Elementary Calculus by H. Jerome Keisler
Elementary Calculus - Table of Contents
1. Real and Hyperreal Numbers
2. Differentiation
3. Continuous Functions
4. Integrals
5. Limits, Analytic Geometry, and Approximations
6. Applications of the Integral
7. Trigonometric Functions
8. Exponential and Logarithmic Functions
9. Infinite Series
10. Vectors
11. Partial Differentiation
12. Multiple Integrals
13. Vector Calculus
14. Differential Equations
15. Appendices and Addenda
What You Will Learn in Elementary Calculus
"Elementary Calculus: An Approach Using Infinitesimals" by H. Jerome Keisler introduces "calculus" through the intuitive use of "infinitesimals" and "hyperreal numbers". This approach allows students to understand fundamental concepts like "derivatives" and "integration" directly, reflecting the historical ideas behind calculus while maintaining rigorous mathematical validity. The book provides a clear, accessible foundation for beginners and those exploring alternative methods of learning calculus.
Keisler’s text begins with the basics of continuity, derivatives, and integrals using infinitesimals, making abstract concepts more tangible. It gradually introduces the traditional "limit" definitions, and extends the curriculum to include series, transcendental functions, vectors, partial derivatives, and multiple integrals. By combining intuitive reasoning with standard methods, the book ensures that learners gain both conceptual understanding and practical problem-solving skills.
Ideal for undergraduates, independent learners, and instructors, the text encourages exploration and curiosity in calculus. Its unique use of infinitesimals helps students build confidence while reinforcing rigorous thinking. "Elementary Calculus: An Approach Using Infinitesimals" equips readers with the tools to master fundamental calculus topics, bridging the gap between intuitive understanding and formal mathematical analysis, and providing a strong foundation for further studies in mathematics, physics, and engineering.
Book Details & Specifications
Title:
Elementary Calculus by H. Jerome Keisler
Publisher:
Bodgen & Quigley
Year:
2012
Pages:
992
Type:
PDF
Language:
English
ISBN-10 #:
0486484521
ISBN-13 #:
978-0486484525
License:
CC BY-NC-SA 3.0
Amazon:
Amazon
About the Author: Howard Jerome Keisler
The author
Howard Jerome Keisler
is an American mathematician and professor emeritus at the "University of Wisconsin–Madison", renowned for his work in "Nonstandard Analysis" and mathematical logic. He studied under Alfred Tarski and has advanced rigorous approaches to calculus using infinitesimals. His book "Elementary Calculus: An Approach Using Infinitesimals" presents "Infinitesimal Calculus" in a clear, intuitive, and rigorous way. By offering an alternative to traditional epsilon-delta methods, it emphasizes "Mathematical Foundations" and logical reasoning.
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