Achieving Infinite Resolution: A Gentle Look at the Role of Infinity in Calculus

Achieving Infinite Resolution is a book on infinity, one of the most profound yet illusive ideas in the history of human intellectual thought. It is written by a 35-year veteran of mathematics teaching and research who uses an intuitive approach to presenting mathematical ideas that relies extensively on illustrations, analogies, examples and thought experiments in order to explain important, complex ideas. Equations are not avoided but their use is minimized.The pace of the book is leisurely and its emphasis is on explaining rather than lecturing or training. Its aim is to give a precise descripton of the concept of inifnite resolution, or limit, using converging infinite sequences as tools to "zoom in" on infinitesimal quantities. A finite analogy is the way a microscope resolves tiny features of material objects. With the sequence-based approach it is possible to define and explain all the basic ideas of calculus (derivatives, integrals, infinite series, etc) in an efficient and intuitive manner that makes the essential role of infinity in these ideas crystal clear.This book is intended primarily for non-mathematicians: scientists, engineers, philosophers and others curious about infinity who have had exposure to typical freshman year college mathematics. It aims to offer the public a source where a precise understanding of infinity and its ramifications can be gained at low cost and without having to take a junior level college course in advanced calculus or real analysis. As a text supplement or as independent reading, it may also help resourceful mathematics students spice up their often cut-and-dry training with interesting facts and connections that are often overlooked in textbooks.