Preface

Customization

Calculus Volume 1 is licensed under a Creative Commons Attribution 4.0 International (CC BY) license, which means that you can distribute, remix, and build upon the content, as long as you provide attribution to OpenStax and its content contributors.

Because our books are openly licensed, you are free to use the entire book or pick and choose the sections that are most relevant to the needs of your course. Feel free to remix the content by assigning your students certain chapters and sections in your syllabus, in the order that you prefer. You can even provide a direct link in your syllabus to the sections in the web view of your book.

Faculty also have the option of creating a customized version of their OpenStax book through the aerSelect platform. The custom version can be made available to students in low-cost print or digital form through their campus bookstore. Visit your book page on openstax.org for a link to your book on aerSelect.

Errata

All OpenStax textbooks undergo a rigorous review process. However, like any professional-grade textbook, errors sometimes occur. Since our books are web based, we can make updates periodically when deemed pedagogically necessary. If you have a correction to suggest, submit it through the link on your book page on openstax.org. Subject matter experts review all errata suggestions. OpenStax is committed to remaining transparent about all updates, so you will also find a list of past errata changes on your book page on openstax.org.

Format

You can access this textbook for free in web view or PDF through openstax.org, and for a low cost in print.

Coverage and Scope

Our Calculus Volume 1 textbook adheres to the scope and sequence of most general calculus courses nationwide. We have worked to make calculus interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. With this objective in mind, the content of the three volumes of Calculus have been developed and arranged to provide a logical progression from fundamental to more advanced concepts, building upon what students have already learned and emphasizing connections between topics and between theory and applications. The goal of each section is to enable students not just to recognize concepts, but work with them in ways that will be useful in later courses and future careers. The organization and pedagogical features were developed and vetted with feedback from mathematics educators dedicated to the project.

Pedagogical Foundation

Throughout Calculus Volume 1 you will find examples and exercises that present classical ideas and techniques as well as modern applications and methods. Derivations and explanations are based on years of classroom experience on the part of long-time calculus professors, striving for a balance of clarity and rigor that has proven successful with their students. Motivational applications cover important topics in probability, biology, ecology, business, and economics, as well as areas of physics, chemistry, engineering, and computer science. Student Projects in each chapter give students opportunities to explore interesting sidelights in pure and applied mathematics, from determining a safe distance between the grandstand and the track at a Formula One racetrack, to calculating the center of mass of the Grand Canyon Skywalk or the terminal speed of a skydiver. Chapter Opening Applications pose problems that are solved later in the chapter, using the ideas covered in that chapter. Problems include the hydraulic force against the Hoover Dam, and the comparison of relative intensity of two earthquakes. Definitions, Rules, and Theorems are highlighted throughout the text, including over 60 Proofs of theorems.

Assessments That Reinforce Key Concepts

In-chapter Examples walk students through problems by posing a question, stepping out a solution, and then asking students to practice the skill with a “Checkpoint” question. The book also includes assessments at the end of each chapter so students can apply what they’ve learned through practice problems. Many exercises are marked with a [T] to indicate they are suitable for solution by technology, including calculators or Computer Algebra Systems (CAS). Answers for selected exercises are available in the Answer Key at the back of the book. The book also includes assessments at the end of each chapter so students can apply what they’ve learned through practice problems.

Early or Late Transcendentals

Calculus Volume 1 is designed to accommodate both Early and Late Transcendental approaches to calculus. Exponential and logarithmic functions are introduced informally in Chapter 1 and presented in more rigorous terms in Chapter 6. Differentiation and integration of these functions is covered in Chapters 3–5 for instructors who want to include them with other types of functions. These discussions, however, are in separate sections that can be skipped for instructors who prefer to wait until the integral definitions are given before teaching the calculus derivations of exponentials and logarithms.

Comprehensive Art Program

Our art program is designed to enhance students’ understanding of concepts through clear and effective illustrations, diagrams, and photographs.

Student and Instructor Resources

We’ve compiled additional resources for both students and instructors, including Getting Started Guides, an instructor solution manual, and PowerPoint slides. Instructor resources require a verified instructor account, which can be requested on your openstax.org log-in. Take advantage of these resources to supplement your OpenStax book.

Partner Resources

OpenStax Partners are our allies in the mission to make high-quality learning materials affordable and accessible to students and instructors everywhere. Their tools integrate seamlessly with our OpenStax titles at a low cost. To access the partner resources for your text, visit your book page on openstax.org.

Reviewers

Marwan A. Abu-Sawwa, Florida State College at Jacksonville

Kenneth J. Bernard, Virginia State University

John Beyers, University of Maryland

Charles Buehrle, Franklin & Marshall College

Matthew Cathey, Wofford College

Michael Cohen, Hofstra University

William DeSalazar, Broward County School System

Murray Eisenberg, University of Massachusetts Amherst

Kristyanna Erickson, Cecil College

Tiernan Fogarty, Oregon Institute of Technology

David French, Tidewater Community College

Marilyn Gloyer, Virginia Commonwealth University

Shawna Haider, Salt Lake Community College

Lance Hemlow, Raritan Valley Community College

Jerry Jared, The Blue Ridge School

Peter Jipsen, Chapman University

David Johnson, Lehigh University

M.R. Khadivi, Jackson State University

Robert J. Krueger, Concordia University

Tor A. Kwembe, Jackson State University

Jean-Marie Magnier, Springfield Technical Community College

Cheryl Chute Miller, SUNY Potsdam

Bagisa Mukherjee, Penn State University, Worthington Scranton Campus

Kasso Okoudjou, University of Maryland College Park

Peter Olszewski, Penn State Erie, The Behrend College

Steven Purtee, Valencia College

Alice Ramos, Bethel College

Doug Shaw, University of Northern Iowa

Hussain Elalaoui-Talibi, Tuskegee University

Jeffrey Taub, Maine Maritime Academy

William Thistleton, SUNY Polytechnic Institute

A. David Trubatch, Montclair State University

Carmen Wright, Jackson State University

Zhenbu Zhang, Jackson State University