2
Preface
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 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
Volume 3
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 AnswerKey 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.
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
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