1, with many concepts and proofs in mathematical analysis, is a method to study complex variable functions. The main purpose of advanced mathematics is to solve some problems encountered in engineering.
2. Advanced mathematics focuses on application, and mathematical analysis focuses on theoretical derivation.
3. Every theorem in mathematical analysis has been strictly proved, and all theorems finally come down to six equivalence principles; Advanced mathematics pays attention to application, and many theorems are directly given or simply described. There is a lot about applications in the book.
4. Mathematical analysis focuses more on the derivation process, while advanced mathematics focuses more on the application of results.
5. Mathematical analysis, as a basic course for undergraduates majoring in mathematics, is the basis of the whole analysis, and it is the benchmark to test whether a person is interested in mathematics.
Note: The main content of mathematical analysis is calculus. The theoretical basis of calculus is limit theory, and the theoretical basis of limit theory is real number theory. Calculus is a general term for differential calculus and integral calculus, which is abbreviated as calculation in English, because early calculus was mainly used for calculation problems in astronomy, mechanics and geometry.
Later, people also called calculus analysis, or infinitesimal analysis, especially the knowledge of using extreme processes such as infinitesimal or infinity to analyze and deal with calculation problems.
Early calculus has been used by mathematicians and astronomers to solve a large number of practical problems, but it has not been developed for a long time because it cannot give a convincing explanation for the concept of infinitesimal. Many mathematicians are skeptical about this theory, and Cauchy and later Wilstrass perfected the limit theory as the theoretical basis.
Get rid of the vague description of limit, such as "the smaller the better" and "infinite tendency", and use accurate mathematical language to describe the definition of limit, so that calculus gradually evolves into a basic mathematical discipline with strict logic, called "mathematical analysis", which is translated into Chinese.
The most important feature of real number system is continuity. Only with the continuity of real numbers can limit, continuity, differential and integral be discussed. It is in the process of discussing the legitimacy of various limit operations of functions that people gradually establish a strict theoretical system of mathematical analysis.