Selected Chapters in the Calculus of Variations by Jürgen Moser

Book Contents :-
1. One - Dimensional Variational Problems 2. Extremal Fields and Global Minimals 3. Discrete Systems , Applications

About this book :-
"Selected Chapters in the Calculus of Variations" is a concise, advanced mathematics book based on lectures by Jürgen?Moser, aimed at readers interested in deeper theoretical and modern aspects of "calculus of variations". It blends classical foundations with more recent developments, particularly the "Aubry-Mather theory", which connects variational methods to "dynamical systems" and minimal invariant structures. The text bridges historic ideas from Jacobi, Legendre, and Weierstrass with later techniques, making it both a solid theoretical resource and a gateway to research topics. ([Springer][1]) The book is organized into three main parts: one-dimensional variational problems, extremal fields and global minimals, and discrete systems with applications. Throughout, Moser highlights how abstract variational principles lead to meaningful results in geometry and dynamics, such as minimal geodesics on tori and twist map behavior. Although not a beginner’s text, this work is highly valued by graduate students and researchers for its clear synthesis of classical theory, rigorous proofs, and connections to modern mathematical themes. With its mix of theory, exercises, and applications, it’s a compact but rich guide to the subject.

Book Detail :-
Title: Selected Chapters in the Calculus of Variations by Jürgen Moser
Publisher: Birkhäuser
Year: 2003
Pages: 140
Type: PDF
Language: English
ISBN-10 #: 3764321857
ISBN-13 #: 9783764321857
License: External Educational Resource
Amazon: Amazon

About Author :-
The author Jürgen Moser was a "German-American mathematician" born on 1928 in "Königsberg, Germany" (now Kaliningrad, Russia). He completed his doctorate in 1952 at the "University of Göttingen", studying under Franz Rellich and later influenced by Carl?Siegel. Moser became an expert in "dynamical systems, partial differential equations, analysis, and the calculus of variations", helping shape modern stability and small-divisor theories. After moving to the "United States", he taught at "MIT" and "New York University", then at "ETH Zürich" in Switzerland, where he became professor emeritus. His work, deeply insightful and broadly impactful, includes contributions to Hamiltonian systems and variational methods.

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