The Fractional Calculus: Theory and Applications by Keith B. Oldham and Jerome Spanier
The Fractional Calculus: Theory and Applications - Table of Contents
- 1. Introduction
- 2. Differentiation and Integration
- 3. Fractional Derivatives and Integral Definitions and Equivalences
- 4. Differintegration of Simple Functions
- 5. General Properties
- 6. Differintegration of More Complex Functions
- 7. Semiderivatives and Semiintegrals
- 8. Techniques in the Fractional Calculus
- 9. Representation of Transcendental Functions
- 10. Applications in the Classical Calculus
- 11. Applications to Diffusion Problems
What You Will Learn in The Fractional Calculus: Theory and Applications
The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order by Keith B. Oldham and Jerome Spanier stands as a comprehensive, historically significant introduction to the specialized field of fractional calculus. This seminal textbook extends the traditional boundaries of standard derivatives and integrals into arbitrary, non-integer orders. This authoritative volume is uniquely ideal for advanced undergraduate students, graduate-level researchers, and applied mathematicians seeking a much deeper conceptual understanding of this profound mathematical area and its broad, rapidly expanding range of academic applications.
The authors carefully and systematically explain the underlying mathematical theory behind advanced differintegral operators, providing exceptionally detailed discussions on semiderivatives, semiintegrals, fractional differential equations, and complex transcendental functions. Throughout the text, the authors masterfully balance rigorous mathematical proofs with clear, practical examples, demonstrating exactly how a verified the fractional calculus oldham spanier pdf edition can be utilized to model highly complex physical phenomena within theoretical physics, chemical engineering, and modern material sciences.
Divided logically into two distinct pedagogical parts, the comprehensive text first masterfully covers foundational non-integer calculus concepts and then explores real-world applied sciences, such as anomalous diffusion problems, transport theory, and classical calculus extensions. Oldham and Spanier’s exceptionally clear writing style, combined with their highly structured mathematical approach, makes traditionally difficult topics fully accessible. For global academics seeking a trusted oldham spanier fractional calculus free download resource, this landmark publication remains an invaluable, highly cited asset for mathematicians, engineers, and scientists interested in innovative mathematical modeling.
Book Details & Specifications
Title:
The Fractional Calculus: Theory and Applications by Keith B. Oldham and Jerome Spanier
Publisher:
Dover Publications
Year:
1974
Pages:
234
Type:
PDF
Language:
English
ISBN-10 #:
0486450015
ISBN-13 #:
978-0486450018
License:
CC PDM 1.0
Amazon:
Amazon
About the Author: Keith B. Oldham
The author Keith B. Oldham
is an acclaimed chemistry professor at Trent University, specializing in the field of fractional calculus and its practical applications in modeling highly complex systems. Throughout his career, his innovative research has successfully bridged advanced abstract mathematical theory with hands-on practical use across multiple branches of physical science and chemistry. His deep insights into how non-integer calculus can explain real-world electrochemistry problems allowed him to introduce groundbreaking analytical perspectives to modern science.
Jerome Spanier was a distinguished mathematician at the University of California, Irvine, widely known for his immense academic contributions to the differentiation and integration of arbitrary order. Together, their historic collaboration led to co-authoring the definitive textbook, and accessing this foundational the fractional calculus oldham spanier pdf work highlights how they systematically synthesized advanced arbitrary order calculus concepts. Their joint effort created a key mathematical resource that continues to guide and inspire scientists, engineers, and applied researchers globally.
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