The difference between engineering mathematical analysis and advanced mathematics is that there is no differential equation in mathematical analysis, but there is one in advanced mathematics; Compared with advanced mathematics, mathematical analysis requires mastering triple integral, curve integral, surface integral, Green formula, Gaussian formula and Stokes formula, while advanced mathematics only requires understanding triple integral.
In a broad sense, all mathematics except elementary mathematics are advanced mathematics, and some call algebra, geometry, simple set theory and logic in middle school intermediate mathematics, which is the transition between elementary mathematics in primary and secondary schools and advanced mathematics in universities. Generally speaking, advanced mathematics is a basic subject formed by calculus, algebra, geometry and their intersection. The main contents include: series, limit, calculus, spatial analytic geometry and linear algebra, series, ordinary differential equations. Advanced mathematics is a basic subject for postgraduate examinations in engineering, science and engineering and finance.
Analysis of Engineering Mathematics (Volume II) is an engineering mathematics analysis textbook compiled according to the Basic Requirements for Teaching of Advanced Mathematics in Engineering promulgated by the Engineering Mathematics Curriculum Steering Committee of the Ministry of Education. On the basis of offering the course of engineering mathematical analysis for many years, we have extensively absorbed the teaching experience of famous universities at home and abroad. It is an important compulsory course of basic theory, which not only includes all the contents of Advanced Mathematics for general science and engineering. Moreover, it strengthens and broadens the theoretical basis of calculus, pays attention to the application of infinitesimal analysis thought, and also has certain requirements and training in mathematical logic, rigor and abstraction.
Are all the advanced mathematics textbooks in universities the same? No, even among different departments in a university, the theme is different. For example, the physics department generally uses Advanced Mathematics published by Tongji University, and other departments/colleges will make some adjustments according to the difficulty of the subject. For example, finance majors may have their own textbooks, and the coverage and difficulty of different textbooks should be different.