Albert Einstein praised Josiah Willard Gibbs as the greatest mind in American history. As a scientist, together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics. As a mathematician he created Vector Calculus, which he developed in order to simplify the mathematical descriptions of the dynamics of physical quantities, like the electric and magnetic fields. His techniques are still used today in electrodynamics and fluid mechanics. This reprint of the final 1913 edition of this classic mathematical work has been scrupulously checked for perfect legibility and set with somewhat larger margins to allow the student to make notes.
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