1, limit
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.
2. Stones
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.
3. Spatial analytic geometry
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.
Historical development of extended data
It is generally believed that the mathematics disciplines developed before16th century generally belong to the category of elementary mathematics, so the mathematics disciplines established after17th century are basically the contents of advanced mathematics. It can be seen that the category of higher mathematics can not be explained clearly by a few simple sentences or listing its branches.
Of the three branches of mathematics established before19th century, the first two were originally branches of elementary mathematics and later developed into a part of advanced mathematics, and only analysis belonged to advanced mathematics from the beginning.
Calculus, the basis of analysis, is regarded as the beginning of "mathematics of variables", so studying variables is one of the characteristics of higher mathematics. The original concept of variables is a direct abstraction of variables that change in the material world, and the concept of variables in modern mathematics contains a higher level of abstraction.
References:
Baidu encyclopedia-advanced mathematics