The common methods of finding limit (seven indefinite formulas), such as four limit operations, equivalent infinitesimal replacement, Lobida rule and Taylor formula, are the key points. Monotone bounded discriminant and pinch discriminant are two commonly used methods to calculate the limit of sequence, which have certain flexibility and difficulty. The judgment and classification of discontinuous points of functions and the properties of continuous functions on closed intervals (especially the mean value theorem) are also common knowledge points in past years' exams, which are key contents, but they are very basic and not difficult, so this part must not lose points.

Second, the differential calculus of unary function

This part is the basis and focus of the whole differential calculus. The common examination contents are mainly the definition of derivative, the relationship between derivability and continuity; Derivation of implicit function and function determined by parametric equation, especially the discussion of differentiability of piecewise function and function with absolute value; In addition, the application of derivatives, especially the monotonicity and extremum of functions, must also be paid attention to, which is the place where calculation problems often appear in postgraduate entrance examination; The properties of continuous functions on closed intervals, Rolle theorem, Lagrange mean value theorem, Cauchy mean value theorem and Taylor theorem are also places that like to prove problems and cannot be ignored.

3. Integral calculus of unary function

The calculation of indefinite integral and definite integral is the key and difficult point of one-dimensional integral and the basis of the whole integral. You should study hard in the exam. In the process of solving the integral, the basic properties of indefinite integral and definite integral, substitution integral method and integration by parts will be used. Among them, substitution integration method is the key, which will involve trigonometric function substitution and inversion. This method has a fixed routine to follow, but how to exchange elements accurately to get the final answer needs more practice, and whoever makes it perfect. The application of definite integral is also the key point, in which the area of plane figure and the volume of rotator are the key points. Students should deeply understand the idea of infinitesimal method and master problem-solving skills through more practice. The application of definite integral in physics (one of the best), such as work, gravity, pressure, centroid, centroid, etc. Basically, I don't participate in the exams in recent years. Candidates only need to remember the solution formula.

Fourth, the differential calculus of multivariate functions

This part focuses on the existence of implicit function, partial derivative and total differential and the causal relationship between them. The requirement for candidates is to judge whether a binary function is continuous at one point, whether the partial derivative exists, whether it is differentiable and whether the partial derivative is continuous; Will find the first and second partial derivatives of multivariate functions (especially those with abstract functions) and the first and second partial derivatives of implicit functions; Will find the directional derivative and gradient of binary and ternary functions; Find the tangent plane and normal of the surface and the tangent plane and normal of the space curve. This kind of problem is a comprehensive problem of multivariate function differential calculus, vector algebra and spatial analytic geometry, which should be reviewed together. The application of extreme value or conditional extreme value of multivariate function in geometry, physics and economy; Find the maximum and minimum of binary continuous function in bounded plane region. This part of the application problem needs knowledge from other fields, so candidates should pay attention to it when reviewing.

Verb (abbreviation of verb) Integral of multivariate function

One of the key points of multivariate function integration is the calculation of double integral, which makes use of the properties of double integral and the mutual transformation between rectangular coordinates and polar coordinates. This part of the content will be tested every year, and candidates should pay attention to it, but the double integral is not difficult, and candidates do not need to be afraid of it. Triple integral, curve integral and surface integral belong to number one, mainly to master the calculation of triple integral, Green formula and Gaussian formula, and the necessary and sufficient conditions for curve integral to be independent of path. For the number one candidate, this part is the key and difficult point, which needs special attention.

Six, infinite series

This part is the content of students' exams in number one and number three. This paper mainly introduces the basic properties of series and the necessary conditions for convergence, the comparison discrimination method, ratio discrimination method and radical discrimination method of positive series, and Leibniz discrimination method of staggered series. Will judge the convergence, divergence, absolute convergence and conditional convergence of series terms; Will find the convergence radius and convergence domain of power series; Find the sum function of power series or the sum of several series; Expand the function into a power series (including writing the convergence domain).

Seven, differential equation

The emphasis and difficulty of this part are the concepts, properties and corresponding calculation formulas of differential equations of each order. Will find the general solution or special solution of a typical type of first-order differential equation: this kind of problem is to distinguish the types of equations first. Of course, some equations do not directly belong to the type we have learned. At this time, the common method is to switch or substitute with appropriate variables to turn the original equation into the type we have learned; Can solve the reducible equation; Find the special solution or general solution of homogeneous and inhomogeneous equations with linear constant coefficients; According to practical problems or given conditions, the differential equation is established and solved.