Synopsis
Rigorous, classic treatise on the calculus of variations — a clear pathway from fundamental ideas to deep existence results.
This book compiles lectures delivered in 1901–1904, presenting the theory of maxima and minima for definite integrals that depend on a plane curve. It emphasizes precise definitions, sharp problem formulations, and rigorous proofs, with the emphasis on the theoretical side and accessible references to the broader developments in the field. The text systematically builds from the first and second variations to advanced topics like Weierstrass’s and Hilbert’s contributions, and it discusses isoperimetric problems, variable end-points, and the geometry of extremals.
- Clear definitions of core concepts, problems, and variations.
- Detailed demonstrations of Euler’s differential equation and related theorems.
- Coverage of isoperimetric problems, Jacobi’s condition, and the field of extremals.
- Discussion of variable end-points and the parameter-representation approach.
Ideal for readers with a solid background in real analysis and differential geometry who seek a rigorous, thorough treatment of the calculus of variations.
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Lectures on the Calculus of Variations (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book explores the fascinating world of the Calculus of Variations, a branch of mathematics that deals with finding the maximum or minimum values of definite integrals. The author takes readers on a journey through the history of the subject, tracing its development over the last thirty years. The book delves into the foundational principles of the Calculus of Variations, examining the crucial contributions of mathematicians like Weierstrass, Erdmann, Du Bois-Reymond, Scheeffer, and Schwarz. Readers will learn about the key concepts of the first and second variation, the significance of Weierstrassââ â¢s construction, and the groundbreaking work of Hilbert. Beyond a historical overview, the book delves into the theoretical underpinnings of the field, including rigorous proofs of essential conditions and detailed discussions on the existence of fields and the implications of Hilbertââ â¢s existence proof. The author provides numerous examples to illustrate the applications of these principles, making complex concepts accessible to a broader audience. The bookââ â¢s insights into the Calculus of Variations serve as a foundation for understanding the mathematical tools used to solve optimization problems across a range of disciplines. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332772131_0
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Lectures on the Calculus of Variations Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332772131
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Lectures on the Calculus of Variations Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332772131
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