diary

Just saw a cat, I do not know what causes a broken leg, has been called (rural house cats rarely the case will be called), it must be painful! 10:05
Slowly into the state. 21:00
Back the morning after word diary at night time recording and listen again and again half an hour before going to bed. 21:30
Organize them wearing them ...... 22:17
Finally somehow, but this state is very good, but very hungry (starving, eat mess up biscuits, ha ha), good eye acid, in advance next time to get this, get that done or somewhat useful. 22:44

word

https://www.ximalaya.com/waiyu/31034984/228923599

review

mathematics

5.2 definite integrals Integration by the integration by parts

1. Integration by
\ [f (x) \ in [a, b], \ quad {x} = \ phi (t) satisfy: \\ 1. \ phi (t) is monotonous, and \ phi (\ alpha ) = a, \ phi (\ beta) = b \\ 2. x = \ phi (t) can be turned continuously, the \\ \ begin {align} & \ int_a ^ b {f (x)} \, {\ rm dx} \ overbrace {==} ^ {x = \ phi (t)} \ int_ \ alpha ^ \ beta {f [\ phi (t)] \ phi { '} t} \, {\ rm dt} \ end {align} \]

2. Content will remember. 1:
\ [F (X) \ {C} in [- A, A], (A>), is: \\ \ begin {align} & 1. \ int _ {- a} ^ a {f (x)} \, {dx} = \ int_0 ^ a [f (-x) + f (x)] \, dx \ quad \ text { use integration by x = -t} \\ & derived 2. If f (x) = f (-x ), the \ int _ {- a} ^ a {f (x)} \, {dx} = 2 \ int_0 ^ a {f (x)} \, dx \ \ & 3. If f (x) = - f ( -x), the \ int _ {- a} ^ a {f (x)} \, {dx} = 0 \\ \ end {align} \]

3.必记内容2（推导出3）：
\[ \begin{align} & 1. \int_0^a{f(x)}\,dx\overbrace{==}^{x=-t}\int_0^a \\ & 2. \int_a^b{f(x)}\,dx\overbrace{==}^{x+t=a+b}\int_a^b \\ & 3. \int_a^{a+b}{f(x)}\,dx\overbrace{==}^{x-a=t}\int_0^{b} \\ \end{align} \]

4 will note content. 3:
\ [F (X) \ in [0,1], then: \\ \ begin {align} & 1. \ int_0 ^ {\ frac {\ pi} {2}} f (\ sin {x}) \, dx = \ int_0 ^ {\ frac {\ pi} {2}} f (\ cos {x}) \, dx \ quad \ text { will be referred to using the derived content 2} \\ & 2 . \ int_0 ^ {{\ pi }} xf (\ sin {x}) \, dx = \ frac {\ pi} {2} \ int_0 ^ {{\ pi}} f (\ cos {x}) \, dx \\ \ end {align} \ ]

The contents will be referred to 4:
\ [set f (x) continuously and in a cycle T \\ \ begin {align} & 1. \ int_a ^ {a + T} f (x) \, dx = \ int_0 ^ Tf (x) \, dx \\ & 2. \ int_0 ^ {nT} f (x) \, dx = n \ int_0 ^ Tf (x) \, dx \\ \ end {align} \]

6. Integration by
\ [\ int_a ^ bu \, dv = uv- \ int_a ^ bv \, du \]

7. 5 will note content:
\ [Order I_n = \ int_0 ^ {\ frac {\ pi} {2}} sin ^ nx \, dx = \ int_0 ^ {\ frac {\ pi} {2}} cos ^ nx \, dx, then: \\ \ begin {align} & 1. I_n = \ frac {n-1} {n} I_ {n-2} \ quad \ text { integration by using the derived} \ end {align } \]

8. will note content. 6:
\ [I_n = \ {^ INT_0 \ FRAC {\ {2}}} PI SiN ^ NX \, DX = \ {^ INT_0 \ FRAC {\ {2}}} PI COS ^ NX \ , dx \\ \ begin {align} & 1. I_n = \ frac {n-1} {n} I_ {n-2} \\ & 2. I_0 = \ frac {\ pi} {2}, I_1 = 1 \ quad \ text {SCIENCES derived using the first point and the induction} \\ \ end {align} \ ]

English language

as meaning summary
1. v + ... + as as means of v depends upon the previous
2. as + n as translated as
3. as + sentence as a guide adverbial clause (ignoring attributive clause), as mean (when ... when, because, though ... although, it seems) depends on the meaning of two sentences before and after
than / compare summary
1. not so much as = not even not even: He can not so much as spell a word he could not even spell out a word.
2. not so much A as B A much better to say B: He is not so much a teacher as a poet so much that he was a teacher, but rather that he is a poet.
3. more A than B B so much better to say A: He is more a teacher as a poet so much that he is a poet, but rather that he is a teacher.
4. just more than + n
English grammar summary
1. translate sentence
  1. Go first to a given predicate sentence SVO / table;
  2. Connective find and locate the components conjunction omitted;
  3. Looking noun clauses;
  4. Find attributive, attributive into many small to large attributive and attributive translation in advance;
  5. Find adverbial, adverbial and translation in advance;
  6. Sorting said words, the long sentence into a plurality of small sentences.
2. Attributive clause modifying a noun; appositive noun clause explanation
3. (Shaped) main (fixed / shape) that (tense, voice) Bin / table (set / shape)
4. ~~When they are preparing a examination, ~~ $\,pursing\,stars\,$ ~~ whose singing sounds touching~~ $\,affects\,study\,of\,youngsters.$

Courses

2.1 Definition and basic operation of the linear form

Define a linear table: having the same data type n (n $ \ geq $ 0) finite sequence of data elements, each element adjacent logically, not necessarily physically adjacent.
The basic operation of the linear table:

InitList (& L): initialization table;
Length (L): Table seek length;
LocateElem (L, e): a lookup operation by value;
GetElem (L, i): bit lookup operation;
ListInsert (& L, i, e): insert operation;
ListDelete (& L, i, & e): delete;
PrintList (L): output operation;
Empty (L): Empty judgment operation;
DestroyList (& L): the destruction operation.

Table 2.2 indicates a linear sequence

Define a sequence table: linear sequence storage table, such that the adjacent two logic elements are physically adjacent. The advantage is a random access - can be found in the time specified element O (1) and the first address to the element number, high storage density - the storage node data elements; disadvantage is that insert and delete a large number of elements to be moved.

Static allocation order of Table Type Description:

#define Maxsize 50
typedef struct{
  ElemType data[Maxsize];
  int length;
}SqList;

Dynamic allocation order of Table Type Description:

#define InitSize 100
typedef struct{
  ElemType *data;
  int MaxSize, length;
}SeqList;

L.data = (ElemType*)malloc(sizeof(ElemType)*InitSize) // 为L动态分配内存

NOTE: Dynamic Random Access Mode is still allocated.

Order to achieve the basic operation of the table

Insert

bool ListInsert(Sqlist &L, int i, ElemType e){
  if(i<1||i>L.length+1)
    return false;
  if(L.length>=Maxsize)
    retutrn false;
  for(int j=L.length;j>=1;j--)
    L.data[j]=L.data[j-1];
  L.data[i-1]=e;
  L.length++;
  return true;
}

// 平均时间复杂度O(n)

Deletion

bool ListDelete(Sqlist &L, int i, ElemType &e){
  if(i<1||i>L.length)
    return false;
  e = L.data[i-1];
  for(int j=i;j<Length;j++)
    L.data[j-1]=L.data[j];
  L.length--;
  return true;
}

// 平均时间复杂度O(n)

Find by value

int LocateElem(Sqlist L, ElemType e){
  int i;
  for(i=0;i<L.length;i++)
    if(L.data[i]==e)
      return i+1;
  return 0;
}

// 平均时间复杂度O(n)

Fitness

Ask for leave

calligraphy

English + Chinese copybook half an hour

191116