It is impossible to learn advanced mathematics well without learning advanced mathematics. Advanced Mathematics 1 contains the most basic concepts of advanced mathematics such as limit, differential, integral and derivative. If you learn 2 directly, it will be difficult to understand what you have learned in the future.
Although I don't know which teacher you are talking about, Cai Gaoting's advanced mathematics is very famous all over the country, especially for the postgraduate entrance examination. It is a classic textbook! If you want, I suggest you buy one from Dangdang online bookstore. :search.dangdang./search.aspx？ Select catalog =&key =% CD% AC% BC% C3% B0% E6% B8% DF% CA% FD&; F7 & amp； Directory = & ampSearchFromTop= 1
Who speaks advanced mathematics well? I think what Cai said is also good. View original post >>
Why can't I understand the advanced mathematics taught by China? Advanced mathematics has its own special language model, based on the concept of limit, called ε-δ language, which is basically composed of mathematical symbols. The mathematical derivation process and formula are almost the same all over the world. Therefore, advanced mathematics is the science that is the easiest to be universal and the easiest to achieve knowledge. If the Chinese teacher can't understand the lecture, it is estimated that the foreign teachers can't understand it either. First of all, we should master the limit concept of mathematical system and be familiar with the meaning of ε -δ language pattern expression. Even if I'm not used to it at first, it's not difficult to cross this hurdle. I wish you success! You can do it.
Can you learn advanced mathematics by reading instead of attending classes? Sure, but only if you have your own reading method and plan. If it's only superficial, it can't be done.
Can freshmen learn math by themselves? I don't understand what the teacher said, including advanced mathematics and linear algebra. Thank you for sitting in the front of the class as much as possible, previewing before class, I should be able to understand it in class. If you really don't understand the theory, just listen to his example. Basically, you can understand it by listening to the examples. I don't understand either, but just look at more examples!
Why can't I understand advanced mathematics taught by China, but I can understand what foreigners say? Your Chinese is not good
What is advanced mathematics? How to learn to understand? Advanced mathematics is higher than elementary mathematics. In a broad sense, all mathematics except elementary mathematics are advanced mathematics, and some call algebra, geometry and simple theoretical logic in middle school secondary mathematics, which is the transition between elementary mathematics in junior high school and advanced mathematics in undergraduate stage. It is generally believed that advanced mathematics is a basic subject formed by simple calculus, probability theory and mathematical statistics, as well as in-depth algebra and geometry, and their intersection, mainly including calculus, but other textbooks are slightly different.
Edit the characteristics of advanced mathematics in this paragraph.
Elementary mathematics studies constants and uniform variables, while advanced mathematics studies non-uniform variables.
Advanced mathematics (a general term for several courses) is an important basic subject in universities of science and engineering. As a science, advanced mathematics has its inherent characteristics, namely, high abstraction, strict logic and wide application. Abstract and calculation are the most basic and remarkable characteristics of mathematics-high abstraction and unity, which can profoundly reveal its essential laws and make it more widely used. Strict logic means that in the induction and arrangement of mathematical theory, whether it is concept and expression, or judgment and reasoning, we must use the rules of logic and follow the laws of thinking. Therefore, mathematics is also a way of thinking, and the process of learning mathematics is the process of thinking training. The progress of human society is inseparable from the wide application of mathematics. Especially in modern times, the appearance and popularization of electronic computers have broadened the application field of mathematics. Modern mathematics is becoming a powerful driving force for the development of science and technology, and it has also penetrated into the field of social sciences extensively and deeply. Therefore, it is very important for us to learn advanced mathematics well.
How to learn advanced mathematics well by editing this paragraph
To be fair, advanced mathematics is really a difficult course. The operations of limit, infinitesimal, unary calculus, multivariate calculus and infinite series are quite difficult. Many students are interested in "how to learn this course well?" I feel confused. To learn advanced mathematics well, we should do the following: First, understand the concept. There are many concepts in mathematics. Concepts reflect the essence of things. Only by figuring out how it is defined and what its essence is can we really understand a concept. Secondly, master the theorem. Theorem is a correct proposition, which is divided into two parts: condition and conclusion. In addition to mastering its conditions and conclusions, we should also understand its scope of application and be targeted. Third, do some exercises on the basis of understanding the examples. Especially remind learners that the examples in the textbook are very typical, which is helpful to understand concepts and master theorems. Pay attention to the characteristics and solutions of different examples, and do appropriate exercises on the basis of understanding examples. When writing a topic, you should be good at summing up-not only the methods, but also the mistakes. You will gain something after doing this, so you can draw inferences from others. Fourth, clear the context. We should have an overall grasp of the knowledge we have learned and summarize the knowledge system in time, which will not only deepen our understanding of knowledge, but also help us to further study. Advanced mathematics includes calculus and solid analytic geometry, series and ordinary differential equations. Calculus is the most systematic and widely used in other courses. The foundation of calculus was completed by Newton and Leibniz (only the theoretical basis of calculus they founded was not rigorous enough). (Of course, calculus has been applied before them, but it is not systematic enough. ) Advanced mathematics has two characteristics: 1. Equivalent substitution. In the calculation of limit class, some factors are often replaced by equivalence (which is incomprehensible in the calculation of quantity), but the limit is the calculation of order. 2. If the form of the original function makes the calculation difficult, you can use the integral or differential form of the original function, which is the idea of simplifying the calculation. The relationship between these three functions is the differential equation.
Specific content
I. Functions and limitations
Simplicity of constant and variable functions; Inverse function; Limit function of elementary function sequence; Comparison between infinite quantity and infinitesimal quantity; Properties of continuous function and continuity of elementary function.
Second, derivative and differential
Derivative concept function sum, differential derivative rule function product, quotient derivative rule compound function derivative rule inverse function derivative rule higher derivative implicit function and its derivative rule function differential.
Third, the application of derivatives.
Determination of monotonicity of function in the problem of undetermined differential mean value theorem: extreme value of function and its maximum and minimum value; It applies the concave direction and inflection point of the curve.
Fourth, indefinite integral
The Concept, Properties and Method of Solving Indefinite Integral
Five, definite integral and its application
Concept of definite integral Calculus formula Partial substitution integral method Generalized integral of definite integral
Six, spatial analytic geometry
Direction cosine and direction number of plane and space straight line surface and space curve in space Cartesian coordinate system
Seven, multivariate function differential calculus
The concept of multivariate function, the limit of binary function and its continuous partial derivative, the derivation method of fully differential multivariate composite function, and the extreme value of multivariate function
Eight, multivariate function integral calculus
Concept and properties of double integral and calculation method of double integral concept and calculation method of triple integral
Nine, ordinary differential equations
The basic concept of differential equation can be separated from variable differential equation and homogeneous equation. The structure of the solution of high-order linear differential equation The solution of second-order homogeneous linear equation with constant coefficient The solution of second-order inhomogeneous linear equation with constant coefficient.
X. infinite series
Infinite series is a method to study the convergence of ordered countable infinite numbers or the sum of functions and the numerical value of the sum. The theory is based on series, which is different from divergence and convergence. Only when infinite series converge can there be a sum; Divergent infinite series has no sum. Arithmetic addition can sum finite numbers, but it cannot sum infinite numbers. Some series can be summed by infinite series method. Include several series (including positive series and arbitrary series, wherein any series includes staggered series, etc. ), function series (including power series and Fourier series; Taylor series and Laurent series in complex variable function). The main function of infinite series is to converge a series with infinite terms into a function, or to reversely expand a function into an infinite series, which provides a new approximation method. What needs to be explained here is that not all infinite series can converge to a function, and it is necessary to "check convergence" to determine whether they converge. Common methods include comparison method (including limit comparison method), root value method and ratio method. Mathematics majors need as many as 13 methods to judge whether they converge.
Who are the teachers who teach advanced mathematics in Shanjing? Li Tingting, aha, boys like it best.