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I can recommend a way to learn advanced math online.
The premise is that you must have a set of advanced math textbooks on hand. At the same time, you should have a good foundation in elementary mathematics, so that you may learn faster and more smoothly.
With the above basic conditions, you can learn from the online system.
Cai Gao Hall's high mathematics open class is very good, systematic and detailed, very serious and in place, it can be said that it is tireless, definitely not the kind of pretentious, self-clear people can be compared, but also because the lecture is large and complete, it takes too much time, there is a problem of choice here.
Mr. Cai's high math score is two volumes, the first volume is a unary function, a one-yuan calculus, more than 90 class hours, and it takes three to four months to listen to the general system. But don't feel like a waste of time, once you can stick to it, it's definitely going to be very rewarding.
In addition, if you listen to Mr. Cai Gaoting's ** class, it is best to be careful about the textbooks he relies on, he talks about a lot of example problems, if there is no corresponding textbook, the effect is not very good. Of course, it doesn't have to be.
The reason why I recommend it to you is because I suddenly wanted to use high math last year, but because I have left it for many years, it is almost clean, but I have to use it, and I also follow the recommendation of a friend, and it took about two months (not to listen to all of it, but to listen selectively, but as long as I listen, I will pay full attention and learn all the learning), and the effect is very good. You can try it, but you have to try it for two or three days, and then decide whether to continue or not.
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I wonder why you are studying advanced mathematics? If it's for the graduate school entrance examination, I will figure out every question in Li Yongle's mathematics book, including after-class exercises, if it's for the final exam, I just want to say brother, you think too much, think too early, and it's OK to get old if you have a better relationship with the teacher. Finally, if you really like the kind of high math without any distractions, I suggest you can go to some open classes in high math in Taiwan or abroad, those teachers often explain some concepts very clearly.
Very helpful for my own understanding.
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If a cube with an edge length of 6 cm is submerged in a cuboid tank, then the volume of water drained = the volume of the cube with an edge length of 6 cm = rise 2 cm * length 12 cm * width.
can be derived.
Width = volume of a cube with an edge length of 6 cm (rise of 2 cm * length of 12 cm) = 9 cm.
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Immersion in a cube with an edge length of 6 cm, the volume is 6 x 6 x 6 and the water surface rises 2 cm.
Notice that it is immersion, so it is very simple.
6*6*6 /12x=2
12x is the base area.
So the width is 9 cm.
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The volume of liquid elevation is the volume of the cube, and the width of the cuboid tank = 6 3 12 2 = 9cm
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a^t=a/lna
The logarithm of the base a is taken on both sides.
t=log(a)(a/lna)
Bottom change formula. t=ln(a/lna)/lna
t=[lna-ln(lna)]/lna
t=1-ln(lna)/lna
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Original grip rubber = -x 2sin 2(x) - defense cover (-1 2sin 2(x)) dx=-x 2sin 2(x)+1 2 1 carry skin sin 2(x)dx=cosx 2sinx-x 2sin 2(x)+c
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Take the natural logarithm on both sides, and get - t=-ln2, so t=ln2
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Welcome to it, don't get the answer wrong (.)
This is Bernoulli's equation.
Welcome to it, don't get the answer wrong (.)
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I'm a freshman and I've gone through the college entrance examination, so I have a deep feeling about mathematics, which is summarized as follows
1.The study of mathematics focuses on thinking, and the highest level of mathematics is to draw inferences from one another. It is naturally not easy to achieve this state, my method is to compare different questions applied to the same method, summarize their similarities and differences, and after thinking about it, I will naturally have an extraordinary understanding of it; 2.
Establish a collection of mistakes, specially used to collect your own mistakes, collect armpits into a fur, and take it out when reviewing, your state will reach a very good level, and you will be able to get the ideal results in the exam; 3.Do mock papers before the exam, the test papers are almost the best with the real questions, increase self-confidence and better adapt to the exam room; 4.Flip through the book frequently, immediately recall the vague concept, and make a good mark.
Finally, I would like to say that mathematics requires hard work, you need to think to learn well, and you can make up for the temporary pain of illness by forbearance, and you are a strong man
If you have any specific questions, you can communicate again, and good luck!
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Focus on comprehension, and then practice more to integrate the knowledge points.
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