Abstract

Partial differential equation is one of the important contents of traditional mathematics, which has a broad research prospect and a wide range of applications. From the point of view of mathematics, solving partial differential equations can make mathematics develop more continuously in function theory, algebra, differential, etc. This paper focuses on the overview and application of partial differential equations, hoping to contribute to their development. Partial differential equation is an equation that reflects the restriction relationship between the derivative of unknown variables with respect to time and the derivative of unknown variables with respect to space. Mathematical models in many fields can be described by partial differential equations. The basic equations of many important physics, mechanics and other disciplines are partial differential equations themselves. Partial differential equations have become an important part of contemporary mathematics and an important bridge between many branches of pure mathematics and natural science, engineering technology and other fields. The purpose of this paper is to introduce the origin and history of partial differential equations, and the application of partial differential equations in population survey, infectious disease dynamics and other practical problems. Understand the tortuous development history of partial differential equations and their broad application prospects, so as to encourage readers to further study and study partial differential equations.

Keywords: Partial differential equation, application, analysis