The Theory of Real Variable & Fouriers Series Vol. 1 by E. W. Hobson
Book Contents :-
1. Number
2. Descriptive Properties of Sets of Points
3. The Metric Properties of Sets of Points
4. Transfinite Numbers and Order-Types
5. Functions of a Real Variable
6. The Riemann Integral
7. The Lebesgue Integral
8. Non-Absolutely Convergent Integrals
9. Trigonometric (Fourier) Series
10. Representation of Functions by Fourier Integrals
11. Series of Normal Orthogonal Functions
About this book :-
"The Theory Of Function Of A Real Variable and The Theory Of Fouriers Series Vol. 1" by "E. W. Hobson" is a classical text that provides a rigorous study of "real-variable functions" and the theory of "Fourier series". Hobson begins with the fundamentals of "function theory", exploring continuity, bounded variation, limits, and the properties of sets of points. He develops a careful treatment of integration, particularly Riemann integration, and examines the convergence behavior of sequences and series of functions. This systematic approach builds a strong foundation for understanding both theoretical and applied aspects of real analysis.
The book delves deeply into "Fourier series", presenting criteria for convergence, orthogonality, and representation of periodic functions. Hobson links the behavior of real-variable functions with their harmonic expansions, providing detailed proofs and examples to illustrate concepts. The integration of real analysis with Fourier theory allows readers to understand how functions can be expressed as infinite trigonometric series and how these expansions converge under various conditions.
Historically, Hobson’s work was one of the most comprehensive English-language references on real analysis and Fourier series. It has influenced generations of mathematicians by providing a rigorous, unified treatment of "function theory", convergence, integration, and harmonic analysis. Its clear exposition, logical structure, and depth make it a lasting resource for students and researchers in "mathematical analysis" and applied mathematics.
Book Detail :-
Title:
The Theory of Real Variable & Fouriers Series Vol. 1 by E. W. Hobson
Publisher:
Cambridge University Press
Year:
1927
Pages:
750
Type:
PDF
Language:
English
ISBN-10 #:
054896937X
ISBN-13 #:
978-0548969373
License:
Public Domain Work
Amazon:
Amazon
About Author :-
The author
Ernest William Hobson
(1856–1933) was a British mathematician known for his work in "real analysis" and "function theory". He taught at Cambridge and focused on making advanced topics like convergence, bounded variation, and integration clear and rigorous for students and researchers. Hobson authored influential texts, including "The Theory of Real Variable & Fourier’s Series", which systematically presents "Fourier series" and real-variable functions. His clear exposition and structured approach helped standardize the teaching of real analysis and harmonic analysis, leaving a lasting impact on mathematical education and the development of advanced "function theory".
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