Preface  (Page 2/4)

Cost

Our textbooks are available for free online, and in low-cost print and e-book editions.

About Calculus Volume 1

Calculus Volume 1 is the first of three volumes designed for the two- or three-semester calculus course. For many students, this course provides the foundation to a career in mathematics, science, or engineering. As such, this textbook provides an important opportunity for students to learn the core concepts of calculus and understand how those concepts apply to their lives and the world around them. The text has been developed to meet the scope and sequence of most general calculus courses. At the same time, the book includes several innovative features designed to enhance student learning. A strength of Calculus Volume 1 is that instructors can customize the book, adapting it to the approach that works best in their classroom.

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.

Volume 1

• Chapter 1: Functions and Graphs
• Chapter 2: Limits
• Chapter 3: Derivatives
• Chapter 4: Applications of Derivatives
• Chapter 5: Integration
• Chapter 6: Applications of Integration

Volume 2

• Chapter 1: Integration
• Chapter 2: Applications of Integration
• Chapter 3: Techniques of Integration
• Chapter 4: Introduction to Differential Equations
• Chapter 5: Sequences and Series
• Chapter 6: Power Series
• Chapter 7: Parametric Equations and Polar Coordinates

Volume 3

• Chapter 1: Parametric Equations and Polar Coordinates
• Chapter 2: Vectors in Space
• Chapter 3: Vector-Valued Functions
• Chapter 4: Differentiation of Functions of Several Variables
• Chapter 5: Multiple Integration
• Chapter 6: Vector Calculus
• Chapter 7: Second-Order Differential Equations

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.