1 advanced mathematics (calculus). In this part, I used Advanced Mathematics of Tongji University, Volume One and Volume Two, which are very good textbooks.

Chapter 1 Functions and limitations.

Before this chapter, we should be familiar with the graphs of several common elementary functions. Anti-hyperbolic sine, when I didn't watch it, I personally felt that it didn't matter whether I watched it or not. It is not required to prove the limit outline by definition, but this part of the example depends on it, which is conducive to understanding the definition of limit. This is the knowledge point that multiple-choice questions love to test. This outline does not require consistency and continuity.

Chapter II Derivative and Differential

This chapter is relatively simple. The derivative, correlation rate of change and differential approximate calculation of the function determined by the parametric equation are not tested.

Chapter III Mean Value Theorem and Derivative Application

This chapter is difficult, but it is also the focus of the exam, mainly the proof question. Several mean value theorems are not difficult to understand, but they will be more difficult to use, so practice more questions and learn to prove these theorems. Taylor formula may seem crazy at first glance, but in fact, this proof test should not be taken, it is too complicated. But this formula is very important, we should learn to apply it, and it is not difficult to apply it, so we must master it. The following curvature and the approximate solution of the equation are not tested. In addition, you don't need to read all the examples and exercises related to engineering application in the book. )

The fourth chapter indefinite integral

The exercises given in this part of the book are not difficult, so do them well. Some topics in the book are very annoying. It seems that the outline of rational function integral is no longer needed, but it is still in the book 10. You can look at it, which is good for calculating some integrals. The outline of the integrating table is not needed.

The fifth chapter definite integral

This chapter is very important, and the variable limit integral is often tested. It is necessary to make clear the difference between variable limit integral, indefinite integral and definite integral. Under what conditions there is an original function, and under what conditions it is integrable, and integrable has nothing to do with the existence of the original function. It may be a little confusing at first, so don't panic when you read it carefully, and you will review it later. Section 5: Outline of generalized integral of γ function without trial and error. But I want to talk about gamma function. I really regret not looking carefully at that time. This function is very useful in probability statistics.

Chapter VI Application of Definite Integral

The content of the number three exam is only: the calculation of the plane graphic area, the calculation of the volume of the rotating body, and the calculation of the parallel cross-sectional area as a known solid volume (the examples given in this part of the economic mathematics textbook are better)

Chapter 7 Vector Algebra and Spatial Analytic Geometry (the third question is not needed)

Chapter 8 Differential calculus of multivariate functions

I was crazy at the beginning of this chapter, especially in the case of composite functions and implicit functions. But it is not difficult to understand the questions in this chapter, so you have to do more questions to find some feelings before you can know where your understanding is wrong. The main contents are: fully differential approximate calculation of multivariate function geometry, application of directional derivative and gradient binary function Taylor formula least square method.

Chapter 9 Multiple Integrals

This part only tests the double integral, and the key point is to calculate the double integral. Basically, there are big problems every year. You must learn to calculate all kinds of double integrals and use calculation skills (parity, symmetry. Calculation is very important, so I made a mistake in this year's problem ~)

Chapter 10 Integrals of Curves and Surfaces (Not Required by Mathematics)

Chapter 11 Infinite Series

This chapter hasn't had a big exam in the past two years, which may be mainly due to the merger of March 4th, but this chapter is still very important. It may be a bit difficult at first, and the summation function should be done by yourself. The contents that are not tested are: Cauchy's principle of trial and error; The 09 outline of the root value method of positive series has been deleted, but I think this can be used; The summation of several series in the summation function is deleted 09; Application of power series expansion of function: uniform convergence of function series. Fourier series.

Chapter 12 Differential Equations and Difference Equations

There is no difference equation in engineering mathematics, but the whole chapter is relatively simple. Personally, I think it is enough to read the review book directly.

2 linear algebra. I still use Tongji University's engineering mathematics in this part of the textbook, which is not much different from economics mathematics. Only vector space and linear space and linear transformation need not be tested. The content of linear algebra is abstract and logical. But it is the simplest course in No.3 Middle School, so we should pay attention to the connection of knowledge points before and after, which was taught by Emperor Yongle.

Probability theory and mathematical statistics. I didn't read this part of the book carefully At first, I always felt that I watched more time. Later, I thought I should read it quickly, so I rushed to read it. In fact, there are also reasons why I am tired of learning mathematics. This part of probability theory should be more difficult to learn at first, which may be more difficult than calculus, because it is a brand-new research method in mathematics. But the book must be read well, and it is not so difficult to understand its research methods and various models. There are interval estimation and hypothesis testing in economic mathematics textbooks, which were deleted in 2009; Linear regression analysis ... no test.