柯西-勒贝格微积分原理的根本错误 英文 Xiaoping Ding丁小平微积分数学.pdfVIP

The Radical Mistakes in the Theories on Calculus of Cauchy-Lebesgue System Xiaoping Ding Beijing institute of pharmacology of 21st century Abstract The misunderstanding of the concept of differentials in the theories on calculus of CauchyLebesgue system was exposed in this paper. The defects of the definition of differentials and the associated mistakes in the differentiation of composite functions were pointed out and discussed. Keywords: CauchyLebesgue theories on calculus, differentials, composite functions Introduction In this paper it is suggested that the history of calculus consists of three stages including the period of precalculus before I. Newton established his calculus system initially in 1667, the first period of history of calculus from 1667 until A. L. Cauchy published his monograph ‘cours d’analyse’ in 1821, the second period of history of calculus from 1821 until the novel calculus system was established in 2010 and the third one after 2010. During the period of 189 years from 1821 to 2010, the theories on calculus developed in this second period has never been justified by the application of mathematics in science and technology, which only demonstrated the usefulness of calculus invented by I. Newton and G. W. Leibniz and developed by the subsequent mathematicians as before. In contrast, the history of 189 years has revealed that the theories on calculus in this second period have blocked the development of mathematics significantly. In this paper the radical mistakes in the theories on calculus of CauchyLebesgue system were shown and discussed. The preliminary achievements of novel theories on