Calculus 9th Edition

Book Preface

The ninth edition of Calculus is again a modest revision. Some topics have been added, and some of the topics have been rearranged, but the spirit of the book has
remained unchanged. Users of previous editions have reported success, and we have no intention of overhauling a workable text.
To many, this book would still be considered a traditional text. Most theorems are proved, left as an exercise, or left unproved when the proof is too difficult. When a proof is difficult, we try to give an intuitive explanation to make the result plausible before going on to the next topic. In some cases, we give a sketch of a proof, in which case we explain why it is a sketch and not a rigorous proof. The focus is still on understanding the concepts of calculus. While some see the emphasis on clear, rigorous presentation as being a distraction to understanding calculus, we see the two as complementary. Students are more likely to grasp the concepts of calculus if terms are clearly defined and theorems are clearly stated and proved.
A Brief Text The ninth edition continues to be the briefest of all the successful mainstream calculus texts. We have tried to prevent the text from ballooning up
ward with new topics and alternative approaches. In less than BOO pages, we cover the major topics of calculus, including a preliminary chapter, and the material from limits to vector calculus. In the last few decades, students have developed some bad habits. They prefer not to read the textbook. They want to find the appropriate worked-out example so it can be matched to their homework problem. Our goal with this text continues to be to keep calculus as a course focused on some few basic ideas centered around words, formulas, and graphs. Solving problem sets, while crucial to developing mathematical and problem-solving skills, should not overshadow the goal of understanding calculus.
Concepts Review Problems To encourage students to read the textbook with understanding, we begin every problem set with four fill-in-the-blank items
These test the mastery of the basic vocabulary, understanding of theorems, and ability to apply the concepts in the simplest settings. Students should respond to these items before proceeding to the later problems. We encourage this by giving immediate feedback; the correct answers are given at the end of the problem set. These items also make good quiz questions to see whether students have done the required reading and have prepared for class.
Review and Preview Problems We have also included a set of Review and Preview Problems between the end of one chapter and the beginning of the next.
Many of these problems force students to review past topics before starting the new chapter. For example,
” Chapter 3, Applications of Derivatives: Students are asked to solve inequalities like the ones that arise when we ask where a function is increasingl decreasing or concave up/down.
” Chapter 7,Techniques of Integration: Students are asked to evaluate a number of integrals involving the method of substitution, the only substantive technique they have learned up to this point. Lacking skill using this technique would spell disaster in Chapter 7.
” Chapter 13, Multiple Integration: Students are asked to sketch the graphs of equations in Cartesian, cylindrical, and spherical coordinates. Visualizing regions in two- and three-space is key to understanding multiple integration.
Other Review and Preview Problems ask the student to use what they already know to get a head start on the upcoming chapter.