Theory of Functions of Real Variables 2 by James Pierpont
Theory of Functions of Real Variables 2 - Table of Contents
17. Point Sets and Proper Integrals
18. Improper Multiple Integrals
19. Series
20. Multiple Series
21. Series of Functions
22. Power Series
23. Infinite Products
24. Sets (instead of “Aggregates”)
25. Ordinal Numbers
26. Point Sets (Further Development)
27. Measure
28. Lebesgue Integrals
29. Fourier Series (modern spelling)
30. Discontinuous Functions
31. Derivatives, Extrema, Variation
32. Sub- and Infra-Uniform Convergence
33. Geometric Notions
What You Will Learn in Theory of Functions of Real Variables 2
"James Pierpont’s Theory of Functions of Real Variables, Vol. 2" is a continuation of his foundational work in real analysis. Building on the first volume, it explores advanced topics such as "series", convergence, and the deeper properties of functions of a real variable. Pierpont’s structured approach makes complex concepts accessible while maintaining rigorous mathematical standards.
The book provides detailed treatment of infinite sequences and series, emphasizing conditions for convergence and divergence. Topics like uniform convergence, continuity, and differentiability are carefully explained, showing how series of functions behave under different operations. Integration is also explored in greater depth, highlighting methods, applications, and the connections between integration and series. Students gain a solid understanding of function behavior in more advanced contexts, making it a key text for serious study in "real analysis".
Volume 2 remains influential for its clarity, rigor, and systematic approach. Pierpont’s explanations help readers develop precise mathematical reasoning while exploring the intricacies of real-variable functions. With a focus on "mathematical rigor", "function theory", and series convergence, this volume continues to be a valuable resource for students, teachers, and anyone seeking a deeper understanding of real-variable mathematics.
Book Details & Specifications
Title:
Theory of Functions of Real Variables 2 by James Pierpont
Publisher:
Ginn
Year:
1905
Pages:
668
Type:
PDF
Language:
English
ISBN-10 #:
1164080067
ISBN-13 #:
978-1164080060
License:
Public Domain Work
Amazon:
Amazon
About the Author: James Pierpont
The author James Pierpont
(1866–1938) was an influential American mathematician and Yale professor known for his work in "real analysis", "function theory", and rigorous mathematical education. He helped introduce European-style precision and structure to American mathematics. Pierpont’s two-volume "Theory of Functions of Real Variables" reflects his clear, systematic approach. Volume 2 builds on foundational concepts from Volume 1, covering advanced topics like series, convergence, and integration. His focus on "mathematical rigor", clarity, and detailed explanations has made his work a lasting reference for students, educators, and anyone studying real-variable functions.
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