Foundations of Infinitesimal Calculus by K.D. Stroyan
Foundations of Infinitesimal Calculus - Table of Contents
- PART 1: NUMBERS AND FUNCTIONS
- 1. Numbers
- 2. Functional Identities
- PART 2: LIMITS
- 3. The Theory of Limits
- 4. Continuous Functions
- PART 3: VARIABLE DIFFERENTIATION
- 5. The Theory of Derivatives
- 6. Pointwise Derivatives
- 7. The Mean Value Theorem
- 8. Higher Order Derivatives
- PART 4: INTEGRATION
- 9. Basic Theory of the Definite Integral
- PART 5: MULTIVARIABLE DIFFERENTIATION
- 10. Derivatives of Multivariable Functions
- PART 6: DIFFERENTIAL EQUATIONS
- 11. Theory of Initial Value Problems
- PART 7: INFINITE SERIES
- 12. The Theory of Power Series
- 13. The Theory of Fourier Series
What You Will Learn in Foundations of Infinitesimal Calculus
Foundations of Infinitesimal Calculus by K.D. Stroyan is an acclaimed modern treatise designed to provide a mathematically rigorous treatment of calculus via Abraham Robinson’s nonstandard analysis. Engineered specifically for advanced undergraduates, this comprehensive volume serves as an exceptional resource for infinitesimal calculus hyperreal continuous analysis practice.
The monograph systematically explores hyperreal numbers, extensions of functions, continuity, derivatives, differential forms, integration, and infinite sequences. By replacing complex epsilon-delta limits with intuitive algebraic operations on infinitesimals, Stroyan enables readers to execute fundamental nonstandard mathematical analysis proofs with complete logical confidence.
Praised by university mathematicians for its formal precision and clear pedagogical progression, this open educational text remains an invaluable manual for self-directed study. Stroyan’s practical methodology equips real analysis scholars with the exact analytical tools required for mastering modern infinitesimal differential calculus foundations across technical mathematical domains.
Book Details & Specifications
Title:
Foundations of Infinitesimal Calculus by K.D. Stroyan
Publisher:
University of Iowa
Year:
1997
Pages:
182
Type:
PDF
Language:
English
ISBN-10 #:
0126741506
ISBN-13 #:
978-0126741506
License:
University Educational Resource
Amazon:
Amazon
About the Author: Keith Duncan Stroyan
The author Keith Duncan Stroyan
is Professor Emeritus of Mathematics at the University of Iowa. A distinguished researcher in mathematical analysis and logic, he is widely recognized for his pioneering contributions to nonstandard analysis and technology-enhanced calculus education.
Throughout his academic career, Professor Stroyan authored several influential textbooks and digital resources. His dedicated work stands as a cornerstone reference for university educators seeking accessible nonstandard infinitesimal analysis study materials.
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