was he successful in developing this calculus?
Yes
Josiah Willard Gibbs
Gibbs worked on developing the exterior algebra of Hermann Grassmann into a vector calculus well-suited to the needs of physicists. With this object in mind, Gibbs distinguished between the dot and cross products of two vectors and introduced the concept of dyadics. Similar work was carried out independently, and at around the same time, by the British mathematical physicist and engineer Oliver Heaviside. Gibbs sought to convince other physicists of the convenience of the vectorial approach over the quaternionic calculus of William Rowan Hamilton, which was then widely used by British scientists. This led him, in the early 1890s, to a controversy with Peter Guthrie Tait and others in the pages of "Nature".
who was josiah willard gibbs? An American scientist when was he born? February 11, 1839 which field of science was he involved with? Physics, chemistry, and mathematics. which institution did he complete his education in? Sheffield Scientific School and Connecticut Academy of Arts and Sciences. was he married? No what career did he take up in the year 1880-1903? From 1880 to 84 he worked on developing the exterior algebra into a vector calculus and it was published in a book in 1901.
wiki:19643480
Josiah Willard Gibbs [SEP] Career, 1880–1903
From 1880 to 1884, Gibbs worked on developing the exterior algebra of Hermann Grassmann into a vector calculus well-suited to the needs of physicists. With this object in mind, Gibbs distinguished between the dot and cross products of two vectors and introduced the concept of dyadics. Similar work was carried out independently, and at around the same time, by the British mathematical physicist and engineer Oliver Heaviside. Gibbs sought to convince other physicists of the convenience of the vectorial approach over the quaternionic calculus of William Rowan Hamilton, which was then widely used by British scientists. This led him, in the early 1890s, to a controversy with Peter Guthrie Tait and others in the pages of "Nature".