A Treatise on the Calculus of Variations by Richard Abbatt
A Treatise on the Calculus of Variations - Table of Contents
1. Definitions of a Maximum and Minimum
2. Origin of the Calculus of Variations
3. Definitions of a Differential and Variation
4. Absolute Maxima and Minima
5. Problems of Absolute Maxima and Minima
6. Relative Maxima and Minima
7. When (V) Depends Also Upon Other Integrals
8. To Find the Variation of a Function Which Is Only Given by Means of a Differential Equation
9. On the Variation of Triple, Quadruple, etc., Integrals
What You Will Learn in A Treatise on the Calculus of Variations
"A Treatise on the Calculus of Variations" by Richard Abbatt, is a foundational text in the study of "mathematical analysis" and optimization. The book provides a systematic explanation of the "calculus of variations", the branch of mathematics focused on finding functions that maximize or minimize specific quantities. Abbatt’s work offers a clear and structured approach, introducing both theoretical foundations and classical examples that illustrate practical problem-solving.
Written in the mid-19th century, the treatise reflects the analytical style of its time, bridging earlier geometric reasoning with modern symbolic methods. Abbatt discusses integral functionals and the determination of "extremal curves" and surfaces—concepts that remain central to modern physics, engineering, and applied mathematics. His clear presentation helped make advanced continental mathematical ideas more accessible to English-speaking students and scholars.
Today, the book is valued as a historical reference for those studying the evolution of mathematical thought. Though the language and notation may seem dated, it provides deep insight into the origins of variational methods and optimization theory. Abbatt’s contribution continues to be appreciated for its precision, organization, and influence in shaping how early mathematicians approached calculus and problem-solving.
Book Details & Specifications
Title:
A Treatise on the Calculus of Variations by Richard Abbatt
Publisher:
J. Richardson
Year:
1837
Pages:
225
Type:
PDF
Language:
English
ISBN-10 #:
0266610870
ISBN-13 #:
978-0266610878
License:
Public Domain Work
Amazon:
Amazon
About the Author: Richard Abbatt
The author
Richard Abbatt
(1800–1884) was a British mathematician and "Fellow of the Royal Astronomical Society". He is best known for his influential work, "A Treatise on the Calculus of Variations", published in the early 19th century. Abbatt contributed to advancing "analytical mathematics" in Britain during a time when modern methods were emerging. His treatise helped introduce the "calculus of variations" and "optimization" techniques to English-speaking scholars, bridging the gap between British and continental mathematical traditions.
Read or Downloadable A Treatise on the Calculus of Variations
Free Calculus of Variations Books PDF | Optimization Textbooks