The "rule of four" refers to presenting concepts from the verbal, algebraic, visual, and numerical points of view. In keeping with current pedagogical philosophy, we used this approach whenever appropriate.
Visualization This edition makes extensive use of modern computer graphics to clarify concepts and to develop the student's ability to visualize mathematical objects, particularly those in 3-space. For those students who are working with graphing technology, there are many exercises that are designed to develop the student's ability to generate and analyze mathematical curves and surfaces.
Quick Check Exercises Each exercise set begins with approximately five exercises (answers included) that are designed to provide students with an immediate assessment of whether they have mastered key ideas from the section. They require a minimum of computation and are answered by filling in the blanks.
Focus on Concepts Exercises Each exercise set contains a clearly identified group of problems that focus on the main ideas of the section.
Technology Exercises Most sections include exercises that are designed to be solved using either a graphing calculator or a computer algebra system such as Mathematica, Maple, or the open source program Sage. These exercises are marked with an icon for easy identification.
Applicability of Calculus One of the primary goals of this text is to link calculus to the real world and the student's own experience. This theme is carried through in the example sand exercises.
Career Preparation This text is written at a mathematical level that will prepare students for a wide variety of careers that require a sound mathematics background, including engineering, the various sciences, and business.
Trigonometry Summary and Review Deficiencies in trigonometry plague many students, so we have included a substantial trigonometry review in Appendices A and J.
Appendix on Polynomial Equations Because many calculus students are weak insolving polynomial equations, we have included an appendix (Appendix H) that reviewsthe Factor Theorem, the Remainder Theorem, and procedures for finding rational roots.
Principles of Integral Evaluation The traditional Techniques of Integration is entitled "Principles of Integral Evaluation" to reflect its more modem approach to the material. The chapter emphasizes general methods and the role of technology rather than specific tricks for evaluating complicated or obscure integrals.
Historical Notes The biograph,ies and historical notes have been a hallmark of this text from its original edition and have been maintained. All of the biographical materials have been distilled from standard sources with the goal of capturing and bringing to life for the student the personalities of history's greatest mathematicians.
Margin Notes and Warnings These appear in the margins throughout the text to clarify or expand on the text exposition or to alert the reader to some pitfall.
1 LIMITS AND CONTINUITY
2 THE DERIVATIVE
3 TOPICS IN DIFFERENTIATION
4 THE DERIVATIVE IN GRAPHING AND APPLICATIONS
6 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY SCIENCE, AND ENGINEERING
7 PRINCIPLES OF INTEGRAL EVALUATION
8 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
9 INFINITE SERIES
10 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS
11 THREE-DIMENSIONAL SPACE; VECTORS
12 VECTOR-VALUED FUNCTIONS
13 PARTIAL DERIVATIVES
14 MULTIPLE INTEGRALS
15 TOPICS IN VECTOR CALCULUS
A TRIGONOMETRY REVIEW (SUMMARY)
B FUNCTIONS (SUMMARY)
C NEW FUNCTIONS FROM OLD (SUMMARY)
D FAMILIES OF FUNCTIONS (SUMMARY)
E INVERSE FUNCTIONS (SUMMARY)
ANSWERS TO ODD-NUMBERED EXERCISES