Learning should be gradual, that is, starting from the existing knowledge and keeping a small enough pace.
The chapters of advanced mathematics are interrelated and promoted layer by layer, and each chapter is the foundation of the next chapter, so we must learn step by step. Only when you really understand this chapter can you move on to the next chapter. Haste makes waste, so you must study chapter by chapter.
Review content of advanced mathematics: Chapter 1: Function and limit, Chapter 2: Derivative and differential, Chapter 3: Differential mean value theorem and derivative application, Chapter 4: Indefinite integral, Chapter 5: Definite integral, Chapter 6: Application of definite integral, Chapter 7: Differential equation, Chapter 8: Vector algebra and spatial analytic geometry, Chapter 9: Differential method of multivariate function and its application, Chapter 10: Multiple integral, Chapter 11: Curve integral and surface integral, Chapter 12: Infinite series.
Through this thinking map, the content of the review of advanced mathematics is roughly broken down as follows:
The related formulas must be memorized, mainly including several basic functional formulas, Lobida's law, mean value theorem, derivative formula, integral formula, differential formula and so on.
Limit is the most important difficulty, so we must attach importance to it and firmly grasp it. Definition of limit, two important limits, L'H?pital's seeking limit, etc.
Taylor formula is also difficult to understand, and the calculation of indefinite integral and definite integral is the focus. If you do more problems, you will be able to skillfully use various formulas, such as round integral differential method, method of substitution and integration by parts, to solve them.
Differential equations and infinite series are also difficulties in learning advanced mathematics, which is the focus of applied mathematics, focusing on understanding and practice.
To learn advanced mathematics well, we should have thorough basic concepts, remember basic theorems, clear basic framework, remember basic common sense and master basic questions.
Mathematics is actually a concept+theorem system, including reasoning, so the understanding of concepts is particularly important. Such as limit, derivative, etc. You should have a vivid understanding of them and remember their mathematical descriptions. Don't just memorize. You can draw a picture for yourself. You can learn more by doing more questions. Learn to establish a basic framework, summarize the outline of knowledge and form mathematical thinking.
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The mind map of sequence, vector algebra and geometric and differential equations is Zhihu!
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Don't believe that a university is incomplete without failure. In this case, grades are really important, at least the upper-middle level, which will give you more choices in the future. Freshman grades are more important. Don't be mindless, skip class and fail the exam. It will be very uncomfortable to fail in the exam, which will not only affect your future mentality, but also lose many opportunities. I hope you won't experience such a painful lesson!
Finally, I hope everyone can learn to be fascinated and pass every exam!
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