The Real Calculus vs What You Learned（真正的微积分和你学到了什么）.pdf

The Real Calculus vs . What You Learned HOW LEIBNIZ S ORIGINAL CALCULUS HAS BEEN SUBVERTED by Ern est S c h a p i ro A f alse version of the calculus, based on the Cauchy limit theorem , is now ta ught in the schools. T o revive in ventiveness in the physical sciences, students must learn the rea l creative breakthrough embodied in Leibniz s discovery of the calculus. ©Will Mcintyre/Photo Researchers, Inc. A student in calculus class. But what is she learning?-a set of rules whose discovery has been mystified by the L imit Theorem of Ca uchy, or the actual method of invention utilized by Leibniz in discovering the calculus? 21 30 Fa l l 1 999 st CENTURY nventi on of the calcu l us is one of the greatest d iscoveries. The whole is greater than its part, cou ld be proved by It perm itted the sol ution to a wide range of mathematical a syllogism, of which the major term was a definition, and I p ro b l ems by means of a new l y i n vented langua ge or the mi nor term an identity. For, if