This is a textbook on limits in calculus, written in tutorial style. Numerous examples are worked out in detail, step-by-step, and fully explained in plain language. These step-by-step examples are accompanied by descriptions of the thinking process that are meant to demystify what is typically a very challenging process for first-year university students.
Limits are typically covered in a couple of weeks in a university calculus course, and this is usually not enough time for students to get a good understanding of this foundational concept. This book helps high-school students develop a thorough understanding of limits, which will be a great preparation for university calculus courses.
This book is suitable for a high-school student who doesn’t yet know anything about calculus, and would like to prepare for university calculus courses. University students needing more detailed explanations than are typically found in their first-year calculus courses may also benefit from reading this book. A strong foundation in high-school algebra and functions is assumed; working through the book will definitely improve your high-school algebra skills! The book takes students from zero knowledge of limits all the way up to a facility with using the precise definition of limit.
Download the 279-page pdf file (1.5 MB) here:
Limits in Calculus: A Tutorial Introduction
(originally posted on 26 August 2024; a revised version with only minor changes to the preface was posted on 14 October 2024)