Essential Calculus: Early Transcendental Functions

Book Preface

A Streamlined Text

In recent years, we have heard from some users, reviewers, and colleagues that calculus books are too long and too expensive. To address these concerns, we developed a streamlined version of our calculus text. In doing so, it was important not to compromise our core philosophies: (1) to write a precise, readable book for students with the basic rules and concepts clearly defined and demonstrated; and (2) to design a comprehensive teaching instrument that employs proven pedagogical techniques, freeing the instructor to make the most efficient use of classroom time. To write Essential Calculus: Early Transcendental Functions, we asked our readers: Exactly what are the essential topics for a three-semester calculus sequence? The resulting textbook is approximately the size of our mainstream text. The structure and coverage of the topics enable a faster-paced course to cover the material in a mathematically sound, thorough, and rigorous manner.

While developing the streamlined text, we recognized that some instructors and their students may need additional practice problems or reference materials, so we moved the following material from the text to the website college.hmco.com/pic/larson/EC:
• Material on differential equations
• Material on conics
• Section projects
• PS Problem Solving Exercises
• Chapter overview application and graphics
• Index of Applications

A Text Formed by Its Users
Much has changed since we began writing calculus textbooks in 1973—over 30 years ago. With each edition we have listened to our users, colleagues, and students and incorporated many of your suggestions for improvement. Through your support and suggestions, versions of this text have evolved over the years to include these extensive enhancements:
• Comprehensive exercise sets with a wide variety of problems such as skill-building exercises, applications, explorations, writing exercises, critical thinking exercises, theoretical problems, and problems from the Putnam Exam
• Comprehensive and mathematically rigorous text
• Abundant, real-life applications (many with real data) that accurately represet the diverse uses of calculus
• Open-ended activities and investigations that help students develop an understanding of mathematical concepts intuitively
• Clear, uncluttered text presentation with full annotations and labels and a carefully planned page layout that is designed for maximum readability
• Comprehensive, four-color art program
• Technology used throughout as both a problem-solving and an investigative tool
• Comprehensive program of additional resources available in print and online
• With 9 different volumes of the text available, you can choose the sequence, amount of content, and teaching approach that is best for you and your students.
• References to the history of calculus and to the mathematicians who developed it
• References to over 50 articles from mathematical journals available at www.MathArticles.com
• Worked out solutions to the odd-numbered text exercises provided in the printed
Student Study and Solutions Guide, in Eduspace, and at www.CalcChat.com Although we streamlined the text to create Essential Calculus: Early Transcendental Functions, we did not change many of the things our colleagues and the over two million students who have used other versions of the texts have told us work for them. We hope you will enjoy this text. We welcome any comments, as well as suggestions for continued improvements.

Ron Larson Robert Hostetler Bruce H. Edwards