1. Limit and continuity: Limit is the basic concept of advanced mathematics, but many students will encounter difficulties in understanding and applying it. The concept of continuity is also an important difficulty, and it is necessary to master the continuity of functions and the judgment of discontinuity points.
2. Derivative and differential: Derivative is a concept to describe the rate of change of a function, but its calculation and application are often difficult. Differential is another form of derivative, which also needs some understanding and application ability.
3. Integral and definite integral: Integral is to solve problems such as area and volume, but many students will encounter difficulties in understanding and application. Definite integral is a special form of integral, so it is necessary to master its properties and application methods.
4. Sequence and sequence: Sequence is the sum of infinite numbers, but many students will encounter difficulties in understanding and application. Sequence is a series of orderly numbers, so we should master the judgment of its nature and convergence.
5. Differential equations: Differential equations are equations that describe the relationship between functions and their derivatives, but many students will encounter difficulties in understanding and solving them.
6. Multivariate function and partial derivative: multivariate function refers to a function with multiple independent variables, and partial derivative is the derivative of each independent variable in multivariate function to the dependent variable. These concepts and calculation methods may be complicated for beginners.
7. Spatial analytic geometry: Spatial analytic geometry studies the properties and relationships of geometric objects such as points, lines and surfaces in three-dimensional space, involving concepts such as vector and coordinate transformation, which may be abstract and difficult for beginners to understand.