Solve calculus problem
The best way to solve calculus problem is to eliminate as many options as possible.
Solving calculus problem
Instead of thinking deeply about why Wang Wensu obtained the derivative easily and naturally without using the concepts of limit and infinitesimal, he said that he did not use the limit and that he did not obtain the derivative of calculus. What logic is this? Newton and Leibniz know that there is a problem with the derivative obtained by using the method of abandoning the infinitesimal, which is generally recognized as problematic (otherwise, what is the second generation of calculus of the limit method). Why should the crown of the invention of calculus fall on the two of them who use this problematic method? Wang Wensu did not use the wrong method of abandoning the infinitesimal, and was not the inventor of calculus 140 years earlier than Newton? Moreover, as discussed in the first section above, the derivation of the limit method in the non trivial sense cannot be established in logic at all. In short, only by fully understanding the problems and contradictions in the so-called mainstream limit calculus (second-generation calculus, standard analysis), which is popular at present, can we more fully affirm Wang Wensu's succinct and brilliant treatment of derivatives (Party B) in those years. Of course, all this can be fully understood only under the new definition of derivative. 2、 The error of the traditional sandwich theorem in dealing with the independent variable on the denominator, although it did not prove the basic theorem of calculus and the derivation of trigonometric function, it unexpectedly proved that the derivative of limit calculus was not tenable Although Newton and Leibniz had different methods of studying calculus, they came to the same goal by different paths. They independently completed the great cause of creating calculus, laid the foundation of calculus, and made groundbreaking and pioneering contributions to the rise and development of variable mathematics. The glory should be shared by them. However, there was a fierce debate about the priority of inventing calculus in history The latter may be aware that this problem is a problem, so they adopt a vague and rigorous explanation. Many other textbooks simply do not realize or ignore this problem. However, the textbooks of Fang and Wang did not divide DX to get formula 6 as Thomas did in calculus, but only to formula 7. Maybe they also realized that the derivative obtained by doing this was inconsistent with the derivative obtained by the limit method. In « Preston calculus », there is no formula 7 at all, only the differential is written as Newton and Leibniz were giants of their time. In terms of the creation of calculus, although they have their own characteristics in the background, methods and forms, their achievements are equivalent. They all make calculus a widely used algorithm. It should be said that calculus can become an independent science and bring revolutionary influence to the whole natural science, mainly relying on the work of Newton and Leibniz. 1、 Revelation of logical problems in calculus derivation by limit method_____ It only replaces the obvious Berkeley paradox in the so-called first generation calculus with the hidden Berkeley paradox Most master of mathematics programs do not require students to be majoring in mathematics, but generally require applicants to have a foundation of mathematics related courses, including advanced calculus, linear algebra, complex variables, partial calculus and constant calculus equations, probability theory, etc. If the undergraduate is a student with a non mathematical background, it is recommended to check and make up the prerequisite courses required by the target institution in advance.
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