English [n? l？ t？ Beautiful, beautiful l? t？ ks]

Analytics, analytical science, analytical theory.

Analysis:

A branch of mathematics, with calculus as the basic tool, functions (such as mapping and relationship) as the main research object and limit as the basic idea. Many classical branches of mathematics and their modern extensions are collectively referred to as analysis abbreviation.

Definition:

Analysis in a narrow sense-mathematical analysis

It is based on differential calculus, integral calculus, series theory and real number theory.

Generalized analysis

The concept of limit is not only the core of calculus, but also the important idea of many other disciplines. Calculus is the foundation of modern mathematics, which has produced many new branches of mathematics, such as differential equation, function theory, variational method, functional analysis and so on. , collectively referred to as generalized analysis.

Branch of discipline:

In many classical branches of analysis, or in the classical parts of various disciplines, mathematical analysis, simple complex variable function theory and real variable function theory have basic properties, and they comprehensively study the basic behavior of functions. In addition, most of its branches mainly study functions from one side. For example, harmonic analysis mainly studies the problem that functions are represented by Fourier series (or Fourier transform), and uses this representation to study the behavior of functions.

Facts have proved that this is an important and effective method to study functions, and its ideas and methods have been applied to many branches of mathematics. Function approximation theory studies the possibility and error (approximation order) of approximating general functions with some good functions, and in turn uses these properties to describe functions. Convex analysis mainly studies a kind of important nonlinear function-convex function.

Classical variational method studies the extreme value of functional, and the functional here is generally limited to the integration of functions with independent variables, so it can be said that it is still a study of functions. Today, these classic disciplines centered on functions are still an important part of analytical science.