Thomas Calculus Early Transcendentals – 13th Edition provides a modern introduction to calculus that focuses on conceptual understanding in developing the essential elements of a traditional course. This material supports a three-semester or four-quarter calculus sequence typically taken by students in mathematics, engineering, and therefore the natural sciences. 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 ambitions of today’s students, and the applications of calculus to a changing world.
Many of today’s students have been exposed to the terminology and computational methods of calculus in high school. Despite this familiarity, their acquired algebra and trigonometry skills sometimes limit their ability to master calculus at the school level. In this text, we seek to balance students’ prior experience in calculus with the algebraic skill development they’ll still need, without slowing their progress through calculus itself. We have taken care to supply enough review material (in the text and appendices), detailed solutions, and sort of examples and exercises, to support an entire understanding of calculus for students at varying levels.
We present the material to encourage student thinking, going beyond memorizing formulas and routine procedures, and we show students how to generalize key concepts once they are introduced. References are made throughout which tie a replacement concept to a related one that was studied earlier, or to a generalization they will see later on. After studying calculus from Thomas, students will have developed problem solving and reasoning abilities which will serve them well in many important aspects of their lives.
Mastering this beautiful and artistic subject, with its many practical applications across numerous fields of endeavor, is its own reward. But the real gift of studying calculus is acquiring the ability to think logically and factually, and learning how to generalize conceptually. We intend this book to encourage and support those goals.

### Thomas Calculus Early Transcendentals

Table of Content

1. Functions 1
2. Limits and Continuity 59
3. Derivatives 123
4. Applications of Derivatives 223
5. Integrals 299
6. Applications of Definite Integrals 365
7. Integrals and Transcendental Functions 420
8. Techniques of Integration 456
9. First-Order Differential Equations 536
10. Infinite Sequences and Series 572
11. Parametric Equations and Polar Coordinates 653
12. Vectors and the Geometry of Space 704
13. Vector-Valued Functions and Motion in Space 751
14. Partial Derivatives 793
15. Multiple Integrals 882
16. Integrals and Vector Fields 950
17. Second-Order Differential Equations (online)

#### Thomas Calculus Early Transcendentals – 13th Edition

• Functions In discussing the utilization of software for graphing purposes, we added a quick subsection on method of least squares curve fitting, which allows students to require advantage of this widely used and available application. Prerequisite material continues to be reviewed in Appendices 1–3.
• Continuity We clarified the continuity definitions by confining the term “endpoints” to intervals rather than more general domains, and that we moved the subsection on continuous extension of a function to the top of the continuity section.
• Derivatives We included a quick geometric insight justifying l’Hôpital’s Rule. We also enhanced and clarified the meaning of differentiability for functions of several variables, and added a result on the Chain Rule for functions defined along a path.
• Integrals We wrote a replacement section reviewing basic integration formulas and therefore the Substitution Rule, using them together with algebraic and trigonometric identities, before presenting other techniques of integration.
• Probability We created a replacement section applying improper integrals to some commonly used probability distributions, including the exponential and normal distributions.
• Series We now present the thought of absolute convergence before giving the Ratio and Root Tests, then state these tests in their stronger form. Conditional convergence is introduced afterward with the Alternating Series Test.
• Multivariable and Vector Calculus We give more geometric insight into the thought of multiple integrals, and that we enhance the meaning of the Jacobian in using substitutions to evaluate them. the thought of surface integrals of vector fields now parallels the notion for line integrals of vector fields. we’ve improved our discussion of the divergence and curl of a vector field.