The Theory of Real Variable & Fouriers Series Vol. 2 by E. W. Hobson
The Theory of Real Variable & Fouriers Series Vol. 2 by E. W. Hobson - Table of Contents
1. Sequences and Series of Numbers
2. Functions Defined by Sequences or Series
3. Power Series
4. Functions Representable by Series or Sequences of Continuous Functions
5. Sequences of Integrals
6. The Construction of Functions with Assigned Singularities
7. The Representation of Functions as Limits of Integrals
8. Trigonometric Series
9. The Representation of Functions by Fourier’s Integrals
10. Series of Normal Orthogonal Functions
What You Will Learn in The Theory of Real Variable & Fouriers Series Vol. 2 by E. W. Hobson
The Theory Of Function Of A Real Variable and The Theory Of Fouriers Series, Vol. 2 by E. W. Hobson is a classic mathematical text that expands on the foundations of real analysis introduced in Volume 1. This volume focuses on advanced concepts of real variables, providing rigorous treatments of convergence, integration, and the behavior of functions. Hobson’s clear and systematic approach makes complex ideas accessible to students and researchers, bridging theoretical concepts with practical applications.
A central feature of Vol. 2 is its detailed exploration of Fourier series and orthogonal series. Hobson examines pointwise and uniform convergence, mean-square convergence, and the completeness of function spaces, carefully establishing the conditions under which series accurately represent functions. The book also addresses subtle issues like series rearrangements and integrability, reflecting modern analytic techniques that were emerging in the early 20th century.
Renowned for its depth and clarity, this volume has become an essential reference in the study of mathematical analysis. It continues to influence scholars, mathematicians, and engineers, providing foundational insight into the theory of real variables and Fourier expansions. Hobson’s work remains a bridge between classical analysis and contemporary mathematical rigor, making it a cornerstone in higher mathematics education.
Book Details & Specifications
Title:
The Theory of Real Variable & Fouriers Series Vol. 2 by E. W. Hobson
Publisher:
Cambridge University Press
Year:
1927
Pages:
805
Type:
PDF
Language:
English
ISBN-10 #:
9333495177
ISBN-13 #:
978-9333495172
License:
Public Domain Work
Amazon:
Amazon
About the Author: Ernest William Hobson
The author
Ernest William Hobson
(1856–1933) was a prominent British mathematician renowned for modernizing real analysis in the English-speaking world. Educated at Christ’s College, Cambridge, Hobson was a Senior Wrangler and later became the Sadleirian Professor of Pure Mathematics. His work bridged British mathematics with continental European developments, introducing rigorous concepts like measure theory and integration to students and scholars. Hobson’s influence shaped Cambridge mathematics, moving it from traditional problem-solving toward formal, theoretical approaches. Hobson’s landmark work, The Theory of Functions of a Real Variable and the Theory of Fourier’s Series (Vol. 2), is celebrated for its depth and clarity. The book systematically explores Fourier series, convergence, and orthogonal series, providing one of the first comprehensive treatments in English. Hobson combined detailed proofs with intuitive explanations, making complex ideas accessible while maintaining mathematical rigor. The second volume expanded the material to include advanced topics, reflecting both Hobson’s research and the latest developments in analysis.
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