Thomas’ Calculus: Early Transcendentals, Fifteenth Edition in SI Units, continues its tradition of clarity and precision in calculus with a modern update to the popular text. The authors have worked diligently to add exercises, revise figures and narrative for clarity, and update many applications to modern topics. Thomas’ Calculus remains a modern and robust introduction to calculus, focusing on developing conceptual understanding of the underlying mathematical ideas. This text supports a calculus sequence typically taken by students in STEM fields over several semesters. Intuitive and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets are the foundation of this text. We continue to improve this text in keeping with shifts in both the preparation and the goals of today’s students, and in the applications of calculus to a changing world.

As Advanced Placement Calculus continues to grow in popularity for high school students, many instructors have communicated mixed reviews of the benefit for today’s university and community college students. Some instructors report receiving students with an overconfidence in their computational abilities coupled with underlying gaps in algebra and trigonometry mastery, as well as poor conceptual understanding. In this text, we seek to meet the needs of the increasingly varied population in the calculus sequence. We have taken care to provide enough review material (in the text and appendices), detailed solutions, and a variety of examples and exercises, to support a complete understanding of calculus for students at varying levels. Additionally, the MyLab Math course that accompanies the text provides significant support to meet the needs of all students. Within the text, we present the material in a way that supports the development of mathematical maturity, going beyond memorizing formulas and routine procedures, and we show students how to generalize key concepts once they are introduced. References are made throughout, tying new concepts to related ones that were studied earlier. After studying calculus from Thomas, students will have developed problem-solving and reasoning abilities that will serve them well in many important aspects of their lives. Mastering this beautiful and creative subject, with its many practical applications across so many fields, is its own reward. But the real gifts of studying calculus are acquiring the ability to think logically and precisely; understanding what is defined, what is assumed, and what is deduced; and learning how to generalize conceptually. We intend this book to encourage and support those goals.

Contents

Chapter 1. Functions

Chapter 2. Limits and Continuity

Chapter 3. Derivatives

Chapter 4. Applications of Derivatives

Chapter 5. Integrals

Chapter 6. Applications of Definite Integrals

Chapter 7. Integrals and Transcendental Functions

Chapter 8. Techniques of Integration

Chapter 9. Infinite Sequences and Series

Chapter 10. Parametric Equations and Polar Coordinates

Chapter 11. Vectors and the Geometry of Space

Chapter 12. Vector-Valued Functions and Motion in Space

Chapter 13. Partial Derivatives

Chapter 14. Multiple Integrals

Chapter 1 5. Integrals and Vector Fields

Chapter 16. First-Order Differential Equations

Chapter 17. Second-Order Differential Equations

Chapter 18. Complex Functions

Chapter 19. Fourier Series and Wavelets