Infinitesimal Calculus (Dover Books on Mathematics)

Book Details

• Publisher: Dover

• Author: James M. Henle

• Language: English

• Edition: 1979 Edition

• ISBN: 9780486428864

• Pages: 144

• Cover: Paperback

• Dimensions: 9.1 x 6.3 x 0.7 inches

• Weight: [Not Provided]

About the Book

Introduction to Calculus Using Infinitesimals by James M. Henle offers a rigorous undergraduate treatment of calculus, focusing on theory rather than application. Aimed at students with a solid foundation in high school mathematics, this book introduces the concept of calculus through the lens of infinitesimals, a fundamental approach that is often overlooked in traditional calculus texts.

The contents of the book are carefully structured to build a solid understanding of both differential and integral calculus. Key topics include the language and structure of calculus, the theory behind hyperreal numbers and the hyperreal line, continuous functions, infinite sequences and series, and infinite polynomials. Henle also explores the topology of the real line and discusses the fundamental theorem of calculus in depth.

With numerous black-and-white illustrations and a wealth of figures, this book offers a visual and conceptual understanding of the material. Its theoretical approach provides students with a deeper insight into the foundations of calculus, beyond the typical computational focus found in most introductory texts.

This edition remains a valuable resource for those who seek a more formal and theoretical introduction to calculus, making it an indispensable addition to any student's collection in the field of mathematics.