What are the test points for the certification questions in the postgraduate mathematics high mathem

1. Proof of the limit of the sequence.

The proof of the limit of the sequence is the number.

The key points of the first and second questions, especially the number two, have been tested very frequently in recent years, and there have been several major proof questions, and the method used in the general big questions involves the proof of the limit of the number series, and the method used is the monotonous bounded criterion.

2. Proof of the differential median value theorem.

The proof of the differential median value theorem has always been a major difficulty in the postgraduate entrance examination, and its examination is characterized by strong comprehensiveness, involving a wide range of knowledge, and the equations involving the median value are mainly three types of theorems

1.the zero point theorem and the medium theorem;

2.differential median value theorem;

Including Roll's theorem, Lagrangian median theorem, Cauchy median theorem and Taylor's theorem, of which Taylor's theorem is used to deal with the related problems of higher-order derivatives, and the frequency base is examined, so the first two theorems are the main ones.

3.differential median value theorem;

The effect of the integral median value theorem is to remove the integral sign.

When examining, the three types of theorems are generally combined in pairs, so it is necessary to summarize the types of questions that have been examined so far.

3. The problem of the root of the equation.

Includes a discussion of the uniqueness of the root of the equation and the number of roots of the equation.

4. Proof of inequality.

5. Proof of definite integral equations and inequalities.

The main methods involved are the methods of differential calculus: constant variation method; Methods of integralism: commutation method and distributive integration method.

6. Five equivalence conditions that the integral is independent of the path.

Broadly speaking, there are three test points, monotonous bounded convergence criterion, median value theorem, and inequality. The proof question is a more difficult type of question in the postgraduate entrance examination mathematics, and the score is generally not ideal, but it does not mean that this kind of question is difficult.

Linear algebra is a branch of mathematics that deals with vectors, linear transformations, and systems of linear equations in finite dimensions. Vector space is an important topic in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis. Through analytic geometry, linear algebra can be concretely represented.

The theory of linear algebra has been generalized to operator theory. Since nonlinear models in scientific research can often be approximated as linear models, linear algebra is widely used in the natural and social sciences.

Linear algebra was formed as a separate branch in the 20th century, but it has a very long history. The "chickens and rabbits in the same cage" problem is actually a simple problem of solving a system of linear equations. The oldest linear problem is the solution of a system of linear equations, which has been described in a relatively complete description in the chapter of the ancient Chinese mathematical work "Nine Chapters of Arithmetic and Equations", in which the method described is essentially equivalent to the modern method of performing elementary transformations on the lines of the augmentation matrix of the system of equations and eliminating unknown quantities.

Thanks to the work of Fermat and Descartes, linear algebra in the modern sense essentially appeared in the seventeenth century. Until the end of the eighteenth century, the field of linear algebra was confined to planes and spaces. The transition to n-dimensional linear space was completed in the first half of the nineteenth century.

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To take the logarithm is to prove that b alna>a blnb, both sides are positive numbers, and the pair can be taken again.

Alnbln(LNA)>BLNALN(LNB) were obtained

If a e b, the left is not negative and the right is not positive, obviously.

If a>b>e, divide the following by [aln(lna)] lna> [bln(lnb)] lnb(a=e>b, left zero right negative, a>e=b, left positive right zero, obviously).

Let f(x)=xln(lnx)] lnx(x>e),f'(x)=[ln(lnx)*lnx+1-ln(lnx)] (lnx) 2,lnx>1,ln(lnx)>0,ln(lnx)*lnx+1-ln(lnx) 0+1=1,constant derivative, f(x) increment, f(a)>f(b).

e a>b, except for [aln(lna)] lna> [bln(lnb)] lnb

Let f(x)=xln(lnx)] lnx(1f(b)

As for logarithms, exponents are generally treated like this.

Proof: f is derived on [0,1] so the minimum value theorem of a continuous function is known as the function |f(x)|In [0,1] there is a maximum point m if m=0, then the proposition is true.

So when m (0,1], the counter-argument assumes |f(m)|>0

Applying the Lagrangian median theorem to [0,m] yields f(m) -f(0)=f'(n)(m - 0) n∈(0,m)

f(0)=0 ∴ f(m) =f '(n) m∵ |f '(x)| f(x)| f(m)| =|f '(n) m|≤|f(n)|m<|f(n)|

This contradicts the assumption So|f(m)|=0

So f(x)=0

Most of these proofs use the median value theorem (Lohr, Cauchy, Lagrange), and if it is too troublesome, you can consider Taylor's formula. Memorize several types of questions.

Suppose there is fx>0, then since fx has a continuous second derivative, then there must be x1, making fx1 the maximum value of fx.

Then in the right field of x1, (a small enough field) there must be a shack hall.

In the same way, if there is fx<0, it is also contradictory.

So, and Hu has fx=0