1. Higher algebra: including linear algebra, matrix theory, vector space, etc. This knowledge is very important for understanding the concepts of limit, continuity, differential and integral.
2. Real number theory: Understand the nature, completeness and density of real numbers, and lay the foundation for studying the continuity and differentiability of functions.
3. Elementary mathematics: including basic concepts such as set theory, sequence, function, limit, derivative and integral, it is the basis of unary mathematical analysis.
4. trigonometric functions and complex numbers: trigonometric functions are very useful in solving some geometric and physical problems, and complex numbers are important tools for studying analytic functions and series.
5. Differential equation: Differential equation is an important branch of mathematical analysis, and learning differential equation is helpful to understand the limit process and local properties of function.
6. Elementary function: Understand the properties of elementary functions, such as power function, exponential function, logarithmic function and trigonometric function. These functions often appear in mathematical analysis.
7. Inequalities: Learn some basic inequalities, such as Cauchy-Schwartz inequality and Abel theorem, which are very useful in proving the existence of limits and estimation errors.
8. Sequence and series: It is of great significance for learning the limit and integral of a function to understand the concepts of sequence limit, convergence and divergence, and convergence and discrimination of series.
9. Real variable function and measure theory: Although unary mathematical analysis mainly studies real function, some basic concepts and methods of real variable function and measure theory are very helpful for understanding advanced courses such as integral and functional analysis.
10. Logic and proof methods: Learning some basic logic knowledge and proof methods, such as direct proof, indirect proof and reduction to absurdity, is very important for understanding and mastering theorems and proofs in mathematical analysis.