As a basic science, advanced mathematics has its inherent characteristics, namely, high abstraction, strict logic and wide application. Abstraction and computability are the most basic and remarkable characteristics of mathematics. With a high degree of abstraction and unity, we can profoundly reveal its essential laws and make it more widely used.
The idea of limit is the basic idea of calculus and a series of important concepts in mathematical analysis, such as continuity of function, derivative (maximum value is 0), definite integral and so on. These are all defined by the way of limit. Limit is the basis of solving higher mathematics problems.
Calculus is a branch of mathematics, which studies the differential and integral of functions and related concepts and applications. It is the basic subject of mathematics and has important applications in many fields.
Spatial analytic geometry means that with the help of the concept of vector, geometry can be more easily applied to some natural sciences and technical fields. Therefore, after introducing spatial coordinate system, spatial analytic geometry introduces the concept of vector and its algebraic operation.
Differential equation refers to the relationship with unknown function and its derivative. Solving differential equations means finding unknown functions. Many physical problems can be solved by solving differential equations.
A sequence is a function that sequentially connects the items of a sequence with a plus sign. Typical series include positive series, staggered series, power series, Fourier series and so on.