Calculus of Variation by Gilbert Ames Bliss
Calculus of Variation - Table of Contents
1. Typical Problems of the Calculus of Variations
2. Shortest Distances
3. The Brachistochrone Problem
4. Surfaces of Revolution of Minimum Area
5. A More General Theory
What You Will Learn in Calculus of Variation
"Calculus of Variations" by Gilbert Ames Bliss is a classic mathematical text that introduces the principles of the "calculus of variations", a field focused on finding functions that "optimize" certain quantities. Unlike ordinary calculus, which deals with numbers, this branch of mathematics studies the optimization of functionals, providing a foundation for applications in physics, engineering, and geometry. Bliss presents the subject in a clear and systematic way, making complex concepts accessible to both students and researchers.
The book covers essential topics such as the "Euler–Lagrange equation", which is central to solving variational problems. It also explores conditions for maxima and minima, variational problems with constraints, and functions of multiple variables. Bliss illustrates these ideas with examples from mechanics and geometry, helping readers understand both the theory and practical applications of variational methods.
Renowned for its clarity and rigor, Bliss’s text serves as both an introduction and a reference for anyone studying "optimization" in mathematics and applied sciences. By combining detailed proofs with practical examples, the book remains a foundational resource for understanding the principles, techniques, and real-world applications of the "calculus of variations".
Book Details & Specifications
Title:
Calculus of Variation by Gilbert Ames Bliss
Publisher:
Mathematical Association of America
Year:
1925
Pages:
216
Type:
PDF
Language:
English
ISBN-10 #:
B000TG8J0S
ISBN-13 #:
B000I9562A
License:
Public Domain Work
Amazon:
Amazon
About the Author: Gilbert Ames Bliss
The author Gilbert Ames Bliss
(1874–1951) was an influential American mathematician known for his work in the "calculus of variations". He taught at the University of Chicago and significantly advanced research and education in mathematics, making complex ideas accessible to students and scholars alike. Bliss is best known for his book "Calculus of Variations", which explores the "Euler–Lagrange equation" and methods for "optimization" of functions. His rigorous yet clear approach has made his work a lasting reference in applied mathematics, mechanics, and physics, influencing generations of mathematicians and researchers worldwide.
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