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I am going to write a paper on the proof and application of differential mean value theorem. What books can I read?
The mean value theorem has been thoroughly studied. I really don't understand what you wrote.

Writing a paper without quality is just a waste of time.

As far as the whole mathematical analysis is concerned, it has been thoroughly studied, and the only place to start is the study of Gibbs phenomenon of Fourier series. Secondly, the research on the sum of P series is related to Riemann conjecture.

There is no scientific research at all in other aspects, and what the predecessors have done is already very comprehensive. Even if it is written, it can only be said that it is plagiarism, which is the result of China's pursuit of only the number of papers and not the quality. Might as well not write.

As for the study of mathematical analysis, I can recommend some books to you:

Zhang Zhusheng's new lecture on mathematical analysis, Zhuo Liqi's mathematical analysis, and Fechkin Goltz's calculus course.

Exercise: Zhou Minqiang's mathematical analysis exercise, his exercise handout, Pei can also have a look.