Both the derivation of calculus and the calculation of definite integral need calculation skills. Calculus is not like elementary mathematics. Understanding is the most important thing. If you don't know what calculus is, you can't start by telling you some words in the formula.
Actually, I don't think calculus has much to do with high school stuff. You only need to have a little impression of high school mathematics, but trigonometric functions, logarithms, exponents, and Pythagorean theorem should also be known. The rest is the calculation skills, skills are practiced. If you can do tens of thousands of calculus problems, you don't have to worry about skills. Calculus needs to do more problems.
If you buy books, you should buy some basics. At present, the routines of ordinary calculus textbooks are the review of basic knowledge of functions, such as limits, derivatives, differentiation, derivative applications, mean value theorem, max-min problems, indefinite integrals and definite integrals. In-depth textbooks also bring some Taylor series, vectors, double triple integrals and so on.
Just visit the bookstore according to your own taste. What I recommend to you may not be suitable for you.
Question 2: How to study calculus? 5 points 1. The study of calculus is really different from that of high school mathematics, and the mathematical ideas involved are much deeper than that of high school.
Even college graduates, most of them have studied calculus, but most of them have not.
Understand the ideas and methods of calculus. So, just find a college graduate, especially a graduate.
A few years later, people who are not engaged in teaching or theoretical research ask a simple calculus question. They at least have
More than 90% will definitely say "I studied for a long time and forgot". This shows that they didn't learn well at all.
I don't understand at all. As long as you have learned it from the beginning, you will not forget the truth, and the problem will not be solved and understandable; simple
None of the questions, 100%, are memorized, memorized and swallowed. These people who have studied calculus, in
Old farmers are boastful capital, a disgrace to their children and a permanent pain in their work.
If the landlord wants to be outstanding and not follow the footsteps of most college graduates, he should:
1, you'd better learn by yourself or preview first. This sentence is easier said than done.
Specifically, what do you mean by trying to understand every definition, every formula and every method?
Why? What exactly does this mean?
2. Usually we say that learning with questions, the higher level is to learn with your own understanding and your own predictions.
In other words, you not only have questions you don't understand, but also have your own predicted answers. Or, after reading the last chapter,
Generally, I can predict what will be said in the next chapter. It's hard to say, it's easier said than done. if
When you can roughly predict what you will say in the next chapter, your confidence will increase unprecedentedly, and you will feel that you have
Predictive ability, over time, self-study ability is cultivated. What ordinary people call "self-learning ability" is made up of
Less than this state, their "self-study ability" is only the ability of rote memorization and gang-wearing.
If you have this highest level of "self-study ability", you already have the ability to "write books and make presentations".
Don't be limited by the concept of middle school. Some concepts in middle school are wrong, and some are right under special circumstances.
Middle school knowledge is only a special case. After entering the world of calculus, it gradually enters the general situation.
For example, 0 can't be the denominator, nor can universities, but many students say that the limit of 0/0 type violates mathematical principles.
This is just what a half-baked classmate said. Another example is that the zeroth degree of any number is 1, so many students don't.
Method to understand the limit process of 0 to the power of 0. For another example, the limit that any power of 1 is an infinite power of 1 and 1 is even more.
It's hard to understand.
4. The concept is understood and will be summarized immediately; Then solve more problems and raise awareness through a large number of problems. Study hard.
Most integrated people are unwilling to solve more problems, thinking that solving a few is enough. In fact, I can't understand thousands of questions.
There can be no real understanding! After solving the problem, you should summarize the problem, summarize the method, summarize the problem, and then
Forecast, confirm, forecast,,,. Over time, the master was born. Come on!
The hardest thing is not to be misled by some teachers. For example, equivalent infinitesimal substitution is rendered as having in China.
Teachers and professors are a dime a dozen. In fact, looking at the international situation, it is not so ridiculous. As a student, the only one
The way is to read more international textbooks.
Good luck with your study!
Welcome questions.
I hope I can solve your problem.
Question 3: How to learn calculus, where are the main points and what basis do you need? I bought a book on advanced mathematics at 5 points. At that time, I studied Tongji Sixth Edition. I studied simple derivatives first, so it is easier to learn those who have a high school foundation.
Question 4: How easy is it to teach calculus by yourself? Just understand the formula.
I taught myself. Look at the example.
Just do exercises after class.
Question 5: Is calculus difficult to learn? . . ? How to learn calculus well
The difference between elementary mathematics and advanced mathematics. Elementary mathematics mainly studies discrete quantities, but it is high
Isomathematics is a continuous quantity. Because of this, advanced mathematics is difficult to learn. Here, and
Calculus in advanced mathematics is the basis of other mathematical knowledge, so we study differential calculus in combination with many colleges and universities.
In this article, I will talk about the methods of calculus learning.
First of all, we must affirm the greatness of calculus. The creation of calculus is not so much mathematics.
In history, this is a great event in human history. Today, it is very important for engineering technology.
Just as telescopes are as important to astronomy and microscopes are to biology. Its appearance is not
Not coincidentally, it has a long growing process. As early as ancient Greece, Archimedes and others
His works already contain the seeds of integral calculus. After more than a thousand years of silence, Europe appeared in the text.
After the revival of art, the study of Archimedes theory revived, and many pioneers emerged.
Who?
The real foundation of calculus is in
17
Century,
Starting with Descartes' analytic geometry,
receive
The masterpiece is the creation of calculus, which brings the history of mathematics into a new period-variable mathematics.
Period. Euclidean geometry and algebra in ancient and medieval times were constants.
Mathematics and calculus are real variable mathematics and a great revolution in mathematics. Calculus in mathematics
This can be regarded as a great achievement in the history of development, because the establishment of calculus not only solved
At that time, some important scientific problems and some important branches of mathematics were produced from this.
Such as differential equation, infinite series, differential geometry, variational method, complex variable function, etc.
Calculus has solved some important problems: ① finding instantaneous velocity; ② finding tangent of curve; ③ finding.
The maximum value ④ of the function is to find the curve length. These problems are very important for the development of astronomy, physics and other disciplines.
An important promoting role. Because it is important, it is also difficult to learn, and it is a freshman science.
The main math problems that make students have a headache.
Preview is very important. Preview is not self-study, but browsing for books.
Key and difficult points, in order to "concentrate on class"
.
If you don't have much time, you can browse one
Have a general impression of the main content that the teacher will talk about, which can be to some extent
To some extent, it helps you keep up with the teacher's thoughts in class. If you have enough time, you can keep up with the teacher's ideas.
In addition to browsing, you can also read some contents in detail and prepare questions.
What's the difference between your own understanding and the teacher's explanation?
What problems need to be discussed with the teacher?
If you can do this, then your study will become more active and in-depth and you will achieve something.
Better results. Don't rush to do the problem, think deeply about the textbook first. Do the problem
Don't turn over the answer easily, think it over and discuss it with your classmates. Do the questions or not?
Coming out is more rewarding than doing it. Confidence in learning is also very important. Improve confidence, cultivate
Good psychological quality and courage to overcome all kinds of difficulties; Don't let it go just because you're not interested at the moment.
Abandon,
Interest is not innate,
It is cultivated slowly the day after tomorrow.
Good study tradition,
It is the quality that contemporary college students should have to work hard to realize the glory of their lives.
In class, we should focus on the difficulties in preview and give guidance to teachers for the key difficulties.
After asking questions, the teacher expects the students to "interrupt" his lecture in the university class, teacher.
I also hope that I can exchange and discuss classroom knowledge with students, so that classroom questions can not only get the special attention of teachers.
The explanation can also be on the topic. Dare to ask questions in class. In class, if you have any questions.
Ask, you should ask right away. Because of your question, there may be situations where other students are afraid to ask.
Problems; It could be everyone here.
(
Including teachers.
)
Problems that have not been considered.
Asking questions in class is of great help not only to yourself but also to the whole class. Lively students
A dynamic learning environment is not only created by teachers, but also requires the participation of students and teachers.
Students all hope and attach great importance to students' more positive performance in class. Believe this.
Interactive learning process will definitely make you gain more in the process of learning calculus.
There are many integral formulas in calculus learning, so we must remember and skillfully use some integrals.
Formulas can shorten the time of doing problems, which is of great help to future study, while integral formulas
Many and complex, need special memory. Deducing the formula many times improves the understanding of the formula.
It is also a clever use of other formulas in disguise, and the derivation of formulas in mathematics learning needs other formulas.
With the help of, the basic integral formula has the advantages of complex integral formula. & gt
Question 6: How to teach calculus by yourself? Is there any way? First of all, you should understand that the invention of calculus is a revolution in the history of mathematics. The so-called academic revolution is a great impact on thought, and so is the thought of calculus. Therefore, in order to learn calculus well, we must first fully understand its thought and understand where its effectiveness comes from ―― in fact, in the process of the invention and perfection of calculus, the understanding of its most fundamental thought was also obtained through very difficult exploration. After understanding the basic ideas, you will get twice the result with half the effort, otherwise you will solve the problem again and do well in the exam, but your achievements in it will be limited to this.
The basic idea of calculus is limit. Specifically, it is the idea of local approximation and precision from the limit. Fully understanding the idea of limit is a necessary condition for learning calculus well. In order to better understand the function of this idea in the whole calculus, it is necessary to understand the establishment process of calculus.
The idea of limit has a long history, but it has always been a vague concept, such as the concept of infinitesimal, and even the understanding of founder Newton and others is vague. It was not until the second mathematical crisis broke out that Cauchy and others were strictly defined. It can be seen that it is difficult to understand.
Most textbooks introduce the concepts of differentiation, sequence limit and function limit in this way. In this way, continuity is introduced to describe the relationship between small changes of dependent variables and independent variables. Furthermore, the concept of derivative is introduced to describe the rate of change of dependent variable to independent variable. Then the linear principal part is used to replace the function increment, that is, the concept of differential is introduced to describe the function increment approximately. The above concepts are all based on limit theory.
As for integration, it originated from finding the area of step function and finding the accumulation of functions about independent variables.
Obviously, in Newton and Leibniz's basic theorem of calculus, two seemingly unrelated theories are closely linked. Since then, calculus has shown great power, and people are scrambling to apply it, even ignoring its fuzziness in basic ideas.
The rest are some methodological problems that can be solved by more practice.
As for the concept of multivariate calculus, it is essentially the same, without much leap. Basically, you can understand multivariate calculus as long as you know binary calculus.
In short, sharpening the knife does not mistake the woodcutter, first understand the foundation and then solve the problem. Of course you can realize that the greatness of calculus is not as great as it is. You have learned more than just a math tool.
I wish you a happy study.
Question 7: What basis do you need to learn calculus? To learn calculus, you must first learn all kinds of functions in high school, such as once, twice, exponent, logarithm, power and triangle, then you can learn the derivative of 2-2 and simple integral, and then you can watch calculus kill dragons and rely on heaven. I recommend you to learn the physics competition in high school. It's quite fun. The infinitesimal method commonly used in novice physics competitions is the father of calculus. Knowing it is very helpful to learn calculus.
Question 8: How to learn calculus well 1: Pay attention to the concept and master the origin of each formula theorem. These deduction methods are also the idea of doing the problem.
Calculus is a tool, and it needs to be used well to learn calculus well. For example, in some problems of physics or mathematics. Try to think about whether you can answer it with calculus.
2. Find ways to eliminate the fear of mathematics, find some interesting math topics, build confidence and come back to study calculus. When learning, we should focus on the origin and deduction of calculus formulas, which is much better than simply memorizing formulas. And some problems are solved by the definition of calculus, without calculus formula.
3. Our teacher held out two fingers in class and said, "Learn calculus well and do more exercises."
4. The origin of all concepts of calculus is limit, and the proposal of limit depends on.
A set of mathematical languages is called ε-δ. Therefore, the key to learn calculus well is to master this analytical language (this is a mathematics major). If you can't understand the explanation in the book, don't force the problem, first find a book on calculus or the history of mathematics. The purpose of reading such books is to deeply understand the background of the concept of calculus and understand the evolution of mathematics thoughts at that time (of course, this will also become the evolution of your thoughts). Do this step well and you will understand what the limit is. What is differential? Wait a minute. Then you can study your textbook, supplemented by quantitative exercises. Remember, this is a matter of consolidating understanding, not dealing with those boring exams. If you do this step well, then you will have a deeper understanding of the concept of calculus. At this time, you may be interested in calculus. Of course, you can study further. You can do more questions if you want to cope with the exam. For example, do the classic Jimidovich mathematical analysis problem set (of course, it is optional, not all). Now you are a quasi-master. However, you need further training and reading.
5. First understand the function and actual situation of calculus, memorize the basic formula, have the concept of model in your mind, and it is best to understand the original method of calculus.
6. Math training logical thinking! This is very important. The ability of logical thinking, whether innate or acquired, can certainly be cultivated, and one of the ways is through learning mathematics. Solving mathematical problems will teach you how to approach problems, learn how to see the key of problems, ask appropriate questions, think about problems from different angles and so on. The ability of logical thinking is much more useful than mathematics, such as learning a new language, organizing and planning.
In a word, every student should and can find the motivation to learn calculus. You don't have to agree that calculus is one of the greatest achievements of mankind. The beauty of this theory is dazzling. But at least calculus is regarded as an important tool to master the subject, and it is also an important theory to teach you how to systematically attack and solve problems.
Question 9: What is the basis for learning calculus? To learn calculus, you must first learn all kinds of functions in high school, such as once, twice, exponent, logarithm, power and triangle, then you can learn the derivative of 2-2 and simple integral, and then you can watch calculus kill dragons and rely on heaven. I recommend you to learn the physics competition in high school. It's quite fun. The infinitesimal method commonly used in novice physics competitions is the father of calculus. Knowing it is very helpful to learn calculus.
Question 10: How can we learn college calculus well? If you majored in science in high school, you should feel that many of them were mentioned in high school. I am a freshman, so far I feel that calculus is getting along well. I make a list of things I want to learn, from limit to integral. Just look at the examples in the textbook carefully. At present, the end of the term, just do typical questions and see suggestions, so that you can review more things and accept them quickly. Do a few questions from time to time, read more examples and buy books compiled by school teachers. Many people think it's not very good, but the language of the books compiled by their school teachers (the kind sold to local students) is very popular, and some questions that they don't usually understand may suddenly understand after reading them. It can be said that calculus is still a bit difficult, but it is not that difficult to overcome. Work hard, freshman can only say so much, I hope it will be useful to you.