References are made throughout which tie a new 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 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 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. In this new edition we further blend conceptual thinking with the overall logic and structure of single and multivariable calculus. We continue to improve clarity and precision, taking into account helpful suggestions from readers and users of our previous texts. While keeping a careful eye on length, we have created additional examples throughout the text. Numerous new exercises have been added at all levels of difficulty, but the focus in this revision has been on the mid-level exercises.
A number of figures have been reworked and new ones added to improve visualization. We have written a new section on probability, which provides an important application of integration to the life sciences.
We have maintained the basic structure of the Table of Contents, and retained improvements from the twelfth edition. In keeping with this process, we have added more improvements throughout, which we detail here:.
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. Many examples and exercises apply to the life sciences. Conditional convergence is introduced later on with the Alternating Series Test. Mastering this beautiful and creative subject, with its many practical applications across so many 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. In this new edition we further blend conceptual thinking with the overall logic and structure of single and multivariable calculus.
We continue to improve clarity and precision, taking into account helpful suggestions from readers and users of our previous texts. While keeping a careful eye on length, we have created additional examples throughout the text. Numerous new exercises have been added at all levels of difficulty, but the focus in this revision has been on the mid-level exercises.
A number of figures have been reworked and new ones added to improve visualization. We have written a new section on probability, which provides an important application of integration to the life sciences.
We have maintained the basic structure of the Table of Contents, and retained improvements from the twelfth edition. In keeping with this process, we have added more improvements throughout, which we detail here:. 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. Many examples and exercises apply to the life sciences.
Conditional convergence is introduced later on with the Alternating Series Test. The idea of surface integrals of vector fields now parallels the notion for line integrals of vector fields. We have improved our discussion of the divergence and curl of a vector field.
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