Derivative, differential, etc.
The main contents of integral include definite integral, indefinite integral and so on.
Among them, the most important ones are unary calculus and multivariate calculus, which are also the focus and difficulty of this course. It accounts for 80% of the textbooks, and there are contents with "Advanced Mathematics" (1) test scores above 85. One-dimensional calculus and multivariate calculus are based on limit and study the properties of functions. Differential calculus and integral calculus of unary function are calculus with independent variables of function as variables. Only by mastering unary calculus can we learn multivariate calculus well, and differential equation is the extension and application of calculus. Therefore, if students want to learn advanced mathematics well, they must learn the limit of function and the calculus of unary function well. This part of infinite series is relatively independent, but it is not easy to master. Another key point is the application of mathematics in economy. Students should pay attention to its application in finding extreme value and elastic analysis by using derivative of function.
Calculus is developed in application. At first, Newton used calculus and differential equations to deduce Kepler's three laws of planetary motion from the law of universal gravitation. Since then, calculus has greatly promoted the development of mathematics, as well as astronomy, mechanics, physics, chemistry, biology, engineering, economics and other natural sciences, social sciences and applied sciences. And it is widely used in these disciplines, especially the appearance of computers is more conducive to the continuous development of these applications.
How can we learn calculus well? Here I want to express my personal views, hoping to help you.
1. I think we must understand the textbook. I didn't have time to look at the differential equation for the first time. As a result, I can't do the differential equation part, only 4 points. If I do a differential equation problem with a score of 5, I don't need to take the test again.
2. Be sure to do the exercises at the end of the book, because only by constant practice (especially in science courses) can you improve your problem-solving skills and remember the formulas. After you finish, read the answers at the back of the book to see if you are wrong and where you are wrong. Through analysis, we can try to avoid making the same mistakes in the exam.
3. When reading the textbook, do an exercise after reading the textbook. After reading a chapter, you should pay special attention to the "conclusion" part at the end of the book, review the whole chapter by reading the summary, and master the key knowledge according to the requirements of "Basic Requirements of this Chapter" and "Learning Suggestions". For those unnecessary parts, you can spend less time or give up and focus on what you need. It is recommended to read more summaries, which can make your learning purpose clear and targeted, and you don't have to spend too much time on secondary (non-required) content. After reading each chapter, I will ponder over the summary at the back of the book (it takes about 4 or 5 times to read the summary of each chapter), and then learn the key knowledge in the book after finding the key points, so as to master the key knowledge and do the corresponding exercises.
4. One month before the exam, do several sets of test questions or exercises issued by the teacher, find out the types of test questions, and see which part of the content accounts for more points in the exam. For the part with few scores and great difficulty, you can give up selectively if there is not enough time.
If you have friends around you, please ask questions that you can't do or examples that you can't understand in the book, and try your best to do everything that the book requires you to master. There is no one around to consult, so I discuss with my teacher and improve myself in the discussion.
The above is my personal opinion. In my opinion, the labor paid is directly proportional to the result. Start studying as early as possible and spend more time studying, the greater the chance of success!