INTRODUCTION TO THE CALCULUS OF VARIATIONS

Book Details:

• Publisher: Dover

• Author: Fox, Charles

• Language: English

• Edition: New

• ISBN: 9780486654997

• Pages: 304

• Cover: Paperback

• Dimensions: 8.4 x 6.4 x 0.7 inches

About The Book:

"Variational Methods" by Charles Fox is an essential text for students and researchers interested in the study of mathematical physics and applied mathematics. This highly regarded book provides an in-depth exploration of variational methods, which form the foundation for critical theorems such as the principle of least action and its various generalizations. These principles are pivotal for understanding both the mathematical theory and its application in fields like classical mechanics, quantum mechanics, and elasticity theory.

The text begins with a thorough discussion of the first and second variations of an integral, illustrated through applications of the principle of least action to dynamical problems. In Chapters III and IV, Fox ventures into pure mathematics, addressing generalizations and isoperimetric problems, enriching the theoretical foundation of variational calculus.

The applied mathematics sections (Chapters V to VII) take the reader through essential concepts such as Hamilton's principle, its role in dynamical problems related to the special theory of relativity, and approximation methods like the Rayleigh-Ritz method, with practical applications to the theory of elasticity. The final chapters focus on more advanced topics like variable end points and strong variations, including a detailed account of Weierstrass's theory of strong variations, based on Hilbert’s work.

Fox’s clear presentation of variational calculus is complemented by numerous illustrative examples, making the material more accessible. The book also includes references for further reading, allowing students to explore topics more deeply. This text is ideal for advanced undergraduate and graduate students who have a basic understanding of partial differentiation and differential equations, offering a solid foundation in variational methods and their application in modern mathematical physics.