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

Inhaltsangabe

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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