Theory of Functions of Real Variables Volume 1 by James Pierpont
Theory of Functions of Real Variables 1 - Table of Contents
1. Rational Numbers
2. Irrational Numbers
3. Exponentials and Logarithms
4. The Elementary Functions; Notion of a Function in General
5. First Notions Concerning Point Sets
6. Limits of Functions
7. Continuity and Discontinuity of Functions
8. Differentiation
9. Implicit Functions
10. Indeterminate Forms
11. Maxima and Minima
12. Integration
13. Proper Integrals
14. Improper Integrals, Integrand Infinite
15. Improper Integrals, Interval of Integration Infinite
16. Multiple Proper Integrals
What You Will Learn in Theory of Functions of Real Variables 1
"Theory of Functions of Real Variables, Vol. I" by "James Pierpont" is a classic work that helped shape early modern real analysis. Written in the early 1900s, the book focuses on building mathematics from rigorous "foundations", introducing readers to precise definitions and logical structure. It reflects the shift from intuitive calculus to a more formal, set-theoretic approach that was transforming mathematical thinking at the time.
Pierpont begins with the basics of sets, functions, and the construction of real numbers, leading into core topics such as limits, continuity, and differentiation. His explanations are detailed and historically grounded, often connecting new ideas with the mathematical developments of his era. The text also explores early forms of measure and integration, especially the Jordan approach, offering a window into analysis before the full adoption of Lebesgue theory.
Though dense by today’s standards, the book remains valuable for understanding the evolution of real analysis. It is best suited for readers interested in mathematical history or the development of rigorous analysis. Pierpont’s careful attention to logical structure and early "measure" concepts makes the work both informative and culturally significant in the progression of mathematical thought.
Book Details & Specifications
Title:
Theory of Functions of Real Variables Volume 1 by James Pierpont
Publisher:
Ginn & Co
Year:
1905
Pages:
584
Type:
PDF
Language:
English
ISBN-10 #:
1429703156
ISBN-13 #:
978-1429703154
License:
Public Domain Work
Amazon:
Amazon
About the Author: James Pierpont
The author James Pierpont
was an American mathematician known for helping bring rigorous European-style analysis to the United States. As a professor at Yale, he focused on real and complex analysis and played a major role in shaping early American mathematical education. His book "Theory of Functions of Real Variables, Vol. 1" became one of the first comprehensive English texts on real analysis. It introduced limits, continuity, integration, and measurable sets with clear structure and precision, influencing generations of students. "Real analysis", "mathematical rigor", and "function theory" remain the core themes associated with his work.
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