The difficulty of high numbers seems to be a mystery. Some people even give up their favorite majors in order to avoid high numbers. Shu Gao, is it really that terrible? It is not difficult for those who know, and it is not difficult for those who are difficult. When you can clearly know the knowledge system of advanced mathematics, what are you afraid of?

There are three subjects in the postgraduate entrance examination, namely advanced mathematics, linear algebra, probability theory and mathematical statistics. However, candidates who prepare for math always like to review from high numbers. Why? There are two reasons: first, advanced mathematics has the highest score in the test paper, reaching 56% of the total score, and its difficulty ranks first among the three subjects. Second, the successive connection between subjects leads to the review of advanced mathematics first.

Linear algebra, probability theory and mathematical statistics, especially probability theory and mathematical statistics, are disciplines based on advanced mathematics. Without advanced mathematics, it is difficult to understand the following subjects, and college mathematics is also carried out in order, which shows its scientific nature.

In order to better understand the subject of advanced mathematics for postgraduate entrance examination, it is necessary for us to know its knowledge system before reviewing. Only in this way can we have a global view and clearly know the relationship and key points between chapters, instead of seeing the forest for the trees.

What exactly is a high number?

Higher mathematics can be divided into univariate function calculus and multivariate function calculus in a big way.

One-dimensional calculus includes limit, derivative, indefinite integral and definite integral; Multivariate function calculus includes multivariate function differential calculus (mainly binary function) and multivariate function integral calculus. There are also differential equations and series, which can be regarded as the application of calculus.

In addition, there are vector algebra and spatial analytic geometry. Among them, the number one is the triple integral, curve integral and surface integral in vector algebra, spatial analytic geometry and multivariate function integral, and the other is the part of the number three * * *, which has some subtle differences, which we will introduce in the following chapters.

Unary calculus

1 restriction

Limit is a very important chapter in higher mathematics, and this concept runs through the whole process of higher mathematics. The concepts of derivative, definite integral, partial derivative, multivariate function integral and series are all defined by limit.

It is with the concept of limit that mathematics sublimates from finite to infinite, which is also the watershed between higher mathematics and elementary mathematics. Limit is also a compulsory content in mathematics for postgraduate entrance examination every year, and the direct test score is as high as 14- 18.

2 reciprocal

With the concept of limit, the concept of derivative has a theoretical basis. Derivative is the soul of differential calculus of unary function. This chapter is the focus of the postgraduate entrance examination, which is mandatory every year, flexible and comprehensive. This chapter can be reviewed from three aspects: the concept, calculation, application and mean value theorem of derivative differential.

3 untimely integration

Indefinite integral is essentially the inverse operation of derivative. This chapter focuses on calculation, and its importance cannot be described too much. Because integral is the key chapter that determines the success or failure of higher mathematics learning, it will be used in the following chapters, such as definite integral, double integral, triple integral, curve and surface integral, differential equation and so on.

4 definite integral

Definite integral is the integral mentioned in calculus. In addition to mastering the basic concepts, we should also master its calculation related content and the application of definite integral, and take the exam every year. Differential equation is essentially the calculation of indefinite integral.

multivariate calculus

The calculus system of multivariate function is similar to that of univariate function. Differential calculus includes basic concepts (double limit, partial derivative and differentiability), partial derivative calculation and partial derivative application.

Multivariate function integral includes double integral, triple integral, curve and surface integral, and the examination focuses on calculation, which is a compulsory question every year. The last chapter series includes three parts: constant series (mainly investigating the discrimination of convergence and divergence), power series (mainly investigating expansion and summation) and Fourier series (respectively investigating the number one). This chapter is also compulsory.

How to learn advanced mathematics?

Although there are many knowledge points in the postgraduate entrance examination, the content level of each subject is very clear. If you want to master the knowledge of various subjects quickly in a limited time, you must grasp the main knowledge, highlight the key points of the exam, pay attention to the connection and synthesis of knowledge points, and have a clear aim.

Because the main knowledge of advanced mathematics is differential calculus and integral calculus, the unary function calculus and multivariate function calculus are the key knowledge in our examination, so we must master these knowledge points skillfully in the process of reviewing for the exam.

At the same time, as the theoretical basis of calculus, limit runs through the whole knowledge system of higher mathematics, so the calculation of limit is particularly important. Finally, the postgraduate entrance examination is designed for the country to select talents after all. In order to test everyone's comprehensive application ability of knowledge, the relationship between knowledge points must be very clear, especially the internal relationship between differential, integral, differential equation and infinite series. Only in this way can we predict which knowledge can be combined into a big problem and realize it.

Life is wonderful only when you dream, and brilliant only when you are down to earth. Choose the right direction and stick to it, and you will have good results. Finally, I wish you all the best in the 20 19 postgraduate entrance examination.