Calculus Set Free: Infinitesimals to the Rescue

Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimal methods. The procedures used throughout make many of the calculations simpler and the concepts clearer for undergraduate students, heightening success and easing a significant burden of entry into STEM disciplines.
This text features a student-friendly exposition with ample marginal notes, examples, illustrations, and more. The exercises include a wide range of difficulty levels, stretching from very simple “rapid response” questions to the occasional exercise meant to test knowledge. While some exercises require the use of technology to work through, none are dependent on any specific software. The answers to odd-numbered exercises in the back of the book include both simplified and non-simplified
answers, hints, or alternative answers.
Throughout the text, notes in the margins include comments meant to supplement understanding, sometimes including line-by-line commentary for worked examples. Without sacrificing academic rigor, Calculus Set Free offers an engaging style that helps students to solidify their understanding on difficult theoretical calculus.

Additional ISBNs:

∗ Print ISBN: 0192895605, 978-0192895608, 9780192895608

Contents

Review
1: Hyperreals, Limits, and Continuity
2: Derivatives
3: Applications of the Derivative
4: Integration
5: Transcendental Functions
6: Applications of Integration
7: Techniques of Integration
8: Alternate Representations: Parametric and Polar Curves
9: Additional Applications of Integration
10: Sequences and Series

About the Authors

C. Bryan Dawson has been teaching calculus for three decades and currently holds the title University Professor of Mathematics at Union University in Jackson, Tennessee, USA. Originally trained in functional analysis, in 2013 Dawson began working in nonstandard calculus, developing many of the infinitesimal procedures featured in this book. Dawson and his wife Martha are both enrolled citizens of the Cherokee Nation, the largest federally recognized tribe of Native
Americans. They have three grown children.

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