1. 1 Object, function and characteristics of numerical analysis

1. 1. 1 Mathematical Science and Numerical Analysis

Mathematics is the mother of science, and science and technology cannot be separated from mathematics. It is closely related to mathematics by establishing mathematical models, and mathematics is applied to various fields of science and technology in various forms. Numerical analysis, also known as computational mathematics, is a branch of mathematical science. It studies the numerical calculation method of solving various mathematical problems by computer and its theoretical and software realization. Using computers to solve scientific and technological problems usually goes through the following steps:

① Establish a mathematical model according to practical problems.

② The mathematical model gives the numerical calculation method.

(3) According to the calculation method, the algorithm program (mathematical software) is compiled and the results are calculated on the computer.

The first step is to establish a mathematical model, which is usually the task of applied mathematics. The second and third steps are the tasks of computational mathematics, which is the object of numerical analysis, involving various branches of mathematics and covering a wide range of contents. As a course of "Numerical Analysis", only the most basic and commonly used numerical calculation methods and theories are introduced, including interpolation and data approximation, numerical differentiation and integration, numerical solution of linear equations, nonlinear equations and equations, eigenvalue calculation, numerical solution of ordinary differential equations and so on. They all study mathematical problems, but unlike pure mathematics, they only study the theory of mathematics itself, but closely combine theory with calculation, focusing on numerical algorithms and their theories of mathematical problems. Like other mathematics courses, numerical analysis is a course with rich content, profound research methods and its own theoretical system. It has the characteristics of high abstraction and rigor of pure mathematics, extensive application and high technology of practical experiments. It is a mathematics course which is closely combined with the use of computers and has strong practicability.