Elementary Calculus: An Infinitesimal Approach (Dover Books on Mathematics)

Book Details:

• Author: H. Jerome Keisler

• Publisher: Dover

• Edition: 3rd ed.

• Binding: Paperback

• Format: Illustrated

• Pages: 1008

• Release Date: 18-01-2012

• ISBN: 9780486484525

• Dimensions: 9.4 x 6.6 x 2.2 inches

• Language: English

About The Book:

Elementary Calculus: An Infinitesimal Approach by H. Jerome Keisler offers an innovative approach to the foundational concepts of calculus. The book is built around the use of infinitesimals — a method largely overlooked in traditional calculus courses due to its lack of rigor. By reintroducing infinitesimals, the author seeks to provide a more intuitive understanding of key concepts like derivatives and integrals.

In the first chapters, the focus is on quickly developing core ideas using infinitesimals to approach derivatives, continuity, and integrals. Later chapters introduce the traditional limit concept and expand into more advanced topics like transcendental functions, series, vectors, partial derivatives, and multiple integrals. Despite the departure from traditional calculus theory, the book uses standard notation and practical problem-solving techniques that align with the conventional methods.

With an emphasis on both intuitive understanding and rigorous application, this book provides a fresh perspective on calculus, making it ideal for students in fields like natural and social sciences, as well as those looking to grasp the essential tools for scientific and engineering applications.