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

Oskar Bolza

Hardcover

ISBN 10: 033160650X ISBN 13: 9780331606508

Publisher: Forgotten Books, 2018

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.

About this title

About the Author

Oskar Bolza (1857–1942) studied mathematics at the University of Berlin and later at Strasbourg. He taught at Johns Hopkins, Clark University, and the University of Chicago, returning to Germany 22 years later but retaining the University of Chicago title of Non-resident Professor of Mathematics for the rest of his life. He taught mathematics at the University of Freiburg until his 1933 retirement.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 033160650X
• ISBN 13: 9780331606508
• Binding: Hardcover
• Number of pages: 289