A History of the Progress of the Calculus of Variations During the Nineteenth Century (Classic Reprint)

Discover the origins and growth of the calculus of variations through the 19th century, traced chapter by chapter by a careful historian.

This volume offers a clear, accessible account of how leading mathematicians—Poisson, Ostrogradsky, Sarrus, Delaunay, Cauchy, Jacobi, Legendre, and others—shaped the subject. Readers glimpse the evolution from early ideas to more advanced criteria for maxima and minima, and see how these ideas influenced subsequent work in geometry and analysis.

Structured as a historical survey, the book compiles key memoirs and treatises, explaining what they achieved and how they influenced later developments. It emphasizes the progress of the Calculus of Variations across major figures and includes discussion of the methods and problems that guided the field in the nineteenth century. The author also reflects on the accessibility and reception of these works, providing context for students and researchers approaching the subject today.

• Who contributed essential ideas about variable limits and the variation of double and multiple integrals.
• How Jacobi’s and Legendre’s methods influenced later work, including proofs and applications.
• How the subject intersected with geometry, differential equations, and mechanics.
• What the history reveals about the development of criteria distinguishing maxima from minima.

Ideal for readers of the history of mathematics, and for students seeking a clear map of the Calculus of Variations’ nineteenth‑century trajectory.