191118
目录
日记
- 今天喝了一个亲戚的小孩子的满月酒，对“喝酒”一点兴趣都没有，还是喜欢一个人看看书、玩玩鱼、打打游戏、看看直播、睡睡觉，当然，这段时间的打游戏和看直播是被禁止了。我怎么就变成宅男了，宅男一枚，尴尬，哈哈20:00
- 眼睛很酸，所以练字和专业课学习计划都取消了，想着早点弄完这个，然后早点休息，但是在回顾知识点的时候，眼睛一点都不酸。现在刚结束回顾，酸死了，眼睛都有点疼了，被网瘾废掉的眼睛也不知道什么时候能好一点，以前挖下的坑，以后都需要慢慢补上。睡觉了，晚安。21：29
- 虽然没有人提醒我做这个，但是内心还是有一种压迫感的，担心有人来找我要钱。下午本来就是因为一些事可以找个理由搪塞过去的，但是想到晚上要总结回顾，担心这个逼装不好，强行还是学了点东西，不至于写个无字。21：34
- 今天学习的英语的特殊结构是非常简单的，但是中学就是学不会，就很好的印证了《如何高效记忆》中说的一句话，最好的记忆方法就是（稍有改造）：用心并刻意的去学习、去记忆，而不是我接下来说的一些花里胡哨的方法。用心并刻意能让你有90%，其他的方法可以让你在90%的基础上提升；如果你不用心，也许只有10%，其他方法有2倍作用，也是白搭。21：36
单词
回顾
数学
6.1节 元素法
1.经典积分思想回顾
[egin{aligned}
& 1.\,a = x_0<x_1<ldots<x_n = b; \
& *{[a,b]}=[x_0,x_1]igcup[x_1,x_2]igcupldotsigcup[x_{n-1},x_n]; \
& Delta{x_i}=x_i-x_{i-1}\,(1leq{i}leq{n} \
\
& 2.\,foralldelta_iin[x_{i-1},x_i];\
& Delta{s_i}approx{f(x_i)}Delta_{x_i}; \
& Sapproxsum_{i=1}^n{f(x_i)}Delta_{x_i} \
\
&3.\,lambda=max{Delta_{x_1},Delta_{x_2},cdots,Delta_{x_n}};\
&S = lim_{lambda=0}sum_{i=1}^nf(delta_i)Delta_{x_i}=int_a^bf(x)dx
& end{aligned}
]
2.元素法思想
[egin{aligned}
&1.\,取[x,x+dx]subset[a,b]; \
&2.\,dA=f(x)dx;\
&3.\,A=int_a^bdA=int_a^bf(x)dx
end{aligned}
]
6.2节 几何应用
一、面积
1.单条函数面积
[egin{aligned}
&1.\,取[x,x+dx]subset[a,b]; \
&2.\,dA=f(x)dx;\
&3.\,A=int_a^bdA=int_a^bf(x)dx
end{aligned}
]
2.多条函数重合面积
[egin{aligned}
&1.\,取[x,x+dx]subset[a,b]; \
&2.\,dA=[f(x)-g(x)]dx;quad ext{注：f(x)$geq$g(x)}\
&3.\,A=int_a^bdA=int_a^b[f(x)-g(x)]dx
end{aligned}
]
3.极坐标下求面积
[egin{aligned}
& L:\,r=r( heta);\
&1.\,取[ heta, heta+d heta]subset[alpha,eta]; \
&2.\,dA=frac{1}{2}r^2( heta)d heta;quad ext{扇形面积}\
&3.\,A=int_alpha^eta{dA}=int_alpha^eta[frac{1}{2}r^2( heta)]dx
end{aligned}
]
二、体积
1.旋转函数时的体积-绕x轴
[egin{aligned}
&1.\,取[x,x+dx]subset[a,b]; \
&2.\,dV_x=pi{y^2}dx=pi{f^2(x)}dx;quad ext{圆柱体}\
&3.\,V_x=piint_a^bf^2(x)dx
end{aligned}
]
2.旋转函数时的体积-绕y轴
[egin{aligned}
&1.\,取[x,x+dx]subset[a,b]; \
&2.\,dV_y=2pi{|x||f(x)|}dx; quad ext{看成A4纸的体积}\
&3.\,V_y=2piint_a^b|x||f(x)|dx
end{aligned}
]
3.截口面积已知几何体体积
[egin{aligned}
&截口面积函数为A(x)\
&1.\,取[x,x+dx]subset[a,b]; \
&2.\,dV=A(x)dx;quad ext{看成圆柱体}\
&3.\,V=int_a^bA(x)dx
end{aligned}
]
4.弧长
[egin{aligned}
&1.\,取[x,x+dx]subset[a,b]; \
&2.ds=sqrt{(dx)^2+(dy)^2}=sqrt{1+f'^2(x)}dx;\
&3.l=int_a^bsqrt{1+f'^2(x)}dx
end{aligned}
]
5.参数方程下求弧长(求体积同理)
[L:egin{cases}
x=phi(t)\
y=psi(t)
end{cases}
quad(alphaleq{t}leqeta)
]
[egin{aligned}
&1.\,取[t,t+dt]subset[alpha,eta]; \
&2.ds=sqrt{(dx)^2+(dy)^2}=sqrt{(frac{dx}{dt})^2+({frac{dy}{dt}})^2}dt=sqrt{phi^2(t)+psi^2(t)}dt;\
&3.l=int_a^bsqrt{phi^2(t)+psi^2(t)}dt
end{aligned}
]
英语
7.1节 强调句型
It is ... that ... ，强调句型只需要把强调的部分放入is ... that中间，其余部分不动，需要注意的是强调句型只有两个谓语动词is和was，并且强调句型的框架中的单词毫无意义。
I met my old flame in the yesterday. / It was I that met my old flame in the yesterday.
Because of you, I failed to pass the examination. / It was because of you that I failed to pass the examination.
作文中的任何一句话都可以写成强调句，除了谓语动词之外其余的成分都可以强调。
7.2节 倒装
- 把一句话写成一般疑问句的形式就是倒装，也就是说把一句话的助动词放在句首就是倒装。
- Do you love me?
- Have you been to Japan.
- 否定词用在句首就是倒装，否定词如下有：never、seldom、little、few、scarcely、rarely、by no means
- I will never love you. / Never will I love you.
- Under no circumstances, we can keep a blind eye on the significance of teamwork. / Under no circumstances, can we keep a blind eye on the significance of teamwork.
- So、nor/neither放在句首，表示承前的肯定和倒装
- I can speak Japanese. / So can I speak Japanese.
- I can't speak Japanese. / Nor/Neither can I speak Japanese.
- So...that...的倒装，so引导的部分放在句首用倒装。出现形容词和副词都可以使用so...that...，也就是说可以使用倒装
- My mother keeps so kind that she never kill an ant. / So kind does my mother keep that she never kill an ant.
- Only后跟状语倒装
- I love you deeply. / Only deeply do I love you.
- The phenomenon can be handled by the action above. / Only by the action above can the phenomenon be handled.
- 虚拟语气的倒装：省略if的虚拟语气用倒装
- If every youngster were addicted to surfing on the internet, they would achieve nothing until the end of their life. / Were every youngster addicted to surfing on the internet, they would achieve nothing until the end of their life.
- As引导的让步状语从句，从句的表语可以放在句首构成部分倒装
- As she looks elegant, she is actually a thief. / Elegant as she looks, she is actually a thief.
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