Mathematical analysis, also known as advanced calculus, is the oldest and most basic branch of analysis. Generally speaking, it refers to a relatively complete mathematical subject with the general theory of calculus and infinite series as the main content, including their theoretical basis (basic theory of real number, function and limit). It is also a basic course for college mathematics majors. The branch of analysis in mathematics is a branch of mathematics that specializes in studying real numbers and complex numbers and their functions. Its development began with calculus and extended to the continuity, differentiability and integrability of functions. These characteristics help us to study the material world and discover the laws of nature. Mathematical analysis does not include the contents of space solid geometry and ordinary differential equations in higher mathematics.
The department of mathematics has specially set up two compulsory courses, analytic geometry and ordinary differential equations, to discuss these two parts.
Higher mathematics refers to a more complicated part of mathematical objects and methods compared with elementary mathematics. 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: limit, calculus, spatial analytic geometry and vector algebra, series, ordinary differential equations.
Strictly speaking, mathematical analysis is more difficult than advanced mathematics, and its content is similar, but it is a basic course for mathematics majors, and its learning depth is unmatched by any other advanced mathematics. It mainly focuses on theoretical things, while advanced mathematics is studied by engineering majors such as physics, computer and economy, and is mainly used in computing and other applications.
Mathematical analysis is mainly to cultivate students' analytical thinking about mathematics, and to master the ideological work to solve those problems. General mathematical analysis is more difficult than advanced mathematics. As for the content of learning, it is hard to say, because the content of general mathematical analysis is involved in higher mathematics, but mathematical analysis is more in-depth. Moreover, in terms of teaching methods, advanced mathematics may focus on how to find a solution to a problem and give you a bunch of commonly used methods. You practice mastering. Mathematical analysis doesn't do this, he pays more attention to theoretical calculation and analysis. Mathematical analysis is an important basic course for mathematics majors, which is rich in content and difficult, and has a direct and important influence on the following courses: differential equation, mathematical equation, complex variable function, real variable function and functional analysis.