1, content
From the content, advanced mathematics includes: limit theory (but not basic proof), one-dimensional differential and integral, arc differential, multivariate differential and integral, elementary ordinary differential equation, series, spatial analytic geometry, vector algebra and so on.
Mathematical analysis includes: real number theory, limit theory (explaining how rational numbers expand into real numbers from three angles of Dydykin division, interval set and sequence), (including basic proofs, such as the proof of Cauchy convergence theorem), one-dimensional differential and integral, multivariate differential and integral, series and so on. ?
2. formally
Formally, every theorem in mathematical analysis has been strictly proved, and all theorems finally come down to six equivalence principles. Many books choose one of them as an axiom. Advanced mathematics pays attention to application, and many theorems are given directly or simply. There are a lot of applications in the book, such as elementary ordinary differential equations.
3. Purpose
From the purpose, mathematical analysis is mainly studied by undergraduates of mathematics department and a few students of other departments (such as information students). Mainly to develop good proof habits and lay a good foundation for future math work. Advanced mathematics is mainly for engineering students and students majoring in physical economy.
Related information:
Mathematical analysis: In the early days of ancient Greek mathematics, the results of mathematical analysis were given implicitly. For example, Zhi Nuo's dichotomy paradox implies the sum of geometric series. Later, ancient Greek mathematicians such as eudoxus and Archimedes made the mathematical analysis more explicit, but it was not very formal.
When they calculate the area and volume of regions and solids by exhaustive method, they use the concepts of limit and convergence. In the early days of ancient Indian mathematics, Pashgaro, a mathematician in the12nd century, gave a second example of derivative.