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1. Derivatives 2. Optimization 3. Integrals 4. Definite Integrals 5. Exponent and Logarithm Functions
"Yet Another Calculus Text" by Dan Sloughter offers a fresh and intuitive approach to learning "calculus" using the concept of "infinitesimals". Unlike traditional textbooks that focus heavily on limits, this book introduces infinitesimals—extremely small quantities—to help students understand derivatives, integrals, and rates of change in a more natural way. This approach simplifies complex ideas and supports a deeper grasp of fundamental calculus concepts. The book is designed for learners with some basic background in algebra and trigonometry, but it doesn’t require advanced math knowledge. Sloughter carefully guides readers through key topics such as optimization, the fundamental theorem of calculus, and practical applications. Its clear explanations and structured lessons make it ideal for self-study or supplemental course material. Available as an open-access resource under a Creative Commons license, "Yet Another Calculus Text" is freely accessible to students and educators. Dan Sloughter’s work is valued for making calculus concepts more approachable through the use of the "hyperreal number system" and an emphasis on conceptual understanding. This book is a great choice for anyone seeking an alternative, modern introduction to calculus.
Title: Yet Another Calculus Text: A Short Introduction with Infinitesimals by Dan Sloughter Publisher: Orange Grove Texts Plus, eBook (Furman University; Creative Commons Licensed) Year: 2007 Pages: 147 Type: PDF Language: English ISBN-10 #: 1616100893 ISBN-13 #: 978-1616100896 License: CC BY 4.0 Amazon: Amazon
The author Dan Sloughter is a dedicated math educator at Schoolcraft College, Michigan. With degrees in mathematics and engineering from top universities, he focuses on creating "open educational resources" to make learning accessible. Corral emphasizes "clear mathematical exposition" in his work, using innovative concepts like "infinitesimals" to help students better understand calculus.
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