Two textbooks on vector analysis: Gibbs and Runge (Q6609981)

The first textbook on vector analysis, with the same title, was written by Edwin Wilson (1879--1964) and published in 1901 [JFM 33.0096.01]. It was based on the lectures of his doctoral advisor J. Willard Gibbs (1839--1903), American mathematician and theoretical physicist known for the Gibbs phenomenon regarding trigonometric series and the Gibbs-Thomson equation. Another highly influential textbook on the subject, \textit{Vektoranalysis}, was published in Germany by Carl Runge (1856--1927) in 1919 [JFM 47.0696.03)], translated into English in 1923 [JFM 49.0557.03].\N\NThe authors give a critical analysis and comparative study of the two textbooks which form the basis of modern vector analysis. In the first part, biographical sketches of Gibbs and Runge are presented, then the textbooks are analysed chapter by chapter with particular emphasis on integral calculus and vector operators. The final part is devoted to the introduction to tensors from Runge's book.\N\NFor the entire collection see [Zbl 1531.01004].