Foundations of Infinitesimal Calculus by H. Jerome Keisler
Foundations of Infinitesimal Calculus - Table of Contents
- 1. Real and Hyperreal Numbers
- 2. Differentiation
- 3. Continuous Functions
- 4. Integration
- 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
What You Will Learn in Foundations of Infinitesimal Calculus
Foundations of Infinitesimal Calculus by Howard Jerome Keisler is a clear and rigorous guide to understanding infinitesimal calculus using the hyperreal numbers. Unlike traditional calculus texts, it presents a logically sound approach to derivatives, integrals, and continuity with infinitesimals, providing an intuitive yet precise framework for advanced learners looking to master modern mathematical analysis.
The book explores core concepts of calculus through the lens of nonstandard analysis, offering an alternative to the standard epsilon-delta approach. Keisler develops the foundations step by step, explaining how infinitely small and large quantities can be used to rigorously define derivatives and integrals. Downloading a comprehensive foundations of infinitesimal calculus pdf reference helps instructors and students restore the intuitive methods originally used by pioneers like Leibniz and Newton, now formalized with mathematical precision.
Ideal for instructors, advanced undergraduates, or anyone studying mathematical analysis, this text bridges the gap between elementary calculus and higher-level theory. It provides exercises and detailed explanations that reinforce conceptual understanding and demonstrate the sheer power of infinitesimal methods. This volume equips readers with both a conceptual and technical grasp of calculus, preparing them to confidently explore further topics in nonstandard analysis.
Book Details & Specifications
Title:
Foundations of Infinitesimal Calculus by H. Jerome Keisler
Publisher:
University of Iowa
Year:
2022
Pages:
213
Type:
PDF
Language:
English
ISBN-10 #:
0871502151
ISBN-13 #:
978-0871502155
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 known for his pioneering work in nonstandard analysis. This foundations of infinitesimal calculus pdf serves as a key reference, introducing students to a unique foundational theory of calculus using infinitesimals.
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