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Mathematical Treasure: Lagrange on Calculus

Frank J. Swetz (The Pennsylvania State University)

While Joseph-Louis Lagrange (1736–1813) is perhaps best known for his work in mechanics, he also published influential works on the calculus. Born in Italy, he did most of his mathematical work in France. Appointed the first Professor of Analysis at the École Polytechnique in 1787, Lagrange would teach there for the rest of his life. In 1797 he published his lectures on the theory of real functions. Shown above is the title page for the 1813 edition of Theorie des Fonctions Analytiques, the first volume of this work. In it Lagrange stressed an algebraic approach in obtaining his calculus results.

Lagrange divided Theorie des Fonctions Analytiques into three parts, and the first page of the first part is shown above. In the first part, he provided an introduction to the general theory of functions, within which he gave an algebraic proof of Taylor’s Theorem.

In the second part of this book, Lagrange considered geometric applications and, in the final section, applications of calculus to mechanics.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in Mathematical Treasures. In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Lagrange on Calculus," Loci (June 2014)