Calculus of Variation by Gilbert Ames Bliss
Calculus of Variation - Table of Contents
- 1. Typical Problems of the Calculus of Variations
- 2. Shortest Distances and shortest distance between two points
- 3. The Brachistochrone Problem and brachistochrone curve derivation
- 4. Surfaces of Revolution of Minimum Area and catenary minimal surface of revolution
- 5. A More General Theory of general variational field theory
What You Will Learn in Calculus of Variation
Calculus of Variations by Gilbert Ames Bliss is a fundamental Carus Mathematical Monograph that provides a lucid and rigorous introduction to the analytical foundations of variational problems. Written by one of the leading pioneers of the Chicago school of analysis, this volume systematically develops the core principles required to optimize real-valued integrals, offering a clear treatment of first and second variations, the Euler-Lagrange equation, Legendre's condition, Jacobi's conjugate points, and the Weierstrass E-function.
Tailored for undergraduate mathematics majors, graduate researchers, and theoretical physicists, Prof. Bliss connects classic geometric formulations—such as the shortest distance between points, the brachistochrone, and surface of revolution problems—with general theoretical frameworks. Readers are guided step-by-step through field construction, Hilbert's invariant integral, variable endpoints, and the problem of Lagrange.
Prized for its elegance, structural clarity, and historical significance, it stands as one of the best introductory calculus of variations textbooks pdf available for foundational study. It systematically equips students with essential analytical tools for mastering classical variational mechanics with confidence.
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
(1876–1951) was an eminent American mathematician and long-time Chairman of the Department of Mathematics at the University of Chicago.
A former President of the American Mathematical Society, Prof. Bliss was an internationally recognized authority on the calculus of variations, differential equations, and algebraic functions, guiding dozens of distinguished doctoral students throughout his career.
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