Abstract:
We will talk the development of the main mathematical elements of the electromagnetic picture of the world chronology.
In electrical and magnetic studies, the potential is defined so that the resulting force in any direction is measured by the decrease in potential in this direction. This method of using the expression makes it corresponding in sign to the potential energy, which always decreases when bodies move in the direction of the forces acting on them.
The geometric nature of the relationship between the potential and the vector obtained from it is clarified thanks to Hamilton's discovery of the form of the operator by which the vector is derived from the potential.
The St. Petersburg mathematician and mechanic O. I. Somov was the first in Russia to use the apparatus of vector calculus in a course on theoretical mechanics. Somov deeply studied Hamilton's works and took from them the most necessary and useful for presenting mechanics on a fundamentally new level.
Somov expanded the concept of a differential parameter, giving it a vector meaning. He singled out the differential parameter of the first order (gradient) and the second order (divergence). He is credited with introducing the mathematical concept of gradient, hodograph, vector product, level line and surface, potential and their geometric and vector meaning. However, the works of academician Somov have been undeservedly forgotten. We will try to fill this gap in our lecture.
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