How should I learn calculus? How do you learn calculus?

1. When a new concept emerges, be clear:

a. What went wrong with the old concept;

b. What is the specific definition of the new concept;

c. What problems can not be solved by the new concept?

2. From the new concept, we derived:

a. What are the most basic methods and formulas, such as calculus, which only have five most basic formulas;

b. What are the most basic laws, such as derivatives, there are only three most basic laws;

c. What are the most basic applications, such as approximate calculations, such as implicated rate of change, such as shadow area, such as kinematic problems.

Keep talking to yourself and asking and answering yourself. If you can "deceive" (that is, explain) yourself, you are an expert.

Go for it! At least 90% of college students learn calculus just for fun, and they are done with it, completely ignorant of what they are doing. Because they don't understand at all, but rely on memory, forgetting everything, forgetting all the time, forgetting all the time.

If you want to stand out from the crowd, you must: think more and practice more. There is no other way!

You should practice more ...... on the basis of a full understanding, to understand the true meaning of the letter in each formula, should not simply remember what the letter represents......

Keep the formula in mind first. Then do more exercises.

There are no requirements for the college entrance examination. But it's also in textbooks...

Learn the ways and means of calculus:

First: In fact, there is still a lot of content to learn in college calculus, which is relatively difficult, and in class, the speed of the teacher's lecture is much faster, and it takes a lot of effort to really understand it.

Second: If you want to learn calculus well, then you must listen carefully to the lectures during class, especially for each part of the teacher's lecture, you must take good notes.

Third: I believe everyone knows that there will be an exam week in college, and some students use this exam week to review, in fact, if you want to learn calculus, after all, you have to rely more on your own review after class, rather than studying temporarily.

Fourth: If you want to learn calculus well, you can also do more test papers, only by doing more can you better understand each knowledge point, and the exam will be much smoother.

Fifth: The review work after class must be done well, and this is when notes come in handy. After reviewing the notes, do the relevant exercises in the textbook and memorize them. Learning never ends, and neither should we stop.

Sixth: Mindset is the most important thing, don't think of calculus as a flood beast. Put your mindset in a good way and face up to the difficulties you encounter in the learning process.

If you don't understand, just ask, teachers, students, they will be happy to help you answer. Don't think of calculus as difficult, as long as you are willing to study and study hard, then you will definitely achieve excellent grades.

Finally, I would like to remind you that you must have a study partner to learn calculus well, because calculus is more difficult and boring. When you encounter problems and knowledge points that you don't understand, you must consult the teacher in time to solve the problem in time, and don't accumulate more and more.

First of all, according to the teacher's requirements, no more, no less, and complete the teacher's tasks in class and after class with high quality. This is the first stage. The teacher's detailed explanations should be carefully calculated, and I have the impression that the Lagrangian median value theorem.

Proof of the Stokes integral formula.

Wait. If the teacher doesn't explain the ins and outs of a theorem in detail, then put it aside for a moment and move it to the second stage.

Because if the content of a math textbook is calculated at 100%, the teacher may only cover 15%-20% of the content in class, so the teacher will skip a lot of theorem proofs, and even some important chapters, which are not covered in the final exam. If you get caught up in it, you will definitely lose time, delay your progress, and end up with bad grades.

At this stage, it is not advisable to do a lot of exercises, and to complete the exercises assigned by the teacher, at most a little practice. Mastering what the teacher wants to teach you in class is fundamental to learning. Test scores don't matter, so I do some exercises that I think are important, and that's a mistake I made back then.

Since you think the exam is easy, why not do it well?

There are two conditions for entering the second stage, first, there is room for learning; Second, do well in math. It's not right to rush into something more advanced without getting the basics right. After completing the tasks of the first phase, start the second phase.

In the second stage, you should expand your horizons, and you need to do a lot of problems to understand the basic abstract concepts of mathematics. Find some good textbooks and workbooks. Former Soviet Union.

Fichgin Goertz has a set of six copies of Calculus.

Tutorial", the content is solid, the questions are also very challenging, and it is a collection of exercises that many great people have laid the foundation for. Equally solid is Richard Courant's Calculus and Mathematical Analysis.

Introduction. The mathematical analysis is followed by complex variable functions.

Analysis and real analysis, these two courses should not be exposed to you, but they are very important to mathematics majors, and real analysis is very difficult, and in some schools you will only learn it after graduate students. Don't worry about the future, just do what you can do well. Finally, if you want to develop in mathematics, you have to go to a more specialized place, and you can't just be general"Hobbies"。

1. The basis of calculus is indefinite integral and definite integral, and the basis of indefinite integral and definite integral is the continuity, limit, and derivative of the function.

2. Then, start to learn indefinite integrals, the key to indefinite integrals is to find the original function of the integrand;

3. To further understand the methods of finding the various limits of functions, the non-conditional extreme value problems are mainly the derivatives of each order, the stationary point, the boundary and other problems, and the calculation of the area, volume and even some physical quantities under nonlinear conditions, such as the center of gravity, gravity, potential energy, etc.;

4. Learn the basic knowledge of multiple integral knowledge and multivariate function differentiation;

5. Learn spatial analytic geometry and series problems.

The key to learning calculus well is to clarify the concepts of limits, derivatives, and integrals. In the process of learning and solving problems, it is necessary to constantly summarize and summarize. Practice more practical problems to enhance your ability to solve problems.

It is recommended to study in combination with the original English books to expand the learning ability.

Be sure to preview the knowledge points in the textbook, listen carefully when the teacher talks in class, read the notes carefully after class, do exercises, and it is best to look at the historical stories of various problems in mathematics, so that you can have a sense of intimacy with these names, and your interest can also be cultivated, and you will slowly feel that mathematics is magical.

To learn any new knowledge, the first thing to do is to understand this knowledge, the teacher should listen carefully when explaining in class, and then the essence of mathematics is to do more questions on the basis of understanding, and it is also necessary to do more questions, and you can't make a choice of aimless brushing questions.

The difference between calculus and high school mathematics is that it involves more formulas, concepts, and methods, while high school has many varied topics and pays attention to innovation, and there are not many knowledge points.

This requires the study of calculus to focus on memorizing formulas and concepts, and grasping the main example questions to cope with college exams.

First of all, understand the concepts, operations depend on laws and formulas, especially the concept of derivatives and limits, and then calculus.

Read books, do more questions, and summarize and summarize. Mr. Su Buqing said: He learned 10,000 calculus before he learned the real calculus. Share!

Doing problems, continuously, to learn step by step, to learn the basic knowledge such as limits and derivatives first, and then learn to find integrals, this is a reverse process, you need to memorize formulas, and you also need to make appropriate use in doing problems.

1. Pay attention to the concept and grasp the origin of each formula theorem, and these derivation methods are also the ideas of doing questions.

2. Find a way to eliminate your fear of mathematics, find some interesting math problems to look at, and build confidence to come back to learn calculus later.

3. Do more exercises, believe that practice makes perfect, and practice more.

4. The key to learning calculus well is to master this analytical language (this is for mathematics majors).

5. First understand the role of calculus and the actual situation, memorize the basic formulas, and have the concept of models in your head.

6. Mathematics trains logical thinking! This is very important.

Calculus

In advanced mathematics, the study of the differentiation and integration of functions, as well as the branches of mathematics related to concepts and applications. It is a fundamental subject of mathematics. The content mainly includes limits, differential calculus, integral science and their applications.

Differential calculus consists of the operation of finding derivatives and is a set of theories about the rate of change. It makes it possible to discuss functions, velocities, accelerations, and slopes of curves in a common set of notations. Integralism, including the operation of finding integrals, provides a general set of methods for defining and calculating area, volume, etc.

The generation of limits

In the third century B.C., Archimedes of ancient Greece implied the idea of modern integralism in his research and solution to the problems of the area of the parabolic bow, the area of the sphere and the crown of the sphere, the area under the spiral and the volume of the rotating hyperbolic body. As far as the limit theory is the basis of differential calculus, it has been relatively clear since ancient times. For example, in the "Tianxia Chapter" of the book "Zhuangzi" written by Zhuang Zhou in China, it is recorded that "one foot of air, half of it is taken in a day, and it is inexhaustible for eternity".

Liu Hui of the Three Kingdoms period mentioned in his circumcision technique that "the cutting is fine, the loss is small, and the cutting is small, so that it cannot be cut, then it is with the circumference and the body without loss." "These are simple, but also very typical concept of limits.

The significance of the founding of calculus

The establishment of calculus has greatly promoted the development of mathematics, and many problems that elementary mathematics was helpless in the past, the use of calculus is often easy to solve, showing the extraordinary power of calculus As mentioned earlier, the establishment of a science is by no means the achievement of a certain person, he must be after the efforts of many people, on the basis of accumulating a large number of achievements, and finally summarized by a person or several people. The same is true of calculus.

Calculus is not just a basic course in engineering schools, but a subject.

There are basic courses in science and engineering, accounting, finance, and even geography, medicine, philosophy, and other majors.

It's not easy to learn it well, what math teacher in primary and secondary school hasn't learned calculus? You take whatever you want.

Give them solutions to calculus problems and see how many of them can solve them right away? To be sure, most of them are rooted.

Ben was powerless.

This is true for math teachers, let alone the average college graduate? Almost more than 95% of college graduates have studied it.

Calculus, a few years after they graduated, almost 99% of them are no longer capable of solving problems, and their excuses are:

I haven't touched it for a long time, and I forgot it."

In fact, the vast majority of college graduates are accompaniments and fun, and they didn't study well in the first place.

Like the vast majority of college students today, their unanimous view was: "Memorize the familiar."

A few formulas will be enough for the exam." This is destined for them to finish their studies in this life.

They are "the front foot has just finished the test, and the back foot is completely forgotten".

The word "calculus" became their bragging rights in front of people who didn't go to college, in front of their children.

Shame, because on the one hand, they say that calculus is not difficult, and on the other hand, they have no ability to solve problems, including many high school teachers.

The same is true for teachers.

A few suggestions: 1. Focus on clarifying the concepts of limits, derivatives (differentials), and integrals. They all involve a process.

2. We must continue to summarize and summarize. Problem solving, induction, interweaving. It's important to think, not to memorize.

3. Only by solving more practical problems can you have understanding and the ability to solve problems.

A common Achilles' heel of the average calculus teacher is that they lack the ability to solve problems.

He majored in theoretical physics, astronomy, meteorology, electrical engineering, hydrology, and physics.

In front of learning, their ability to solve problem problems is almost 0, because many problems, they can't cube.

Cheng and Er will not write the conditions for the solution, because they don't know the specific major except mathematics.

As long as the landlord's ability to solve the problem is formed, you can laugh proudly.

4. It is best to combine English learning, can read the original books, and try not to read Chinese books, because we are domestic.

There are quite a few systematic deviations.

To learn calculus well, you should first master the basic knowledge points in the textbook, understand the homework assigned by the teacher thoroughly, and at the same time do some supplementary exercises appropriately.

Learning calculus is not limited to memorizing formulas or doing problems, in fact, calculus has a very wide range of applications in practical problems in many disciplines. For example, in mathematics, the area of complex geometries is calculated, and in physics, Gauss's theorem is used to calculate fluxes, and so on. You can learn about calculus through concrete examples, so that you can better understand and master calculus.

In addition, we recommend Mathematica, which is also very useful for calculus calculations for the vast majority of integration or differentiation problems that have analytic solutions, and can be found in detail by simply calling Wolfram Alpha.