Analysis and Application of the Related Concepts of Infinitesimal in Advanced Mathematics
Through the description of the tortuous process of understanding infinitesimals,the philo-sophical speculative color contained in infinitesimals is revealed and its connotation is explained.From the perspective of comparing the order of infinitesimals,the essence and relationship between the derivative and differential ofunary function are explained.The Taylor formula is used to compare the order of infini-tesimals and explain the essence of equivalent infinitesimals.It is pointed out that the root cause of the er-ror in the use of equivalent infinitesimals is that the accuracy of the Taylor polynomial used for substitution cannot meet the required requirements.Finally,the application of infinitesimal comparison in the limit convergence method is presented.
advanced mathematicsinfinitesimalinfinitesimal of higher orderequivalent infinitesi-malTaylor's formula
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维普
