In this work the new notion of "external analysis", representing mathematical analysis of the objects constructed with the help of exterior algebra, in particular, exterior forms arising when solving of boundary problems with topological method is carried out, is introduced. External analysis in this case has no connection to algebra, being a mathematical analysis needed to solve a problem. The external analysis the part of the study without which the study and solving of a boundary problem with topological method cannot be carried out. It is not associated with the construction of exterior forms for topological manifolds, which refers to the exterior algebra, but with mathematical analysis of the exterior forms that have arisen in the application of topological methods for boundary problems, and has found numerous applications in many studies. This concept has already come into use in many studies, suggesting that the mathematical analysis of exterior forms and of pseudo differential, integral and functional equations arising from these is applied in the research process. In this work a more precise definition of the external analysis is given and its relation to the exterior algebra is considered. Examples of application of the external analysis in the study of boundary problems in the theory of strength and collapse, as well as seismology, quantum mechanics and mathematical physics are given. In particular, the use of external analysis for the study of the preliminary stage and the possibility of occurrence of a starting earthquake because of harmonic oscillations of lithospheric plates and the basis on which they are located, caused by a vertical harmonic influence, is demonstrated. Firstly, the representation of the boundary problem functional equation for the lithospheric plates is constructed, using the method of exterior algebra. Then the mathematical analysis of the exterior forms built for lithospheric plates is carried out, which is called external analysis. As a result of its application the arising pseudo-differential and functional equations are constructed and studied, which has no relation to the exterior algebra. It is shown that in this case the occurrence of the starting earthquake is possible, and the possibility of its occurrence is even higher than in the static case.

В работе введено новое понятие "внешний анализ", представляющее математический анализ объектов, построенных посредством внешней алгебры, в частности, внешних форм, возникающих при решении топологическим методом граничных задач. В настоящей работе приводятся примеры работ, где имеют место применения внешнего анализа, выполненные при изучении граничных задач как теории прочности и разрушения, так и сейсмологии, квантовой механики, математической физики. В частности, демонстрируется применение внешнего анализа для исследования подготовки и возможности возникновения стартового землетрясения при гармонических колебаниях литосферных плит и основания, на котором они расположены, вызванных вертикальным гармоническим воздействием. Показано, что и в этом случае возможно стартовое землетрясение, причем возможность его возникновения даже выше, чем в статическом случае. Дается более точное определение понятия внешнего анализа, рассматривается его отношение к внешней алгебре.