Lectures on the Calculus of Variations (the Weierstrassian Theory) (Classic Reprint) - Hardcover

Harris Hancock

Hardcover

ISBN 10: 0331826038 ISBN 13: 9780331826036

Publisher: Forgotten Books, 2018

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.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0331826038
• ISBN 13: 9780331826036
• Binding: Hardcover
• Number of pages: 315