Synopsis
Explore the Weierstrassian approach to the calculus of variations and its classic problems.
This nonfiction work guides you through how tiny changes to curves and surfaces reveal when a path or surface minimizes area or time. It blends rigorous proofs with geometric intuition to build a deep understanding of variation, conjugate points, and optimality conditions.
Readers will encounter foundational ideas like the second variation, Jacobi’s discoveries, and the Weierstrass conditions that dictate when a solution is truly optimal. The text uses concrete problems to frame these concepts, including surfaces of revolution, the brachistochrone problem, and the study of catenaries, all within the broader theory of minimizing or maximizing functionals.
- Learn how small variations of a curve or surface lead to necessary conditions for optimality.
- Explore the geometric meaning of conjugate points and their role in minimality.
- See how classical problems are solved within a rigorous variational framework.
- Understand the interplay between differential equations and variational principles.
Ideal for readers with an interest in advanced calculus, mathematical analysis, or the historical development of optimization theory.
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Lectures on the Calculus of Variations (the Weierstrassian Theory)
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Paperback. Condition: New. Print on Demand. This book introduces readers to the fascinating world of the Calculus of Variations, a field that has played a pivotal role in shaping our understanding of nature and its laws. The author, a renowned mathematician, presents the subject in a clear and accessible manner, making it approachable for those with a curious mind and a background in basic mathematics. Exploring the historical development of the Calculus of Variations from its humble beginnings to its present-day applications, the author sheds light on the contributions of eminent mathematicians such as Newton, Bernoulli, Euler, Lagrange, and Weierstrass. Through detailed explanations and illustrative examples, the book delves into the intricate concepts of minimum and maximum values, leading readers to grasp the essence of variational problems. With an emphasis on the profound implications of the Calculus of Variations in various scientific disciplines, the author demonstrates its indispensable role in areas such as mechanics, physics, and engineering. The book not only unravels the mathematical intricacies of the subject but also highlights its practical significance in shaping our technological advancements. Delving into the depths of the Calculus of Variations, this book offers a comprehensive exploration of its theoretical underpinnings, historical trajectory, and practical applications. It is an invaluable resource for students, researchers, and anyone seeking to expand their knowledge of this captivating field. 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 # 9781333890131_0
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Lectures on the Calculus of Variations (the Weierstrassian Theory) (Classic Reprint)
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333890131
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Lectures on the Calculus of Variations (the Weierstrassian Theory) (Classic Reprint)
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LECTURES ON THE CALCULUS OF VA
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Condition: New. KlappentextrnrnExcerpt from Lectures on the Calculus of Variations (the Weierstrassian Theory)The vanishing of the first variation and the differential equation The curvature expressed in terms of F and F.About the Publisher. Seller Inventory # 2148092697
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