Mathematical analysis is one of the compulsory courses for mathematics majors, and its basic content is calculus, but it is quite different from calculus.
Calculus is the general name of differential calculus and integral calculus, which is abbreviated as calculation in English, because early calculus was mainly used for calculation problems in astronomy, mechanics and geometry. Later, people also called calculus analysis, or infinitesimal analysis, especially the knowledge of using extreme processes such as infinitesimal or infinity to analyze and deal with calculation problems.
The early calculus was not developed for a long time because it could not convincingly explain the concept of infinitesimal. Cauchy and later Wilstrass perfected the limit theory as the theoretical basis, which made calculus gradually evolve into a basic mathematical discipline with strict logic, called "mathematical analysis", which is translated into Chinese.
The basis of mathematical analysis is real number theory. The most important feature of real number system is continuity. Only with the continuity of real numbers can limit, continuity, differential and integral be discussed. It is in the process of discussing the legitimacy of various limit operations of functions that people gradually establish a strict theoretical system of mathematical analysis.
Mathematical analysis is a basic course for mathematics majors. Learning mathematical analysis (and advanced algebra) well is the necessary basis for learning other subsequent mathematics courses such as differential geometry, differential equations, complex variable functions, real variable functions and functional analysis, calculation methods, probability theory and mathematical statistics.
As one of the most important basic courses in the department of mathematics, the logic and historical inheritance of mathematical science determine the decisive position of mathematical analysis in mathematical science, and many new ideas and applications of mathematics come from this solid foundation. Mathematical analysis is based on the rigor and accuracy of calculus in the theoretical system, thus establishing its basic position in the whole natural science and applying it to various fields of natural science. At the same time, the subject of mathematical research is the object after abstraction, and the mathematical thinking mode has distinct characteristics, including abstraction, logical reasoning, optimal analysis, symbolic operation and so on. The cultivation of these knowledge and abilities needs to be realized through systematic, solid and strict basic education, and the course of mathematical analysis is the most important link.
We are based on cultivating outstanding talents with solid mathematical foundation, wide knowledge, innovative consciousness, pioneering spirit and application ability to meet the requirements of the new century. From the perspective of personnel training, whether a student can learn mathematics well depends largely on whether he can really master the course of mathematical analysis after entering the university.
The goal of this course is to master the basic theoretical knowledge of mathematical analysis through systematic study and strict training; Cultivate strict logical thinking ability and reasoning ability; Skilled computing ability and skills; Improve the ability of establishing mathematical model and applying calculus to solve practical application problems.
Calculus theory is inseparable from the development of physics, astronomy, geometry and other disciplines. Calculus theory has shown great application vitality since its birth. Therefore, in the teaching of mathematical analysis, we should strengthen the connection between calculus and adjacent disciplines, emphasize the application background and enrich the application content of theory. The teaching of mathematical analysis should not only reflect the strict logical system of this course, but also reflect the development trend of modern mathematics, absorb and adopt modern mathematical ideas and advanced processing methods, and improve students' mathematical literacy. Many people say it's hard to tell the difference, which is true. However, it is quite simple compared with the last question of mathematics in the college entrance examination. I mean, compared to complexity. It is very important to learn a subject well through thinking and understanding, especially a subject with strong mathematical logic thinking. Of course, there is a lot of hard work. I think a person who only holds books in class every day but rarely turns them over will be at a loss. After all, it is not difficult to learn, but as long as he studies hard, it is actually a very basic course, laying the foundation for many mathematics majors in the future. I recommend some books that you can read. I recommend Fudan Chen's book and Chen Jixiu's book, but the topic after class is better than the last one. It is best not to use Tongji version of calculus. I don't think even novices look at it. Reference books, this is the most important.
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What if advanced algebra and mathematical analysis are difficult to do? I can't hear you clearly.
Reading a book a hundred times is self-evident. You don't have to read it a hundred times. Do you think you have read the textbook twice? University is a little different from middle school, which requires self-study ability. It is unrealistic to expect to understand everything in class. It is important to preview and study by yourself. Read the textbook twice in advance, or the teacher will talk for 30-40 pages at a time, and you won't even know where he has been. In addition, find a set of matching problem sets by yourself. Do it again, not to mention the exercises in the book.
There are many videos of mathematical analysis on the Internet. Fudan, Beijing Normal University. Both of them are available at China University of Science and Technology. You can just watch one episode. But you can't rely entirely on this. Learning by yourself is fundamental.
Is mathematical analysis difficult to learn?
First of all, we should have good learning methods, that is, how to improve learning efficiency.
Experience 1:
1, you might as well set yourself some time limits. It's easy to get tired of studying for a long time. At this time, you can divide your homework into several parts and limit the time of each part, for example, finish this exercise within one hour and finish that test before eight o'clock. This will not only help to improve efficiency, but also avoid fatigue. If possible, gradually shorten the time used, and soon you will find that the homework that you couldn't finish in an hour before is now finished in 40 minutes.
2. Don't do other things or think about other things while studying. Everyone knows that you can't do two things at once, but there are still many students who listen to music while studying. Maybe you will say that listening to music is a good way to relax your nerves, so you can concentrate on studying for an hour and then relax listening to music for a quarter of an hour, which is much better than doing your homework with headphones on.
Don't review the same lesson all night. I used to spend an evening watching math or physics. Practice has proved that it is not only easy to get tired, but also has a poor effect. Later, I arranged to review two or three classes every night, and the situation was much better.
You don't need to take detailed notes in class except for very important content. Busy taking notes in class will be inefficient, and there is no guarantee that you will take notes after class. The main work in class should be to digest and absorb the teacher's lecture content and make some brief notes appropriately.
Experience 2:
I have also talked to many people about learning efficiency. We often see such a situation: a classmate studies very hard, studying at school, studying at home, sometimes staying up late and doing countless problems, but his grades are always not up. In fact, I am also very anxious in the face of such a situation. Originally, what you paid should be rewarded. Moreover, if you pay more, you should get a lot of rewards. This is a natural thing. But this is not the case. There is an efficiency problem here. What does efficiency mean? Just like learning, some people will practice it ten times, while others need to practice it a hundred times. There is an efficiency problem.
How to improve learning efficiency? I think the most important thing is to combine work and rest. What is most needed to improve learning efficiency is a clear and agile mind, so proper rest and entertainment is not only beneficial, but also necessary, which is the basis of improving learning efficiency. So how to improve the efficiency of class? In my experience, it is necessary to preview before class, but my preview is rough, and I only glance at the teaching materials, so that the contents and key points of the teaching materials are roughly in my mind and I can be more targeted when I attend classes. When we preview, we don't need to be too detailed. If we are too detailed, it is a waste of time. Second, I will be a little lax in class, and sometimes I will ignore the most useful things. It is of course necessary to listen carefully in class, but as one of my former teachers said, no one can concentrate in a class, which means it is impossible to concentrate for more than 40 minutes, so there is also a problem of time allocation in class. Teachers can relax when they talk about familiar things. In addition, taking notes sometimes hinders the efficiency of class. Sometimes a class is busy copying notes, and sometimes something very important is ignored, but this does not mean that you can not take notes, which is not enough. Everyone will forget that with notes, there will be a basis for review. Sometimes the teacher talks a lot and writes a lot on the blackboard, but you don't need to remember them all. Of course, you should remember some books. Otherwise, remember what you see, which will inevitably affect the efficiency of class, and the loss will outweigh the gain.
How to improve the efficiency of doing problems? The most important thing is to choose a "good topic", and never do it as soon as you see it, which will often get twice the result with half the effort. The questions are all around knowledge points, and many questions are quite similar. First, choose the knowledge point you want to strengthen, and then choose the questions around this knowledge point. There are not many problems, but one similar problem is enough. After choosing the topic, you can do it seriously. The improvement of problem efficiency largely depends on the process after the problem is solved. For the wrong question, we should seriously think about the cause of the error, whether it is because the knowledge points are unclear or careless. After the analysis, do it again to deepen the impression, so that the efficiency of doing the problem will be much higher.
Comments: Yu Xia comments ... >>
Ordinary differential equations or mathematical analysis, which is more difficult!
Of course, ordinary differential equations are more difficult.
1. As an ordinary major, advanced mathematics, that is, calculus, is called mathematical analysis.
Actually, it's an exaggeration, just a bluff.
Generally, only calculus in the department of mathematics can be called mathematical analysis, even if it is general.
Applied mathematics and advanced mathematics in normal universities, called mathematical analysis, are exaggerated.
Resign. Ordinary differential equation is a follow-up course of mathematical analysis, so it is impossible to learn it first.
Ordinary differential equations, and then learn the truth of mathematical analysis.
As an ordinary differential equation and a partial differential equation, you need a lot of physical knowledge.
Knowledge, as well as Mathematical Analysis, relatively speaking, students with weak physical foundation can
To study. Differential equation is a subject that studies physics, physics, chemistry and engineering.
The application of equation is a subject summarized from the perspective of differential equation.
Ordinary differential equations and partial differential equations are basic principles that can't be taught by general mathematics department.
Because those teachers' physical and engineering foundations are too weak and lack common sense,
The most typical thing is that the physical mechanism is not understood and the boundary conditions are not clear, so it is impossible to discuss it in depth.
Open. Middle school students can solve more than one problem, that is, learn to bully; But differential equations are powerful.
It focuses on multiple solutions to a problem and uses differential equations to divide all the problems in nature.
For example, you will know the specific situation:
High school math teachers often prefer common logarithm to natural logarithm. Each batch of goods
When using the base-changing formula, they write it conveniently and casually, and almost 100% is the common logarithm.
And all phenomena in nature are natural logarithms; ; we
The law of birth and death, the highest level of bank interest, and even our hair loss, aging and death.
The cooling process after death is closely related to the natural logarithm.
Natural logarithms are related to everything, and ordinary logarithms are only occasionally seen. however
Our soul engineers in Qian Qian rely entirely on people's wealth to support themselves, but they are at a loss.
As you can imagine, more and more people enjoy teaching at the university level.
How tall a person can be is completely predictable. Look at those solutions that are full of crooked ways,
All kinds of stubborn college calculus and differential equation textbooks can understand everything.
Is mathematical analysis difficult? Is there any good way to learn well?
Not difficult. There is an adaptation process. If you have used a similar way of thinking before, you will feel relaxed. If not, it will take some time to get used to it. A good way is to sum up more, think more, classify more, and just take a few kinds of exams. I wish you a good exam ~
I feel that mathematical analysis is so difficult to learn. What should I do?
Is a course difficult? Different people have different opinions. To learn mathematical analysis well, the following conditions must be met: 1) Not stupid: generally, people who can be admitted to universities are not stupid; 2) Intention: preview attentively, listen attentively, review attentively and exercise attentively. So the key is to be careful. Have you put your heart into it?
Which is more difficult, mathematical analysis or advanced mathematics?
Advanced mathematics is the application of mathematics, that is to say, it is mainly based on the application of formulas; Mathematical analysis is theoretical, mainly based on formula derivation. Speaking of difficulty, it's like the difference between using a computer and being a computer. Which is more difficult?
Which is more difficult, mathematical analysis or counting?
Count to one, that's the dead old genius.
Mathematical analysis is difficult to learn.
Is a course difficult? Different people have different opinions. To learn mathematical analysis well, you must meet the following requirements:
1) Not stupid: being admitted to a university is generally not stupid;
2) Intention: preview attentively, listen attentively, review attentively and exercise attentively.
So the key is to be careful. Have you put your heart into it?
Is a course difficult? Different people have different opinions. To learn mathematical analysis well, you must meet the following requirements:
1) Not stupid: being admitted to a university is generally not stupid;
2) Intention: preview attentively, listen attentively, review attentively and exercise attentively.
So the key is to be careful. Have you put your heart into it?
How to teach yourself mathematical analysis? Is it difficult?
I think I am qualified to answer this question.
The first is to use an entry-level textbook. I use the version of East China Normal University, which is generally simple and has a set of after-school exercises.
Then other better textbooks on the Internet, such as Chen Jixiu and Chen, from Fudan University, are also good, but they are suitable for further study.
Third, it's a good video. I watched Chen Jixiu's excellent video, which was very good.
Finally, do more questions. This is necessary. Jimmy can have a look. If you want to enter a good school, Pei Liwen will definitely go and see it.