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We have watched the game for three times. -5. My mother will fly back to China next month. - -## 实意动词的否定/提问/回答 - -使用助动词进行否定 - -在助动词do does did后面加not - -do、does:一般现在时,do一般使用在非第三人称单数的上面,而does使用在第三人称单数上 - -did:一般过去时 - -do not/don't - -does not/doesn't - -did not/didn't - -1. I don't go to school by bus/我不坐公共汽车去学校 -2. She doesn't watch TV everyday/她每天都不看电商 -3. They didn't swim last night/昨天晚上他们没有游泳 - -使用助动词进行提问 - -- He often plays golf. - - Does he often play golf? - - Yes,he does / No,he doesn't -- They go to school by bus. - - Do they go to school by bus? - - Yes,they do / No,they don't -- Sam had breakfast yesterday. - - Did Sam have breakfast yesterday?(这里的had需要变为原型) - - Yes,he did / No,he didn't - -# 使用疑问词进行提问和回答 - -使用疑问词进行提问 - -- when:什么时候 -- where:哪 -- who:谁 -- what:什么 -- how:怎么 -- how long:多长时间 -- how far:多远 -- how often:多长时间一次 -- why:为什么 - -He bought three books yesterday. - -谁买的:Who bought three books yesterday? - -买了什么:What did he buy yesterday? - -什么时候买的:When did he buy three book? - -1. They have been in China for three years. - - How long have they been in China?(将have提到主语的前面) - -2. It is about 4 kilometers from Beijing to Xi'an. - - How far is it from Beijing to Xi'an? - -3. They come to visit me once a week. - - How often do they come to visit me?(这里的do是因为原句中不存在助动词,所以借出一个并让主语后面的动词变为原型) - -4. She came late,because she missed the bus. - - Why did she come late?(这里的come是变为了原型,did是过去时) - -# 名词 - -名词分两类: - -1. 可数名词(countable noun) - - 指数得过来的概念 - -2. 不可数名称(uncountable noun) - - 无法计算的数量或抽象概念 - -- 可数名词:apple,pencil,student -- 不可数名称:salt,coffee,water,history,love - -两个或两个以上的名词,需要变为复数 - -可数名词有单数和复数之分: - -- apple-apples -- pencil-pencils -- tomato-tomatoes - -不可数名称无复数,只用单数表征: - -- salt-salt -- coffee-coffee -- water-water - -名称变复数的规则 - -1. 一般末尾加上后缀-s,friend->friends -2. 以s、z、x、ch、sh结尾的词,在该词末尾加上后缀-es,bus -> buses -3. 辅音字母+y结尾的名词,将y改为i,再加-es,candy->candies -4. 以-o结尾的名词,如果不是外来词或缩写,就加-es,tomato->tomatoes,hippo(河马)->hippos[河马这个单词较长,所以被省略了很多,只加s] - -元音字母:a、e、i、o、u - -辅音字母:其他都是辅音字母 - -外来词:不是英语词汇 - -缩写词:将一段长词汇简略就是缩写词 - - - -可数名词前可以加a(an)或量词 - -- apple - - an apple(以元音字母开头的单词用an表示一个) - - apples - - a box of apples -- tomato - - a tomato - - tomatoes - - a bag of tomatoes - -不可数名称前不可加a(an).没有复数,但前面可以加量词 - -- coffee - - a cup of coffee - -# 指示代词和不定代词 - -- 指示代词:标识人或事物的代词,用来替代前面已提到过的名称 - -- this:这个 - - these:这些 - - that:那个 - - those:那些 - -- 不定代词:指代不确定的人或事物。 - -- one:一个 - - the other:另外一个 - - some:一些 - - any :一些 - - something:某物/事 - - nothing:什么都没有 - -- No one knows where he is.(没有一个人知道他在哪,这里的one不明确) -- x // 中缀表达式转后缀表达式并计算public static String computedInfixResult(List list){    // 初始化两个栈,数栈和结果栈    Stack stack1 = new Stack();    Stack stack2 = new Stack();    for (String val : list) {        if (val.matches("\\d+")){            // 数字载入数栈            stack1.push(val);       }        else{            // 不为数栈            // 则为运算符或小括号            // 判断结果栈是否为空,为空或为小括号就直接加入            if(stack2.isEmpty() || stack2.peek().equals("(")){                stack2.push(val);           } else if (priority(val) == -1) {                // 为小括号,则直接压入栈中                if (val.equals("("))                    stack2.push(val);                else{                    // 右括号                    while (true){                        if (stack2.peek().equals("(")){                            // 当比较后不为(时,进行循环,依次弹出每一个顶上的数据                            stack2.pop();                            break;                       }else {                            // 存入其它运算符                            stack1.push(stack2.pop());                       }                   }               }           } else if (priority(val) >= priority(stack2.peek())){                // 如果新的运算符优先级大于栈顶运算符的优先级的话                stack1.push(stack2.pop());                // 当结果栈不为空时,比较优先级                while (!stack2.isEmpty()){                    if (priority(val) >= priority(stack2.peek())){                        stack2.push(val);                   }else break;               }           }       }   }    while (!stack2.isEmpty()){        stack1.push(stack2.pop());   }    StringBuilder res = new StringBuilder();    int size = stack1.size();    for (int i = 0; i < size; i++) {        res.append(stack1.pop() + " ");   }    return String.valueOf(res.reverse());}​// 返回运算符的优先级,自定,返回的数字越大优先级越高public static int priority(String operation){    if (operation.equals("*") || operation.equals("/")){        return 1;   } else if (operation.equals("+") || operation.equals("-")) {        return 0;   }else{        return  -1;     // 假定的表达式只有加减乘除   }}​​// 将中缀表达式转成对应的Listpublic static List toInfixExpressionList(String s){    // 定义List,存放中缀表达式对应的内容    List ls = new ArrayList<>();    int i = 0;  // 指针,用于遍历表达式中的字符串    String str; // 多位数拼接    char c; // 遍历每一个字符,放入到c中    do{        // 如果c不是数字,就加入到ls        if ((c = s.charAt(i)) < 48 || (c = s.charAt(i)) > 57){            ls.add("" + c); // 不为数字,说明是运算符,直接加入            i++;    // 指针后移       }else{            // 如果是数字,需要考虑多位数的情况            str = "";   // 每一次都需要重置该字符串            while (i < s.length() && (c=s.charAt(i)) >= 48            && (c=s.charAt(i)) <= 57){                // 48 - 57 -> 0 ==> 9                str += c;   // 对数字进行拼接                i++;           }            ls.add(str);       }   }while (i < s.length());    return ls;}java - -# 形容词 - -形容词通常形容人或事物的状态,性质,大小等,通常用在名词前,be动词后 - -- beautiful-the beautiful girl -- The girl is beautiful - -The + 形容词 = 复数名词,表示一类。后面的动词使用复数 - -- old-the old -- young-the young -- The old need more care than the young - -# 副词 - -副词可以修饰动词,形容词,其他副词以及其他结构 - -- He runs fast -- She is very beautiful -- They work very hard - -副词的位置: - -1. 根据情况,放在助动词之后,实意动词之前或之后 -2. 形容词之前,其他副词之前或之后 -3. 多个助动词时,副词一般放在第一个助动词后 - -- He speaks very fast -- They have already left -- They have already been repaired - -常用的频度副词(always,usually,often,sometimes,never)的位置通常放在一般动词前面,be动词后面,助动词和实意动词之间。 - -- They always come early. -- Sam often writes homework at 7:00. - -# 不定量表达法 - -- some:一些 -- any:一些 -- most:大多数 -- every:每一个 -- all:所有的 - -**some,any都表示"一些",some主要用于肯定句,希望得到肯定回答时,也可用在疑问句中,any主要用在否定和疑问句中。** - -- I'd been expecting some letters the whole morning,but there weren't any for me - -**most作形容词时表示大部分的,后面接复数名词** - -- Most people here are from China. - -**every表示"每一个,所有"后面接单数名词** - -- Every one likes the film - -**all表示"所有",后面接可数名词复数,不可数名词单数。** - -- All the cars are parked in the parking lot. -- All the coffee is served on time. - - - -- both:表示两者都,可作形容词,代词,副词 -- either:是两者之一 -- neither:是两者都不 - -1. **Both** his eyes were serverly burned. -2. There are trees on **either** side of the street. -3. **Neither** answer is correct. - - - -- many:修饰可数名词,表示“许多” -- much修饰不可数名词,表示“许多” -- a lot of[lots of],plenty of 均可修饰可数和不可数名词 - -many books、much water - -a lot of/ lots of books / water - - - -- a few:为肯定含义“几个” -- few:为否定含义“没几个” - -以上两个词均可和**可数名词**连用 - -- A few books are put into the box. -- Few books are put into the box - - - -- a little为肯定含义“一点儿” -- little为否定含义“没多点” - -以上两个词均可和**不可数名词**连用 - -- There is a little water in the bottle -- There is little water in the bottle - - - -none和no one的意思相同,主要作代词,翻译为“一个也不,一点也不”,用法稍有区别 - -1. none**可以**接of短语,动词可用单数也可用复数 -2. no one**不能**接of短语,动词只能用单数 - -- No one knows the answer -- None of us have(has) arrived - - - -# There/Here be句型 - -There/Here + (be) 根据上下文,有多种翻译方法,可以翻译成“有”,“这是”,be动词根据后面的名词有单复数变化 - -- There is a book on the bookshelf. -- There are some books on the bookshelf. -- Here is the bus stop. -- Here are your books. - - - -# 一般现在时和现在进行时 - -一般现在时,表示通常性、规律性、习惯性的状态或者动作。主语是单数第三人称时,动词有单三的变化,主语是非第三人称单数时,动词变为原形 - -1. They often get up at 7:00. -2. He often gets up at 7:00 - -一般现在时,动词的单三变化: - -1. 在动词尾直接加s - - 如:play-plays - -2. 以字母s、x、ch或o结尾的动词加-es,如:guess-guesses - -3. 以辅音字母+y结尾的动词,先变y为i,再加-es,如:study-studies - -- 一般现在时否定和疑问句用do,does帮助构成 - 1. He doesn't like the car.(does用在单三上,do用于非单三) - 2. Does he like the car ? - - Yes,he does./No he doesn't - - - -现在进行时表示现在正在进行或发生的动作。句子通常有now等时间副词呼应,基本构成形式为**be + doing** - -1. They are watching TV. -2. He is watching TV. -3. I am watching TV. - - - -动词现在分词的变化规则: - -1. 一般情况下,直接在动词后加-ing,如:work - working -2. 动词以不发音的 -e 结尾,要去e加Ing,如:take - taking -3. 重读闭音节的动词,要双写词尾字母,再加 -ing,如:cut - cutting -4. 以-ie结尾的动词,变y再加-ing,如:lie - lying - - - -现在进行时变否定句和疑问句时,将be动词否定或提前 - -1. They aren't watching TV. - - Are they watching TV? -2. He isn't watching TV. - - Is he watching TV? -3. Am I watching TV? - - Yes,you are / No,you aren't. - -# 一般过去时和过去进行时 - -一般过去时表示过去某个时间里发生的动作或状态;过去习惯性、经常性的行为 - -- 基本结构:主语+动词过去式+其他,一般动词在动词后面加ed,还有一些不规律动词不规则变化 - -- play-played、come-came - 1. He worked very hard last night. - 2. They came here by car. - -动词一般过去时变化规则: - -1. 一般在动词后加-ed。如:play-played -2. 在以字母e结尾的动词后,只加-d。如:like-liked -3. 在以"辅音字母+y"结尾的动词后,改y为i,再加-ed。如:supply-supplied -4. 在以重读闭音节结尾且末尾只有一个辅音字母的动词后,双写最后一个辅音字母,再加-ed。如:plan-planned - - - -过去进行时表示在过去某一时刻或某一时间内进行或发生的动作。 - -其形式为was / were + doing - -1. They were waiting for you. -2. He was talking with his friends just now. - -# 将来时 - -一般将来时表示将来某一时刻的动作或状态,或将来某一段时间内经常发生的动作或状态。常常和表示将来的时间状语连用。 - -- tomorrow(明天) -- next week(下周) -- int the future(将来) - - - -”助动词will或shall + 动词原形“,表示将来发生的事情。 - -1. They will go to Shanghai by ship tomorrow. -2. We shall leave for Shanghai in next month. - - - -"be going to + 动词原形"用来表示近期或事先考虑过的将要发生的动作以及已有迹象表明必将发生某事,意为“打算;就要”。 - -- They are going to play football this afternoon -- She is going to learn French next year. - - - -“be doing”表示位置转移的动词。如:go,come,leave,start,arrive,可用现在进行时表示将来时。 - -1. They are leaving for Japen. -2. She is arriving tomorrow. - -# 完成时 - -现在完成时(have + p.p.[过去分词]),动作过去发生,已经完成,对现在造成影响或后果,动作可能还会持续,可使用的时间状语为:already(已经) 和 yet(还) - -1. They have already arrived in Shanghai. -2. She has played soccer for 3 hours.(这里的has是根据单三的形式发生变化) -3. She hasn't finished the homework yet. - - - -过去完成时(had + .p.p),表示句中的动作发生在过去之前,即过去的过去,已经完成,对过去造成了一定的影响或后果 - -1. They had arrived in Shanghai. -2. She had played soccer for 3 hours. -3. They hadn't finished the work yet. - - - -# 动词用法 - -动词根据功能分为四类 - -- 实意动词(Notional Verb) -- 系动词(Link Verb) -- 助动词(Auxiliary Verb) -- 情态动词(model Verb) - -1. 动词有数量和时态的变化,时态通常有三大时态:现在,过去和将来时 -2. 根据动作进行的状态可分为:一般时,进行时和完成时 -3. 使用动词时通常将(1)和(2)结合。例如:一般现在时,过去进行时 - -- He goes to school every day. -- He went to hospital last night. - -image-20240508192138589 - -# 情态动词 - -1. can/could 表示能力,用be able to代替can/could 现在/过去的能力客观可能性(can的可能性大),表示请求和允许 - - - -- He can/could/is able to swim. -- He can/could come tomorrow. -- Can/could I stay here? - - - -1. may/might 表示可能性,may的可能性大,在请求、允许中might更委婉 - -口语中常用的回答: - -- Yes,please. -- No,you can't/mustn't(禁止,不准) - - - -1. He may/might come here by bus. -2. May/might join you? - - Yes,please/No,you can't/No,you mustn't diff --git "a/docs/assets/\350\213\261\350\257\255\350\257\255\346\263\225-DhlN2-Wa.md" "b/docs/assets/\350\213\261\350\257\255\350\257\255\346\263\225-DhlN2-Wa.md" new file mode 100644 index 0000000..6bfb46f --- /dev/null +++ "b/docs/assets/\350\213\261\350\257\255\350\257\255\346\263\225-DhlN2-Wa.md" @@ -0,0 +1,814 @@ +--- +title: 英语语法 +abbrlink: 81c4e30a +date: 2024-04-25 19:48:01 +tags: English +categories: + - 基础知识 +description: 英语语法 +--- + + + + + +# 单词速记 + +source 源头 + +growth 成长 + +all things 万物 + +resource 资源 + +cost .n:费用 .v:花费 + +resident citizens 居民 + +uniform 校服 制服 统一的 清一色的 + +catch a cold 感冒 + +fail in 在某方面失败 + +succeded in 在某方面成功 + +# 句子成分 + +在英语中,有八大句子成分,分别是:主语、谓语、宾语、表语、定语、补足语、同位语和状语。 + +其中主要的成分是主、谓、宾,次要的成分是表语、定语、补足语、状语和同位语 + +谓语分为Vt和Vi,分别为及物动词和不及物动词 + +## 主语 + +是一个句子所要说明的人和事物,是一句的主体。(一般位于句首) + +作主语的有:名词、代词、数词、不定式、动名词和主语从句 + +动作的发出者是主语 + +the + .adj(表示一类人或一类物)---考点 + +the + .adj(表示一类人)的话[此时如果它作为主语,那么就是主语从句,此时谓语动词就需要变为复数] + +the + .adj(表示一类物)的话[谓语动词就要用到单数的形式] + +形容词没有单复数 + +It is + adj. + for sb(可省略) + to do + +with就远原则,主谓一致 + +be going to do :将要做某事,将来时 + +not only xxx but also xxx、eithor or、neithor nor就近原则,主谓一致 + +动词不能做主语,出现多个动词要么变成非谓语,要么变成从句 + +## 谓语 + +说明主语的动作或状态。常用动词或动词词组担任,放在主语后面,通常有简单谓语和复合谓语。 + +简单谓语:由单个动词或动词词组充当谓语 + +复合谓语:由情态动词或者其他助动词+动词构成,或由系动词+表语构成,系动词单独不做谓语 + +1. You should clean the house.(情态动词+动词) +2. You look beautiful today.(系动词+表语) +3. My brother is reading a book. (助动词+动词) +4. He has finished homework.(助动词+动词) + +burst into laughter(突然大笑) + +burst into tears(突然大哭) + +and but or并列连词,前后连接的东西要一样,如果前面是个句子,后面就需要是个句子 + +祈使句谓语把动词原形放在开头,省略主语you + +非谓语有ing、to do、done形式 + +## 宾语 + +表示动作的对象,是动作的承受者。宾语一般放在动词或动词短语之后。介词后也会跟宾语。 + +refused to do sth:拒绝做某事 + +cooperate with sb:与某人合作 + +succeed in:在某方面取得成功 + +介词后面要加动词的ing + +**双宾语和宾补** + +宾补:宾语补足语,只补充说明宾语的动作、身份、状态 + +I bought my mother a gift. +主 谓 宾 宾 +We made him a teacher. +主 谓 宾 宾补 + +区别 + +双宾:mother !=a gift两者中间无联系 + +宾补:两者之间有联系,him可以是teacher + +be to do:将来时 + +pay attention to:注意 + +## 定语 + +单词作定语时通常放在它所修饰的名词之前,短语和从句作定语时则放在它所修饰的名词之后 + +a || an || the adj. n.句型 + +## 状语 + +状语用来修饰动词、形容词、副词或者是全句,说明方式、因果、条件、时间、地点、让步、方向、程度、目的等 + +so that 如此,以至于 + +managed to do:设法做某事 + +because + 句子 + +because of + 词或者短语、ing + +## 补语 + +英语有些及物动词,除了要有宾语之外,还要加上宾语补足语,才能使句子的意义更加完整。它起补充说明宾语要干什么,怎么样的作用 + +in good order:井然有序 + +broken in:闯入 + +break up:分手 + +break out:爆发 + +break down:出故障 + +sometimes 有时候 + +some times 几次 + +some time 一些时间 + +sometime某个时候 + +## 表语 + +放在系动词之后。是用来说明主语的性质、特征、状态与身份。表达主语具体情况。 + +不可数:little 几乎没有;a little 有一点 + +可数:few 几乎没有;a few 有一点 + +## 同位语 + +同位语是在名词或代词之后并列名词或代词或名词短语对前者加以说明的成分,近乎于后置定语。 + +# 名词 + +## 特殊规则 + +名词+s是复数,动词+s是单数 + +大多数情况,元音字母用an,辅音字母用a + +少数情况:universe -> a + +- an + - hour + - honest + - honor + +do 后面需要用动词的原型 + +## 可数名词规则变化 + +一般可数名词直接在词尾+s + +看到s、x、ch、sh结尾,加es + +一般情况下o结尾,有生命加es,无生命加s + +以f或者fe,变ves + +看到元音+y,直接加s;看到辅音+y,变ies + +专有名词直接加s + +如果是合成词(由多个单词组成的词),比如Englishman,可以被拆分成English man,那么就让表示人的单词变为复数,说明让man变为复数,也就是说变为Englishmen + +germ 细菌 萌芽 + +## 可数名词不规则变化 + +1. 元音变化 + - woman women + - tooth teeth + - wife wives +2. 词尾变化 + - child children + - ox oxen +3. 单复数同形 + - sheep + - Japanese + - Chinese + - fish + - deer +4. 只有复数形式的名词 + - scissors(剪刀) + - trousers(裤子) + +## 名词所有格 + +名词所有格表示所有的关系意为“........的” + +- 有生命 + - 单数名词后+'s + - 以s结尾的复数 + ' +- 无生命 + - 名词A + of +名词B + +A+B's + n(单数) + v(单数) + +A's+B's+n(复数) + v(复数) + +people -> 人 变为单复数同型 + +people -> 名族|部落 a people || two peoples + +borrow 别人借给自己(借入) + +lend 自己借给别人(借出) + +# 冠词 + +a/an(不定冠词):第一次出现 + +the(定冠词):上文提到过 + +the:这个,那个 + +a/an(元音字母结尾使用):一个,一种 + +a/an 是表示:数量“一” + +a/an也是表示一类人或一类事物 + +a用于以辅音音素开头的单词前 + +an用于以元音因素开头的单词前 + +辅音(特殊):a boy a dog a university + +元音(特殊):an apple an hour + +不定冠词(a/an)一般是泛指,定冠词(the)一般是特指 + +## 定冠词(the) + +1.表示特指某些人或事物 +2.用于序数词前 +3.用于乐器名词前 +4.用于最高级前 +5.用于世上独一无二的事物面前 +6.用于姓氏复数前,表示“一家人” +7.用于形容词前,表示“一类人” + +the a of b + +## 不加the的情况(零冠词) + +在表示三餐、球类运动、游戏等的名词前 +(1) have breakfast/lunch/dinner +(2) play basketball/footbal +(3) play games + +在国名、城市、地名、人名等专有名词前 +China +Shanghai +Beijing +Tom + +在不可数名词前 +I want to eat rice.我想吃米饭 +I want to drink a cup of tea.我想喝杯茶 + +在节假日、季节、星期等名词前 + +Today is Sunday.今天是星期天 +National Day falls on October 1st.国庆节是在10月1号 +Spring is very warm.春天非常温暖 + +在称呼语、官职、头衔等名词前 + +Uncle Sam + +共有是A+B's + 单数 + +各有A's+B's + 复数 + +# 动词 + +表示状态或动作的词叫动词 + +实义动词 +表示行为、动作或状态的词,具有实在的意义,又称为行为动词。如:play,,give,listen + +助动词 + +帮助实义动词构成各种时态的动词,如:do,does, did,will + +情态动词 +表示说话人情感和态度的词,后面接实义动词原型。如:如:can,may,must,need + +系动词 + +用来帮助说明主语“是什么”或“怎么样”的动词,如:be,look,smell,taste, sound,feel,become, get + +## 动词的基本形式 + +动词原形 .v +第三人称单数现在式 .v+s + +现在分词 .v+ing +过去式 .v+ed +过去分词 .v+ed + +## 三单变复数规则 + +- 一般动词,词尾直接十s; +- 以s/x/o/ch/sh 词尾+es; +- 以辅音字母十y结尾的动词,词尾变y为i+es. +- a,e,I,ou 是元音字母,其他都是辅音字母 + +- 特殊变化 + +## 动词现在分词 + +一般动词,词尾直接+ing; +以不发音e结尾动词,去e+ing; +以辅元辅结尾动词,双写词尾辅音字母+ing +以-ie结尾的动词,变ie为y再加ing + +lie 表示说谎时的过去式或过去分词 lied lied + +lie 表示躺的过去式或过去分词 lay(下蛋) lain + +tie 做名词表示领带,动词的ing表示系 + +## 动词过去式和过去分词 + +一般动词,词尾直接+ed; +以e结尾动词,词尾+d; +以辅音字母十y结尾的动词,词尾变y为i+ed. +以辅元辅结尾的动词,双写词尾辅音字母十ed + +leave 的过去式 left + +lose 的过去式 lost + +go 的过去式 went + +go 的过去分词 gone + +run 的过去式 ran + +run 的过去分词 run + +come 的过去式 came + +come 的过去分词 come + +fly 的过去式 flew + +fly 的过去分词 flown + +see 的过去式 saw + +see 的过去分词 seen + +swim 的过去式 swam + +swim 的过去分词 swum + +buy 的过去式、过去分词 bought + +## 双写规则 + +**辅元辅,结尾重读** + +let letting + +run running + +swim swimming + +shop shopping + +**辅元辅,结尾不重读** + +listen listening + +visit visiting + +**我想要不wxy** + +know knowing + +grow growing + +mix mixing + +buy buying + +play playing + +其他情况 +quit **quitting** 停止;放弃 +quiz **quizzing** 小测试 +equip equipping 装备 +forget forgetting 忘记 +regret regretting 后悔;遗憾 +begin beginning 开始 +permit permitting 允许 +admit admitting 承认 +forbid forbidding 禁止 +prefer preferring 宁愿;更喜欢 +refer referring 涉及;参考;查阅 +occur occurring 发生 + +![image-20241218140936382](https://s2.loli.net/2024/12/18/nqDayo8XeW3vVYs.png) + +# 介词 + +介词是英语中很活跃的词,也是介词 prep.(preposition) + +位置:一般置于名词之前 + +它常和名词或名词性词语构成介词短语 + +beside 在...旁边 + +into 在里面 + +out of 在外面 + +among 在...中间(三个及以上) + +past 通过 + +across 穿过 通过 + +along 沿着 + +through 通过(从内部通过) + +**at + 较短的时间 < 1 day(日出日落)** + +**on + 日期(具体时间) / 星期 / 节日 = 1 day(具体时间)** + +**in + 周 / 年 / 季节 / 早中晚 > 1 day(较长时间)** + +in 在...里面 + +on 在...上面(接触表面) + +under 在...下面 + +behind 在...后面 + +in front of 在...前面 + +above 在...上面(不接触表面,不一定在正上方) + +below 在...下面(不接触表面) + +between 在...中间(两者) + +next to 挨着,在...旁边 + +image-20241218164254699 + +at用于表示一个较小的场合 +in表示在较大的地方;在...的里面 +on表示在...之上,强调与某物体有接触 +under强调在某物的下方,完全覆盖两物体表面可以接触也可以不接触 +between表示两者之间 +behind表示在...后面 +in front of表示在...前面 +up表示往上 down表示往下 +near表示有一定距离,只是对于说话者来说是在附近 + +# 连词 + +## 并列连词 + +前后语法地位一致 + +**表示并列关系 and** + +and(和,并且) +I like blue and black. +Tom and Jerry are good friends. +and:用来连接并列的词、词组或句子 + +**表示选择关系 or** + +or(表示“或"“否则”,表示选择或转折) + +Which do you like better, apples or pears?(在疑问句中表示选择) + +He doesn't like milk or juice.(在否定句中表示并列) + +Get up,or you'll be late. + +and通常用在肯定句中,而or通常用在否定句疑问句中 + +**拓展** + +eithor or、neither nor、not only but also就近原则 + +Study hard, or your math will be worse. +(努力学习,否则你的数学成绩将会很差) +Study hard,and your math will be better +(努力学习,那么你的数学成绩将会很好) + +and和or都可以在祈使句中使用 + +“and +句子" 通常是比较好的结果,意思是"...那么就会" +‘or+句子" 则表示不愉快不理想的结果,意思是"...否则就会" + +or 用于疑问或否定句,and用于肯定句 + +**表示转折关系 but** + +but(但是,可是) + +**表示因果关系 so** + +because(因为) + +so(所以) + +because 和 so不能同时出现在句子里 + +## 从属连词 + +引导从句 + +# 代词 + +image-20241219154845508 + +## 人称代词 + +为了避免重复,用来代替前面所提到的人或者物等的代词 +它有两个选择:主格和宾格 + +主格 发出动作,宾格 动作承受者 + +主格:在句子中作主语(一般用在动词前)。 + +宾格:在句子中作宾语。(动作的承受者,多用于动词、介词后) + +## 物主代词 + +形容词性物主代词(形容词) + +名词性物主代词(名词) + +## 代词总结 + +主 宾 形容词性物主代词 名词性物主代词 + +image-20241219162428109 + +# 反身代词 + +表示反射或者强调的代词,表示某某自己;当主语和宾语为同一物时,表反射;当其位置在名词、代词之后,或位于句尾,表强调。 + +我 -- myself + +你 -- yourself + +他/她/它 -- himself/herself/itself + +我们 -- ourselves + +你们 -- yourselves + +他们 -- themselves + +# 指示代词 + +用来指代或标记人或物的代词 +有4大家族: +this(这个) +that(那个) +these(这些) +those(那些) + +this和that后接的谓语动词为单数形式, +these和those后接的谓语动词为复数形式。 + +this和these常用来指代空间上较近的人或物,that和those常用来指代空间上较远的人或物 + +Tips:打电话时,用this指代自己;如果要问对方是谁,通常用that. + +# 数词 + +## 考点 + +①表示概述/不确定的数字,+s:hundreds of 成百上千、dozensof/scores of很多 +②表示确定的数字,不+s:threehundred、threedozen +③“基数词+连字符+名词"可以构成复合形容词,表示数量,此时名词应用单数形式。 +a two-dayaftivity(=two daysactivity)为期两天的活动 +a three-hour drive (=three hoursdrive)三小时的车程 +an-hour trip (=an hour’s trip)一小时的旅途 +a?n→中间是缺了→形容词 +①in one’s twenties +in the1820s/1820's +everytwohours=every secondhour“每两小时/每隔一小时” +The second time第二次a second/third/forthtime又一次;再一次 +③“名词+基数词"可以表示书页、房间、住所等的编号及邮政编码,电话等,此时首字母常大写。另外表示编号时也可用“the+序数词+名词”,此时首字母不用大写 + +在英语当中我们的数词分为基数词和序数词两类。 +**基数词**就是我们平时熟知的数字数量而**序数词**则表示次序 + +描述数量的多少称为基数词 + +13~19 后缀+teen + +20~99 整10位:后缀+ty + +非整十数:整十位数 + 个位数,例如21,twenty one + +100~999 整百位数:后 + hundred +非整百位数:整百+整十+个位数 例如121 one hundred and twenty one + +注意13、15、18的基数词构成 +13:thirteen +15:fifteen +18:eighteen + +非整十位数:整十位和个位数之间需要有连线符 +22: twenty-two +非整百位数中:百位数和十位数之间用and连接 +122:one hundred and twenty-two + +序数词:表示次序的数词称为序数词,在汉语中表示“第几” + +4~19 +基数词后缀+th表示“第” + +20~99 +整十位数:变y为 ie+th; +非整十位数:个位数用序数词 + +百位以上 +结尾处变为序数词即可 + +1-20的序数词如下图所示 + +image-20241219204009524 + +# 形容词 + +形容词在句中用来修饰和描述名词和代词 +形容词是表示人或事物性质、状态和特征的词,一般表示.....的 + +形容词在句中一般放在名词之前; +形容词在句中也可放在am,is,are,was,were之后 + +形容词的同级、比较级和最高级:多数形容词都可以用于比较、说明事物间的等级、程度差别。 +形容词比较构成 +a.大部分形容词:词尾加er或est + +b.以e结尾的形容词:词尾加r或st + +c.以重读闭音节结尾,且结尾只有一个辅音字母的形容词:双写这个辅音字母,再加er或est + +d.以辅音字母+y结尾的形容词:变y为i,再加er或est + +e.两个或两个以上音节的形容词:+比较级的原级 + +**不规则变化的形容词** + +原型-比较级-最高级 + +many-more-most + +much-more-most + +few-fewer-fewest + +little-less-least + +用法小贴士: +many与few用与可数名词前, +much与little用于不可数名词前 + +## 比较级的用法 + +形容词比较级+than+对比成分:表示“..比...更. + +e.g.篮球比排球大 +A basketball is bigger than a volleyball. + +同级比较:形容词的原级也同样可以用于比较 +肯定:as +形容词原级+as表示.......样 +e.g. He is as tall as his brother. + +否定:not as+形容词原级+as表示“不如" +e.g.The vase is not as good as this. + +the + 形容词最高级+(名词)+比较范围:表示“..最..” -> 三者及以上 + +The older the wiser. +人老智多,姜还是老的辣 +Blood is thicker than water. +血浓于水 +Two heads are better than one. +人多智广/三个臭皮匠顶个诸葛亮 +East or west, home is the best +金窝银窝不如自己的草窝 +Experience is the best teacher. +实践出真知 +He knows most speaks least. +大智若愚 + +# 副词 + +副词独白:简写为adv + +是表示时间、场所、状态、频率、疑问及程度等的词。 + +一般是由相应的形容词加ly构成的。 + +副词是可以用来修饰词,词组或整个句子。 +副词位于形容词/副词的前面,动词的后面 + +形容词变副词 +1 直接在形容词后加 ly +如:quiet quietly slow slowly +2 以辅音字母加y结尾的形容词,要先将y变成i,然后再加ly +如:happy happily busy busily +3有些形容词和副词形式完全相同,如:hard,early + +时间副词 then, next, already, finally, today, soon. +频率副词 often, usually, never, frequently, always +疑问副词 how, when, where, why.. + +# 一般将来时 + +I am going to do something. +I am going to wash car/clothes tomorrow +be going to do -> 一般将来时 + +一般将来时表示单纯的将来事实。 +主语后通常有助动词will + 动词原形构成以及对应be动词+going to+动词原形 + +主语 + be going to +动词原形+…=肯定句 +主语+be not going to +动词原形+ ..=否定句 +be +主语+going to+动词原形=一般疑问句 + +一般将来时状语 + +in+将来时间 +in 2020、in 2025、in the future + +next+时间 +next Monday、next year、next week + +不规则 + +tomorrow、from now on、soon + +be going to +一般指已经计划好的事情,强调某个意图,是经过事先考虑好的 + +will + +指主语本身愿意做的事情,没有经过事先考虑,而是在说话的当时临时想到的 + +be going to +表示近期眼下就要发生的事情。 + +will + +表示的将来时间则较远一些 + +will + +主语猜测或希望等内心活动,想得到肯定的、将会发生的事情 + diff --git "a/docs/assets/\350\213\261\350\257\255\350\257\255\346\263\225-u3bQeiWv.js" "b/docs/assets/\350\213\261\350\257\255\350\257\255\346\263\225-u3bQeiWv.js" deleted file mode 100644 index 296fde3..0000000 --- "a/docs/assets/\350\213\261\350\257\255\350\257\255\346\263\225-u3bQeiWv.js" +++ /dev/null @@ -1 +0,0 @@ -const e=""+new URL("英语语法-D4yVjXnE.md",import.meta.url).href;export{e as default}; diff --git "a/docs/assets/\350\256\241\347\256\227\346\234\272\345\237\272\347\241\200-TMY6W8Wt.js" "b/docs/assets/\350\256\241\347\256\227\346\234\272\345\237\272\347\241\200-TMY6W8Wt.js" new file mode 100644 index 0000000..c8b80d5 --- /dev/null +++ "b/docs/assets/\350\256\241\347\256\227\346\234\272\345\237\272\347\241\200-TMY6W8Wt.js" @@ -0,0 +1 @@ +const u="data:text/markdown;base64,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";export{u as default}; diff --git "a/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-5K1Er9R7.js" "b/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-5K1Er9R7.js" new file mode 100644 index 0000000..cea48d4 --- /dev/null +++ "b/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-5K1Er9R7.js" @@ -0,0 +1 @@ +const t=""+new URL("高等数学-7zGgIytn.md",import.meta.url).href;export{t as default}; diff --git "a/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-BqeUsWg8.md" "b/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-7zGgIytn.md" similarity index 73% rename from "docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-BqeUsWg8.md" rename to "docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-7zGgIytn.md" index f2f8c77..437e1be 100644 --- "a/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-BqeUsWg8.md" +++ "b/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-7zGgIytn.md" @@ -112,7 +112,7 @@ cos是邻边比斜边 特殊值及图像 -![image-20240807215332157](https://s2.loli.net/2024/08/08/6FgbuIApzlsZPBR.png) +image-20240807215332157 ### tanx @@ -120,21 +120,21 @@ tanx是对边比邻边 特殊值及基本情况 -![image-20240807215650531](https://s2.loli.net/2024/08/08/2bFtBzsmMc97Uue.png) +image-20240807215650531 tanx图像 -![image-20240807215829893](https://s2.loli.net/2024/08/08/k48lKhpgneX5rf6.png) +image-20240807215829893 ### 三角函数公式 image-20240807220724828 -![image-20240807220702872](https://s2.loli.net/2024/08/08/97u3aUbAtPIEWcY.png) +image-20240807220702872 ### 和差化积 -![image-20240807220545556](https://s2.loli.net/2024/08/08/Orvl9RXb4CS7zD8.png) +image-20240807220545556 ### tan公式 @@ -146,35 +146,35 @@ tanx图像 #### arctanx图像 -![image-20240807221236827](https://s2.loli.net/2024/08/08/uBn7i3lOSTAv1VC.png) +image-20240807221236827 #### 特殊值 arcsin、arccos、arctan与sin、cos、tan相同 -![image-20240807221540546](https://s2.loli.net/2024/08/08/qgpbce8rVv6yTBR.png) +image-20240807221540546 # 因式分解 -提公因式 +## 提公因式 image-20240808204732462 -公式法 +## 公式法 image-20240808205149676 -十字相乘法 +## 十字相乘法 image-20240808205424908 -找根法 +## 找根法 -![image-20240808210315474](https://s2.loli.net/2024/08/08/WhAK1UyF9Gp37cf.png) +image-20240808210315474 # 常见不等式解法 -![image-20240808212741215](https://s2.loli.net/2024/08/08/cL72k4FCrRptEM5.png) +image-20240808212741215 ## 分式不等式 @@ -301,7 +301,7 @@ arcsin、arccos、arctan与sin、cos、tan相同 常见有界:sin、cos、arctan -![image-20240813210845806](https://s2.loli.net/2024/08/13/B1FADLPHrjKeEoI.png) +image-20240813210845806 0乘有界=0 @@ -313,7 +313,7 @@ arcsin、arccos、arctan与sin、cos、tan相同 ## 第二重要极限 -![image-20240814210457482](https://s2.loli.net/2024/08/14/VxGYN25lqQf4X6e.png) +image-20240814210457482 image-20240814211811921 @@ -418,23 +418,23 @@ f(x0) = 左极限 = 右极限 = 连续 常用公式 -![image-20240920220853858](https://s2.loli.net/2024/09/24/SOU8daiqyoNpbCQ.png) +image-20240920220853858 -![image-20240920220944107](https://s2.loli.net/2024/09/24/leNopjiVMhrXzsH.png) +image-20240920220944107 例题 -![image-20240920221140608](https://s2.loli.net/2024/09/24/vSl61NBcF2yd5KH.png) +image-20240920221140608 导数相乘和导数相加减不同 -![image-20240920221403043](https://s2.loli.net/2024/09/24/dtLjJCI8xgm34yH.png) +image-20240920221403043 -![image-20240920221707297](https://s2.loli.net/2024/09/24/vWmpXe5uGjA8Fob.png) +image-20240920221707297 导数相除 -![image-20240920221810272](https://s2.loli.net/2024/09/20/AktVQRm9n4TJFgO.png) +image-20240920221810272 ## 复合函数求导 @@ -446,11 +446,11 @@ f(x0) = 左极限 = 右极限 = 连续 复合函数乘法求导 -![image-20240921205725441](https://s2.loli.net/2024/09/24/sOvwZDrBPoRNUEa.png) +image-20240921205725441 ## 幂指式求导 -![image-20240921210927100](https://s2.loli.net/2024/09/24/cI6xitPAuvo8lSV.png) +image-20240921210927100 计算完成后,改写为原式子 @@ -458,13 +458,13 @@ f(x0) = 左极限 = 右极限 = 连续 例: -![image-20240921212319313](https://s2.loli.net/2024/09/21/TCALpuhKOk28FZD.png) +image-20240921212319313 ## 隐函数求导 隐函数的二阶导直接对一阶导再次求导即可 -![image-20240924205027272](https://s2.loli.net/2024/09/24/Yxl6LuU83FkQIgs.png) +image-20240924205027272 方法 @@ -472,9 +472,9 @@ f(x0) = 左极限 = 右极限 = 连续 例题 -![image-20240924211306480](https://s2.loli.net/2024/09/24/7LW4Nvy8Y6QjVga.png) +image-20240924211306480 -![image-20240924212123558](https://s2.loli.net/2024/09/24/zyGMQWkBXZg1dmj.png) +image-20240924212123558 ![image-20240924213334439](https://s2.loli.net/2024/09/24/NCn6P5wgLmBG4KH.png) @@ -564,7 +564,7 @@ Cxx的求解方式 ## 微分计算 -![image-20241028215055400](https://s2.loli.net/2024/10/28/mZsqjYRKFE3xudH.png) +image-20241028215055400 ![image-20241028215221699](https://s2.loli.net/2024/10/28/YgEIyqJT9RaWf75.png) @@ -1048,3 +1048,250 @@ Cxx的求解方式 ### 齐次式 +解法:换元 + +image-20241129152238603 + +### 伯努利方程 + +解法 + +image-20241129154824038 + +image-20241129154929242 + +## 二阶微分方程 + +### 右侧为0求通解 + +解法 + +image-20241130211023114 + +### 右侧为0求特解 + +特解就是在通解的基础上把xy的值带入求出c1,c2,然后回带即可 + +image-20241130220656082 + +### 右侧不为0求通解(第一类) + +image-20241130223640020 + +根据类型设特解形式 + +image-20241130223609211 + +求出y*对其求导就可以得到原式带入解出其他结果值 + +### 右侧不为0求通解(第二类) + +解法,有点乱 + +总结下来就几步:找出A+bi,先求`y*`,所以要求出对左侧求导为0的结果,带入公式,算出r和a+bi之间的关系,根据关系算出`y*`的公式,求导回带到之前的式子里的二阶导计算,算出真正的`y*`,接着算出Y,带入式子计算即可 + +image-20241130231630467 + +### 右侧不为0求特解 + +在之前通解的情况下,解出c1c2带回原式即可 + +## 求解关于变限积分的等式 + +解法 + +对其求导计算求微分方程即可 + +# 二重积分 + +## 基本概念与性质 + +概念 + +image-20241201151158437 + +性质 + +image-20241201152820335 + +image-20241201153102293 + +## 比大小 + +image-20241201153258192 + +## 估值定理 + +image-20241201153531386 + +## 圆的表达式 + +image-20241201161852983 + +## 椭圆表达式 + +image-20241201162003774 + +## 直角坐标系下的计算公式 + +将二重积分化为定积分来计算 + +公式 + +image-20241201165504629 + +image-20241201165732355 + +image-20241201170014292 + +### 解法 + +image-20241201170940881 + +## 超越积分顺序选择 + +题型,根据对应的x或y确定是哪个型,然后和基本的二重积分一样画图来写 + +image-20241201194700389 + +## 交换积分次序 + +x型与y型的顺序交换 + +image-20241201210102993 + +根据题目已知条件确定类型,然后画图确定范围 + +## 极坐标系的二重积分 + +极坐标如下图所示 + +image-20241201212222125 + +### 极坐标的三角关系 + +image-20241201212531854 + +在极坐标下:x平方+y平方=r平方 + +### 二重积分计算 + +解法 + +image-20241201213357114 + +上下限的确定方法 + +image-20241201214042472 + +半径r的取值范围 + +image-20241201220202398 + +常见的积分图像 + +image-20241201220756013 + +image-20241201221128351 + +image-20241201221347282 + +## 二重积分对称性 + +条件,偶倍奇零,画图,看关于哪个轴对称,然后看对应函数的奇偶性来算 + +image-20241201232156107 + +注:若D对称,首选对称性 + +# 多元函数微分学 + +## 基本概念 + +image-20241202151422828 + +## 定义域 + +image-20241202152756449 + +## 二元函数对应法则 + +解法 + +image-20241202160223137 + +例题 + +image-20241202160541099 + +## 二元函数极限 + +image-20241202161011693 + +例题 + +image-20241202162143839 + +## 一阶偏导 + +关于哪个函数的变化 + +image-20241202163418074 + +写法 + +image-20241202164445756 + +计算方法 + +image-20241202164635347 + +例题 + +dz/dy 就对y求导,x看作常数,反之同理 + +image-20241202165039465 + +## 全微分 + +解法 + +image-20241203192400808 + +## 可微与偏导的关系 + +image-20241203193519444 + +## 二阶偏导 + +一般来说就是正常对x或y求两次导就行,也有特殊的,如下图所示 + +image-20241203195612113 + +## 二元隐函数一阶偏导 + +image-20241203200811459 + +例题 + +image-20241203201540622 + +## 二元隐函数二阶偏导 + +image-20241203202228376 + +## 链式法则 + +从外向里,层层求导 + +链式法则:将每层函数关系罗列 + +## 具体复合函数求导 + +直接对给出条件带入 + +## 抽象复合函数求导 + +解法 + +image-20241203203841533 diff --git "a/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-C8-A8SRj.js" "b/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-C8-A8SRj.js" deleted file mode 100644 index 8340c0a..0000000 --- "a/docs/assets/\351\253\230\347\255\211\346\225\260\345\255\246-C8-A8SRj.js" +++ /dev/null @@ -1 +0,0 @@ -const e=""+new URL("高等数学-BqeUsWg8.md",import.meta.url).href;export{e as default}; diff --git a/docs/friends.yaml b/docs/friends.yaml index 5051b92..abccc47 100644 --- a/docs/friends.yaml +++ b/docs/friends.yaml @@ -1,13 +1,14 @@ - class_name: 友情链接 class_desc: 不要小瞧我们啊,这就是友情的力量! link_list: + - name: Akilarの糖果屋 + url: https://akilar.top/ + avatar: https://npm.elemecdn.com/akilar-friends@latest/avatar/akilar.top.jpg + descr: 欢迎光临糖果屋 - name: 葱苓sama url: https://blog.ciraos.top avatar: https://blog.ciraos.top/avatar1.avif - # https://cdn.jsdelivr.net/gh/ciraos/ciraos-static@main/img/avatar1.avif descr: "Don't worry, Be happy." - # sitehot: https://blog.ciraos.top/custom/siteshot.avif - # https://cdn.jsdelivr.net/gh/ciraos/ciraos-static@main/img/site-shot.avif - name: "Redish101 Blog" url: "https://blog.redish101.top" descr: "学生 人 活的" diff --git a/docs/index.html b/docs/index.html index d8aa5f1..e22039b 100644 --- a/docs/index.html +++ b/docs/index.html @@ -7,7 +7,7 @@ Windy的小站 - + diff --git "a/docs/markdowns/\350\213\261\350\257\255\350\257\255\346\263\225.md" "b/docs/markdowns/\350\213\261\350\257\255\350\257\255\346\263\225.md" index 78e9d7c..6bfb46f 100644 --- "a/docs/markdowns/\350\213\261\350\257\255\350\257\255\346\263\225.md" +++ "b/docs/markdowns/\350\213\261\350\257\255\350\257\255\346\263\225.md" @@ -8,706 +8,807 @@ categories: description: 英语语法 --- -语序和五种基本句型 -=== -## 英语的五种基本句式 -- 主语:主体 -- 谓语:主体执行的动作 -- 系动词:连系作用的动词,连接前面的主语和后面的表语 -- 表语:描述主语的性质、特点、位置 -- 宾语:动作承受者 -- 间接宾语:通常是人 -- 直接宾语:通常是物 -- 宾语补语:补充宾语,补充宾语的信息 + -1. 主 + 谓 -2. 主 + 系 + 表 -3. 主 + 谓 + 表 -4. 主 + 谓 + 间接宾语 + 直接宾语 -5. 主 + 谓 + 宾语 + 宾语补语 +# 单词速记 -### 句式一 +source 源头 -Subject(主语) + Verb(谓语) +growth 成长 -The universe remains:宇宙长存 +all things 万物 -The universe + remains +resource 资源 -### 句式二 +cost .n:费用 .v:花费 -主语 + 系动词 + 表语 +resident citizens 居民 -The food is delicious:这个食物很好吃 +uniform 校服 制服 统一的 清一色的 -The food + is + delicious +catch a cold 感冒 -### 句式三 +fail in 在某方面失败 -主语 + 谓语 + 宾语 +succeded in 在某方面成功 -He took his bag and left:他拿着书包离开了 +# 句子成分 -### 句式四 +在英语中,有八大句子成分,分别是:主语、谓语、宾语、表语、定语、补足语、同位语和状语。 -主语 + 谓语 + 间接宾语 + 直接宾语 +其中主要的成分是主、谓、宾,次要的成分是表语、定语、补足语、状语和同位语 -Her father bought her a dictionary:她爸爸给她买了一本词典 +谓语分为Vt和Vi,分别为及物动词和不及物动词 -### 句式五 +## 主语 -主语 + 动词 + 宾语 + 补语 +是一个句子所要说明的人和事物,是一句的主体。(一般位于句首) -We made him our monitor:我们选他当班长 +作主语的有:名词、代词、数词、不定式、动名词和主语从句 -总结:Nothing is impossible to a willing heart!有志者事竟成! +动作的发出者是主语 -# be动词的形式和用法 +the + .adj(表示一类人或一类物)---考点 -## be动词的形式 +the + .adj(表示一类人)的话[此时如果它作为主语,那么就是主语从句,此时谓语动词就需要变为复数] -be,is,am,are,was,were,being,been +the + .adj(表示一类物)的话[谓语动词就要用到单数的形式] -is,am,are:一般现在时 +形容词没有单复数 -was,were:过去时,was使用在单数主语的后面,were使用在复数主语的后面 +It is + adj. + for sb(可省略) + to do -being,been:being是be动词的现在分词,been是be动词的过去分词 +with就远原则,主谓一致 -1. The man is back. 译:那个男人回来了 -2. They are back. 译:他们回来了 -3. He was back. 译:他(之前就回来了)回来了 -4. They were back. 译:他们(之前就回来了)回来了 -5. They have been back. 译:他们(已经)回来了 +be going to do :将要做某事,将来时 -## be动词的用法 +not only xxx but also xxx、eithor or、neithor nor就近原则,主谓一致 -后面接名词、形容词、地点副词或短语作补足语 +动词不能做主语,出现多个动词要么变成非谓语,要么变成从句 -be动词连接主语及补足语成分 +## 谓语 -1. The man is a teacher. --> a teacher作为补足语,补充说明前面的teacher -2. Mary's new dresses are colorful. --> 第一个is是连接主语和后面的补足语成分 -3. My mother was in the kitchen. --> in the kitchen,说明了主语的位置,be动词连接主语 +说明主语的动作或状态。常用动词或动词词组担任,放在主语后面,通常有简单谓语和复合谓语。 -练习: +简单谓语:由单个动词或动词词组充当谓语 -1. 他们是老师(they,teachers) +复合谓语:由情态动词或者其他助动词+动词构成,或由系动词+表语构成,系动词单独不做谓语 - they are teachers. +1. You should clean the house.(情态动词+动词) +2. You look beautiful today.(系动词+表语) +3. My brother is reading a book. (助动词+动词) +4. He has finished homework.(助动词+动词) -2. 他以前是一名老师(he, a teacher,before) +burst into laughter(突然大笑) - he was a teacher before. +burst into tears(突然大哭) -3. 他已经当了3年的老师(for 3 years) +and but or并列连词,前后连接的东西要一样,如果前面是个句子,后面就需要是个句子 - he has been a teacher for 3 years. +祈使句谓语把动词原形放在开头,省略主语you -# Be动词的否定、提问、回答 +非谓语有ing、to do、done形式 -在am,is,are,was,were后面加not. +## 宾语 -缩略式am not,isn't,aren't,wasn't,weren't +表示动作的对象,是动作的承受者。宾语一般放在动词或动词短语之后。介词后也会跟宾语。 -## 使用be动词提问和回答 +refused to do sth:拒绝做某事 -- Is he a teacher? -- Yes he is / No,he isn't +cooperate with sb:与某人合作 +succeed in:在某方面取得成功 +介词后面要加动词的ing -- Are you a teacher? -- Yes,I am / No,I am not. +**双宾语和宾补** +宾补:宾语补足语,只补充说明宾语的动作、身份、状态 +I bought my mother a gift. +主 谓 宾 宾 +We made him a teacher. +主 谓 宾 宾补 -- Were they teachers? -- Yes,they were / No,they weren't +区别 -# 代词的主格和宾格 +双宾:mother !=a gift两者中间无联系 -## 主格代词 +宾补:两者之间有联系,him可以是teacher -主格代词一般用于主语的位置上 +be to do:将来时 -I,he,she,it,you,we,they +pay attention to:注意 -I:我 +## 定语 -he:他 +单词作定语时通常放在它所修饰的名词之前,短语和从句作定语时则放在它所修饰的名词之后 -she:她 +a || an || the adj. n.句型 -it:它 +## 状语 -you:你/你们 +状语用来修饰动词、形容词、副词或者是全句,说明方式、因果、条件、时间、地点、让步、方向、程度、目的等 -we:我/我们 +so that 如此,以至于 -they:他们 +managed to do:设法做某事 -1. I am a teacher. -2. He is a teacher -3. You are teachers +because + 句子 -## 宾格代词 +because of + 词或者短语、ing -me,him,her,it,you,us,them +## 补语 -意思与上述主格代词相同 +英语有些及物动词,除了要有宾语之外,还要加上宾语补足语,才能使句子的意义更加完整。它起补充说明宾语要干什么,怎么样的作用 -1. He likes me. -2. We like her. -3. I like them. +in good order:井然有序 -# 名词性/形容词性物主代词 +broken in:闯入 -## 形容词性物主代词 +break up:分手 -不可单独,需要形容后面的词 +break out:爆发 -单数形式: +break down:出故障 -- my:我的 -- your:你的 -- his:他的 -- her:她的 -- its:它的 -- one's:某人的 +sometimes 有时候 -复数形式: +some times 几次 -- our:我们的 -- your:你们的 -- their:他们的 +some time 一些时间 +sometime某个时候 +## 表语 -1. This is my book. -2. We love our motherland. -3. Those are your socks. +放在系动词之后。是用来说明主语的性质、特征、状态与身份。表达主语具体情况。 -## 名词性物主代词 +不可数:little 几乎没有;a little 有一点 -本身就含有了名词的概念,后面不能再接名词 +可数:few 几乎没有;a few 有一点 -单数形式: +## 同位语 -- mine -- yours -- his -- hers -- its -- one's:某人的 +同位语是在名词或代词之后并列名词或代词或名词短语对前者加以说明的成分,近乎于后置定语。 -复数形式: +# 名词 -- ours:我们的 -- yours:你们的 -- theirs:他们的 +## 特殊规则 +名词+s是复数,动词+s是单数 +大多数情况,元音字母用an,辅音字母用a -1. The book is ours -2. The apple is hers +少数情况:universe -> a -image-20240505143118850 +- an + - hour + - honest + - honor -# 反身代词 +do 后面需要用动词的原型 -单数形式 +## 可数名词规则变化 -- myself:我自己 -- yourselft:你自己 -- herself:她自己 -- himself:他自己 -- itself:它自己 +一般可数名词直接在词尾+s -复数形式 +看到s、x、ch、sh结尾,加es -- yourselves:你们自己 -- ourselves:我们自己 -- themselves:他们自己 +一般情况下o结尾,有生命加es,无生命加s -作用: +以f或者fe,变ves -- 做宾语 -- 做同谓语 +看到元音+y,直接加s;看到辅音+y,变ies -# 实意动词 +专有名词直接加s -动作有实际意义的动词称为实意动词 +如果是合成词(由多个单词组成的词),比如Englishman,可以被拆分成English man,那么就让表示人的单词变为复数,说明让man变为复数,也就是说变为Englishmen -## 实意动词的特征 +germ 细菌 萌芽 -实意动词 +## 可数名词不规则变化 -- come:来 -- read:读 -- go:去 -- watch:看 -- play:玩 -- fly:飞 +1. 元音变化 + - woman women + - tooth teeth + - wife wives +2. 词尾变化 + - child children + - ox oxen +3. 单复数同形 + - sheep + - Japanese + - Chinese + - fish + - deer +4. 只有复数形式的名词 + - scissors(剪刀) + - trousers(裤子) -单三形式:一般现在时,主语是第三人称单数,需要使用动词的单三形式,在动词后面加入s、es、或将最后的y改成res +## 名词所有格 -1. He comes from Shenyang. -2. She is reading story books. -3. They went to America yesterday. - - 这里的went是由go的过去形式产生的 -4. We have watched the game for three times. -5. My mother will fly back to China next month. +名词所有格表示所有的关系意为“........的” -## 实意动词的否定/提问/回答 +- 有生命 + - 单数名词后+'s + - 以s结尾的复数 + ' +- 无生命 + - 名词A + of +名词B -使用助动词进行否定 +A+B's + n(单数) + v(单数) -在助动词do does did后面加not +A's+B's+n(复数) + v(复数) -do、does:一般现在时,do一般使用在非第三人称单数的上面,而does使用在第三人称单数上 +people -> 人 变为单复数同型 -did:一般过去时 +people -> 名族|部落 a people || two peoples -do not/don't +borrow 别人借给自己(借入) -does not/doesn't +lend 自己借给别人(借出) -did not/didn't +# 冠词 -1. I don't go to school by bus/我不坐公共汽车去学校 -2. She doesn't watch TV everyday/她每天都不看电商 -3. They didn't swim last night/昨天晚上他们没有游泳 +a/an(不定冠词):第一次出现 -使用助动词进行提问 +the(定冠词):上文提到过 -- He often plays golf. - - Does he often play golf? - - Yes,he does / No,he doesn't -- They go to school by bus. - - Do they go to school by bus? - - Yes,they do / No,they don't -- Sam had breakfast yesterday. - - Did Sam have breakfast yesterday?(这里的had需要变为原型) - - Yes,he did / No,he didn't +the:这个,那个 -# 使用疑问词进行提问和回答 +a/an(元音字母结尾使用):一个,一种 -使用疑问词进行提问 +a/an 是表示:数量“一” -- when:什么时候 -- where:哪 -- who:谁 -- what:什么 -- how:怎么 -- how long:多长时间 -- how far:多远 -- how often:多长时间一次 -- why:为什么 +a/an也是表示一类人或一类事物 -He bought three books yesterday. +a用于以辅音音素开头的单词前 -谁买的:Who bought three books yesterday? +an用于以元音因素开头的单词前 -买了什么:What did he buy yesterday? +辅音(特殊):a boy a dog a university -什么时候买的:When did he buy three book? +元音(特殊):an apple an hour -1. They have been in China for three years. +不定冠词(a/an)一般是泛指,定冠词(the)一般是特指 - How long have they been in China?(将have提到主语的前面) +## 定冠词(the) -2. It is about 4 kilometers from Beijing to Xi'an. +1.表示特指某些人或事物 +2.用于序数词前 +3.用于乐器名词前 +4.用于最高级前 +5.用于世上独一无二的事物面前 +6.用于姓氏复数前,表示“一家人” +7.用于形容词前,表示“一类人” - How far is it from Beijing to Xi'an? +the a of b -3. They come to visit me once a week. +## 不加the的情况(零冠词) - How often do they come to visit me?(这里的do是因为原句中不存在助动词,所以借出一个并让主语后面的动词变为原型) +在表示三餐、球类运动、游戏等的名词前 +(1) have breakfast/lunch/dinner +(2) play basketball/footbal +(3) play games -4. She came late,because she missed the bus. +在国名、城市、地名、人名等专有名词前 +China +Shanghai +Beijing +Tom - Why did she come late?(这里的come是变为了原型,did是过去时) +在不可数名词前 +I want to eat rice.我想吃米饭 +I want to drink a cup of tea.我想喝杯茶 -# 名词 +在节假日、季节、星期等名词前 -名词分两类: +Today is Sunday.今天是星期天 +National Day falls on October 1st.国庆节是在10月1号 +Spring is very warm.春天非常温暖 -1. 可数名词(countable noun) +在称呼语、官职、头衔等名词前 - 指数得过来的概念 +Uncle Sam -2. 不可数名称(uncountable noun) +共有是A+B's + 单数 - 无法计算的数量或抽象概念 +各有A's+B's + 复数 -- 可数名词:apple,pencil,student -- 不可数名称:salt,coffee,water,history,love +# 动词 -两个或两个以上的名词,需要变为复数 +表示状态或动作的词叫动词 -可数名词有单数和复数之分: +实义动词 +表示行为、动作或状态的词,具有实在的意义,又称为行为动词。如:play,,give,listen -- apple-apples -- pencil-pencils -- tomato-tomatoes +助动词 -不可数名称无复数,只用单数表征: +帮助实义动词构成各种时态的动词,如:do,does, did,will -- salt-salt -- coffee-coffee -- water-water +情态动词 +表示说话人情感和态度的词,后面接实义动词原型。如:如:can,may,must,need -名称变复数的规则 +系动词 -1. 一般末尾加上后缀-s,friend->friends -2. 以s、z、x、ch、sh结尾的词,在该词末尾加上后缀-es,bus -> buses -3. 辅音字母+y结尾的名词,将y改为i,再加-es,candy->candies -4. 以-o结尾的名词,如果不是外来词或缩写,就加-es,tomato->tomatoes,hippo(河马)->hippos[河马这个单词较长,所以被省略了很多,只加s] +用来帮助说明主语“是什么”或“怎么样”的动词,如:be,look,smell,taste, sound,feel,become, get -元音字母:a、e、i、o、u +## 动词的基本形式 -辅音字母:其他都是辅音字母 +动词原形 .v +第三人称单数现在式 .v+s -外来词:不是英语词汇 +现在分词 .v+ing +过去式 .v+ed +过去分词 .v+ed -缩写词:将一段长词汇简略就是缩写词 +## 三单变复数规则 +- 一般动词,词尾直接十s; +- 以s/x/o/ch/sh 词尾+es; +- 以辅音字母十y结尾的动词,词尾变y为i+es. +- a,e,I,ou 是元音字母,其他都是辅音字母 +- 特殊变化 -可数名词前可以加a(an)或量词 +## 动词现在分词 -- apple - - an apple(以元音字母开头的单词用an表示一个) - - apples - - a box of apples -- tomato - - a tomato - - tomatoes - - a bag of tomatoes +一般动词,词尾直接+ing; +以不发音e结尾动词,去e+ing; +以辅元辅结尾动词,双写词尾辅音字母+ing +以-ie结尾的动词,变ie为y再加ing -不可数名称前不可加a(an).没有复数,但前面可以加量词 +lie 表示说谎时的过去式或过去分词 lied lied -- coffee - - a cup of coffee +lie 表示躺的过去式或过去分词 lay(下蛋) lain -# 指示代词和不定代词 +tie 做名词表示领带,动词的ing表示系 -- 指示代词:标识人或事物的代词,用来替代前面已提到过的名称 +## 动词过去式和过去分词 -- this:这个 +一般动词,词尾直接+ed; +以e结尾动词,词尾+d; +以辅音字母十y结尾的动词,词尾变y为i+ed. +以辅元辅结尾的动词,双写词尾辅音字母十ed - these:这些 +leave 的过去式 left - that:那个 +lose 的过去式 lost - those:那些 +go 的过去式 went -- 不定代词:指代不确定的人或事物。 +go 的过去分词 gone -- one:一个 +run 的过去式 ran - the other:另外一个 +run 的过去分词 run - some:一些 +come 的过去式 came - any :一些 +come 的过去分词 come - something:某物/事 +fly 的过去式 flew - nothing:什么都没有 +fly 的过去分词 flown -- No one knows where he is.(没有一个人知道他在哪,这里的one不明确) -- x // 中缀表达式转后缀表达式并计算public static String computedInfixResult(List list){    // 初始化两个栈,数栈和结果栈    Stack stack1 = new Stack();    Stack stack2 = new Stack();    for (String val : list) {        if (val.matches("\\d+")){            // 数字载入数栈            stack1.push(val);       }        else{            // 不为数栈            // 则为运算符或小括号            // 判断结果栈是否为空,为空或为小括号就直接加入            if(stack2.isEmpty() || stack2.peek().equals("(")){                stack2.push(val);           } else if (priority(val) == -1) {                // 为小括号,则直接压入栈中                if (val.equals("("))                    stack2.push(val);                else{                    // 右括号                    while (true){                        if (stack2.peek().equals("(")){                            // 当比较后不为(时,进行循环,依次弹出每一个顶上的数据                            stack2.pop();                            break;                       }else {                            // 存入其它运算符                            stack1.push(stack2.pop());                       }                   }               }           } else if (priority(val) >= priority(stack2.peek())){                // 如果新的运算符优先级大于栈顶运算符的优先级的话                stack1.push(stack2.pop());                // 当结果栈不为空时,比较优先级                while (!stack2.isEmpty()){                    if (priority(val) >= priority(stack2.peek())){                        stack2.push(val);                   }else break;               }           }       }   }    while (!stack2.isEmpty()){        stack1.push(stack2.pop());   }    StringBuilder res = new StringBuilder();    int size = stack1.size();    for (int i = 0; i < size; i++) {        res.append(stack1.pop() + " ");   }    return String.valueOf(res.reverse());}​// 返回运算符的优先级,自定,返回的数字越大优先级越高public static int priority(String operation){    if (operation.equals("*") || operation.equals("/")){        return 1;   } else if (operation.equals("+") || operation.equals("-")) {        return 0;   }else{        return  -1;     // 假定的表达式只有加减乘除   }}​​// 将中缀表达式转成对应的Listpublic static List toInfixExpressionList(String s){    // 定义List,存放中缀表达式对应的内容    List ls = new ArrayList<>();    int i = 0;  // 指针,用于遍历表达式中的字符串    String str; // 多位数拼接    char c; // 遍历每一个字符,放入到c中    do{        // 如果c不是数字,就加入到ls        if ((c = s.charAt(i)) < 48 || (c = s.charAt(i)) > 57){            ls.add("" + c); // 不为数字,说明是运算符,直接加入            i++;    // 指针后移       }else{            // 如果是数字,需要考虑多位数的情况            str = "";   // 每一次都需要重置该字符串            while (i < s.length() && (c=s.charAt(i)) >= 48            && (c=s.charAt(i)) <= 57){                // 48 - 57 -> 0 ==> 9                str += c;   // 对数字进行拼接                i++;           }            ls.add(str);       }   }while (i < s.length());    return ls;}java +see 的过去式 saw -# 形容词 +see 的过去分词 seen -形容词通常形容人或事物的状态,性质,大小等,通常用在名词前,be动词后 +swim 的过去式 swam -- beautiful-the beautiful girl -- The girl is beautiful +swim 的过去分词 swum -The + 形容词 = 复数名词,表示一类。后面的动词使用复数 +buy 的过去式、过去分词 bought -- old-the old -- young-the young -- The old need more care than the young +## 双写规则 -# 副词 +**辅元辅,结尾重读** + +let letting -副词可以修饰动词,形容词,其他副词以及其他结构 +run running -- He runs fast -- She is very beautiful -- They work very hard +swim swimming -副词的位置: +shop shopping -1. 根据情况,放在助动词之后,实意动词之前或之后 -2. 形容词之前,其他副词之前或之后 -3. 多个助动词时,副词一般放在第一个助动词后 +**辅元辅,结尾不重读** -- He speaks very fast -- They have already left -- They have already been repaired +listen listening -常用的频度副词(always,usually,often,sometimes,never)的位置通常放在一般动词前面,be动词后面,助动词和实意动词之间。 +visit visiting -- They always come early. -- Sam often writes homework at 7:00. +**我想要不wxy** -# 不定量表达法 +know knowing -- some:一些 -- any:一些 -- most:大多数 -- every:每一个 -- all:所有的 +grow growing -**some,any都表示"一些",some主要用于肯定句,希望得到肯定回答时,也可用在疑问句中,any主要用在否定和疑问句中。** +mix mixing -- I'd been expecting some letters the whole morning,but there weren't any for me +buy buying -**most作形容词时表示大部分的,后面接复数名词** +play playing -- Most people here are from China. +其他情况 +quit **quitting** 停止;放弃 +quiz **quizzing** 小测试 +equip equipping 装备 +forget forgetting 忘记 +regret regretting 后悔;遗憾 +begin beginning 开始 +permit permitting 允许 +admit admitting 承认 +forbid forbidding 禁止 +prefer preferring 宁愿;更喜欢 +refer referring 涉及;参考;查阅 +occur occurring 发生 -**every表示"每一个,所有"后面接单数名词** +![image-20241218140936382](https://s2.loli.net/2024/12/18/nqDayo8XeW3vVYs.png) -- Every one likes the film +# 介词 -**all表示"所有",后面接可数名词复数,不可数名词单数。** +介词是英语中很活跃的词,也是介词 prep.(preposition) -- All the cars are parked in the parking lot. -- All the coffee is served on time. +位置:一般置于名词之前 +它常和名词或名词性词语构成介词短语 +beside 在...旁边 -- both:表示两者都,可作形容词,代词,副词 -- either:是两者之一 -- neither:是两者都不 +into 在里面 -1. **Both** his eyes were serverly burned. -2. There are trees on **either** side of the street. -3. **Neither** answer is correct. +out of 在外面 +among 在...中间(三个及以上) +past 通过 -- many:修饰可数名词,表示“许多” -- much修饰不可数名词,表示“许多” -- a lot of[lots of],plenty of 均可修饰可数和不可数名词 +across 穿过 通过 -many books、much water +along 沿着 -a lot of/ lots of books / water +through 通过(从内部通过) +**at + 较短的时间 < 1 day(日出日落)** +**on + 日期(具体时间) / 星期 / 节日 = 1 day(具体时间)** -- a few:为肯定含义“几个” -- few:为否定含义“没几个” +**in + 周 / 年 / 季节 / 早中晚 > 1 day(较长时间)** -以上两个词均可和**可数名词**连用 +in 在...里面 -- A few books are put into the box. -- Few books are put into the box +on 在...上面(接触表面) +under 在...下面 +behind 在...后面 -- a little为肯定含义“一点儿” -- little为否定含义“没多点” +in front of 在...前面 -以上两个词均可和**不可数名词**连用 +above 在...上面(不接触表面,不一定在正上方) -- There is a little water in the bottle -- There is little water in the bottle +below 在...下面(不接触表面) +between 在...中间(两者) +next to 挨着,在...旁边 -none和no one的意思相同,主要作代词,翻译为“一个也不,一点也不”,用法稍有区别 +image-20241218164254699 -1. none**可以**接of短语,动词可用单数也可用复数 -2. no one**不能**接of短语,动词只能用单数 +at用于表示一个较小的场合 +in表示在较大的地方;在...的里面 +on表示在...之上,强调与某物体有接触 +under强调在某物的下方,完全覆盖两物体表面可以接触也可以不接触 +between表示两者之间 +behind表示在...后面 +in front of表示在...前面 +up表示往上 down表示往下 +near表示有一定距离,只是对于说话者来说是在附近 -- No one knows the answer -- None of us have(has) arrived +# 连词 +## 并列连词 +前后语法地位一致 -# There/Here be句型 +**表示并列关系 and** -There/Here + (be) 根据上下文,有多种翻译方法,可以翻译成“有”,“这是”,be动词根据后面的名词有单复数变化 +and(和,并且) +I like blue and black. +Tom and Jerry are good friends. +and:用来连接并列的词、词组或句子 -- There is a book on the bookshelf. -- There are some books on the bookshelf. -- Here is the bus stop. -- Here are your books. +**表示选择关系 or** +or(表示“或"“否则”,表示选择或转折) +Which do you like better, apples or pears?(在疑问句中表示选择) -# 一般现在时和现在进行时 +He doesn't like milk or juice.(在否定句中表示并列) -一般现在时,表示通常性、规律性、习惯性的状态或者动作。主语是单数第三人称时,动词有单三的变化,主语是非第三人称单数时,动词变为原形 +Get up,or you'll be late. -1. They often get up at 7:00. -2. He often gets up at 7:00 +and通常用在肯定句中,而or通常用在否定句疑问句中 -一般现在时,动词的单三变化: +**拓展** -1. 在动词尾直接加s +eithor or、neither nor、not only but also就近原则 - 如:play-plays +Study hard, or your math will be worse. +(努力学习,否则你的数学成绩将会很差) +Study hard,and your math will be better +(努力学习,那么你的数学成绩将会很好) -2. 以字母s、x、ch或o结尾的动词加-es,如:guess-guesses +and和or都可以在祈使句中使用 -3. 以辅音字母+y结尾的动词,先变y为i,再加-es,如:study-studies +“and +句子" 通常是比较好的结果,意思是"...那么就会" +‘or+句子" 则表示不愉快不理想的结果,意思是"...否则就会" -- 一般现在时否定和疑问句用do,does帮助构成 - 1. He doesn't like the car.(does用在单三上,do用于非单三) - 2. Does he like the car ? - - Yes,he does./No he doesn't +or 用于疑问或否定句,and用于肯定句 +**表示转折关系 but** +but(但是,可是) -现在进行时表示现在正在进行或发生的动作。句子通常有now等时间副词呼应,基本构成形式为**be + doing** +**表示因果关系 so** -1. They are watching TV. -2. He is watching TV. -3. I am watching TV. +because(因为) +so(所以) +because 和 so不能同时出现在句子里 -动词现在分词的变化规则: +## 从属连词 -1. 一般情况下,直接在动词后加-ing,如:work - working -2. 动词以不发音的 -e 结尾,要去e加Ing,如:take - taking -3. 重读闭音节的动词,要双写词尾字母,再加 -ing,如:cut - cutting -4. 以-ie结尾的动词,变y再加-ing,如:lie - lying +引导从句 +# 代词 +image-20241219154845508 -现在进行时变否定句和疑问句时,将be动词否定或提前 +## 人称代词 -1. They aren't watching TV. - - Are they watching TV? -2. He isn't watching TV. - - Is he watching TV? -3. Am I watching TV? - - Yes,you are / No,you aren't. +为了避免重复,用来代替前面所提到的人或者物等的代词 +它有两个选择:主格和宾格 -# 一般过去时和过去进行时 +主格 发出动作,宾格 动作承受者 -一般过去时表示过去某个时间里发生的动作或状态;过去习惯性、经常性的行为 +主格:在句子中作主语(一般用在动词前)。 -- 基本结构:主语+动词过去式+其他,一般动词在动词后面加ed,还有一些不规律动词不规则变化 +宾格:在句子中作宾语。(动作的承受者,多用于动词、介词后) -- play-played、come-came - 1. He worked very hard last night. - 2. They came here by car. +## 物主代词 -动词一般过去时变化规则: +形容词性物主代词(形容词) -1. 一般在动词后加-ed。如:play-played -2. 在以字母e结尾的动词后,只加-d。如:like-liked -3. 在以"辅音字母+y"结尾的动词后,改y为i,再加-ed。如:supply-supplied -4. 在以重读闭音节结尾且末尾只有一个辅音字母的动词后,双写最后一个辅音字母,再加-ed。如:plan-planned +名词性物主代词(名词) + +## 代词总结 + +主 宾 形容词性物主代词 名词性物主代词 + +image-20241219162428109 + +# 反身代词 +表示反射或者强调的代词,表示某某自己;当主语和宾语为同一物时,表反射;当其位置在名词、代词之后,或位于句尾,表强调。 +我 -- myself -过去进行时表示在过去某一时刻或某一时间内进行或发生的动作。 +你 -- yourself -其形式为was / were + doing +他/她/它 -- himself/herself/itself -1. They were waiting for you. -2. He was talking with his friends just now. +我们 -- ourselves -# 将来时 +你们 -- yourselves -一般将来时表示将来某一时刻的动作或状态,或将来某一段时间内经常发生的动作或状态。常常和表示将来的时间状语连用。 +他们 -- themselves -- tomorrow(明天) -- next week(下周) -- int the future(将来) +# 指示代词 +用来指代或标记人或物的代词 +有4大家族: +this(这个) +that(那个) +these(这些) +those(那些) +this和that后接的谓语动词为单数形式, +these和those后接的谓语动词为复数形式。 -”助动词will或shall + 动词原形“,表示将来发生的事情。 +this和these常用来指代空间上较近的人或物,that和those常用来指代空间上较远的人或物 -1. They will go to Shanghai by ship tomorrow. -2. We shall leave for Shanghai in next month. +Tips:打电话时,用this指代自己;如果要问对方是谁,通常用that. +# 数词 +## 考点 -"be going to + 动词原形"用来表示近期或事先考虑过的将要发生的动作以及已有迹象表明必将发生某事,意为“打算;就要”。 +①表示概述/不确定的数字,+s:hundreds of 成百上千、dozensof/scores of很多 +②表示确定的数字,不+s:threehundred、threedozen +③“基数词+连字符+名词"可以构成复合形容词,表示数量,此时名词应用单数形式。 +a two-dayaftivity(=two daysactivity)为期两天的活动 +a three-hour drive (=three hoursdrive)三小时的车程 +an-hour trip (=an hour’s trip)一小时的旅途 +a?n→中间是缺了→形容词 +①in one’s twenties +in the1820s/1820's +everytwohours=every secondhour“每两小时/每隔一小时” +The second time第二次a second/third/forthtime又一次;再一次 +③“名词+基数词"可以表示书页、房间、住所等的编号及邮政编码,电话等,此时首字母常大写。另外表示编号时也可用“the+序数词+名词”,此时首字母不用大写 -- They are going to play football this afternoon -- She is going to learn French next year. +在英语当中我们的数词分为基数词和序数词两类。 +**基数词**就是我们平时熟知的数字数量而**序数词**则表示次序 +描述数量的多少称为基数词 +13~19 后缀+teen -“be doing”表示位置转移的动词。如:go,come,leave,start,arrive,可用现在进行时表示将来时。 +20~99 整10位:后缀+ty -1. They are leaving for Japen. -2. She is arriving tomorrow. +非整十数:整十位数 + 个位数,例如21,twenty one -# 完成时 +100~999 整百位数:后 + hundred +非整百位数:整百+整十+个位数 例如121 one hundred and twenty one + +注意13、15、18的基数词构成 +13:thirteen +15:fifteen +18:eighteen + +非整十位数:整十位和个位数之间需要有连线符 +22: twenty-two +非整百位数中:百位数和十位数之间用and连接 +122:one hundred and twenty-two + +序数词:表示次序的数词称为序数词,在汉语中表示“第几” + +4~19 +基数词后缀+th表示“第” + +20~99 +整十位数:变y为 ie+th; +非整十位数:个位数用序数词 + +百位以上 +结尾处变为序数词即可 + +1-20的序数词如下图所示 + +image-20241219204009524 + +# 形容词 -现在完成时(have + p.p.[过去分词]),动作过去发生,已经完成,对现在造成影响或后果,动作可能还会持续,可使用的时间状语为:already(已经) 和 yet(还) +形容词在句中用来修饰和描述名词和代词 +形容词是表示人或事物性质、状态和特征的词,一般表示.....的 -1. They have already arrived in Shanghai. -2. She has played soccer for 3 hours.(这里的has是根据单三的形式发生变化) -3. She hasn't finished the homework yet. +形容词在句中一般放在名词之前; +形容词在句中也可放在am,is,are,was,were之后 +形容词的同级、比较级和最高级:多数形容词都可以用于比较、说明事物间的等级、程度差别。 +形容词比较构成 +a.大部分形容词:词尾加er或est + +b.以e结尾的形容词:词尾加r或st + +c.以重读闭音节结尾,且结尾只有一个辅音字母的形容词:双写这个辅音字母,再加er或est + +d.以辅音字母+y结尾的形容词:变y为i,再加er或est + +e.两个或两个以上音节的形容词:+比较级的原级 + +**不规则变化的形容词** + +原型-比较级-最高级 + +many-more-most + +much-more-most + +few-fewer-fewest + +little-less-least + +用法小贴士: +many与few用与可数名词前, +much与little用于不可数名词前 + +## 比较级的用法 + +形容词比较级+than+对比成分:表示“..比...更. + +e.g.篮球比排球大 +A basketball is bigger than a volleyball. + +同级比较:形容词的原级也同样可以用于比较 +肯定:as +形容词原级+as表示.......样 +e.g. He is as tall as his brother. + +否定:not as+形容词原级+as表示“不如" +e.g.The vase is not as good as this. + +the + 形容词最高级+(名词)+比较范围:表示“..最..” -> 三者及以上 + +The older the wiser. +人老智多,姜还是老的辣 +Blood is thicker than water. +血浓于水 +Two heads are better than one. +人多智广/三个臭皮匠顶个诸葛亮 +East or west, home is the best +金窝银窝不如自己的草窝 +Experience is the best teacher. +实践出真知 +He knows most speaks least. +大智若愚 + +# 副词 +副词独白:简写为adv -过去完成时(had + .p.p),表示句中的动作发生在过去之前,即过去的过去,已经完成,对过去造成了一定的影响或后果 +是表示时间、场所、状态、频率、疑问及程度等的词。 -1. They had arrived in Shanghai. -2. She had played soccer for 3 hours. -3. They hadn't finished the work yet. +一般是由相应的形容词加ly构成的。 +副词是可以用来修饰词,词组或整个句子。 +副词位于形容词/副词的前面,动词的后面 +形容词变副词 +1 直接在形容词后加 ly +如:quiet quietly slow slowly +2 以辅音字母加y结尾的形容词,要先将y变成i,然后再加ly +如:happy happily busy busily +3有些形容词和副词形式完全相同,如:hard,early -# 动词用法 +时间副词 then, next, already, finally, today, soon. +频率副词 often, usually, never, frequently, always +疑问副词 how, when, where, why.. -动词根据功能分为四类 +# 一般将来时 -- 实意动词(Notional Verb) -- 系动词(Link Verb) -- 助动词(Auxiliary Verb) -- 情态动词(model Verb) +I am going to do something. +I am going to wash car/clothes tomorrow +be going to do -> 一般将来时 -1. 动词有数量和时态的变化,时态通常有三大时态:现在,过去和将来时 -2. 根据动作进行的状态可分为:一般时,进行时和完成时 -3. 使用动词时通常将(1)和(2)结合。例如:一般现在时,过去进行时 +一般将来时表示单纯的将来事实。 +主语后通常有助动词will + 动词原形构成以及对应be动词+going to+动词原形 -- He goes to school every day. -- He went to hospital last night. +主语 + be going to +动词原形+…=肯定句 +主语+be not going to +动词原形+ ..=否定句 +be +主语+going to+动词原形=一般疑问句 -image-20240508192138589 +一般将来时状语 -# 情态动词 +in+将来时间 +in 2020、in 2025、in the future -1. can/could 表示能力,用be able to代替can/could 现在/过去的能力客观可能性(can的可能性大),表示请求和允许 +next+时间 +next Monday、next year、next week +不规则 +tomorrow、from now on、soon -- He can/could/is able to swim. -- He can/could come tomorrow. -- Can/could I stay here? +be going to +一般指已经计划好的事情,强调某个意图,是经过事先考虑好的 +will +指主语本身愿意做的事情,没有经过事先考虑,而是在说话的当时临时想到的 -1. may/might 表示可能性,may的可能性大,在请求、允许中might更委婉 +be going to +表示近期眼下就要发生的事情。 -口语中常用的回答: +will -- Yes,please. -- No,you can't/mustn't(禁止,不准) +表示的将来时间则较远一些 +will +主语猜测或希望等内心活动,想得到肯定的、将会发生的事情 -1. He may/might come here by bus. -2. May/might join you? - - Yes,please/No,you can't/No,you mustn't diff --git "a/docs/markdowns/\350\256\241\347\256\227\346\234\272\345\237\272\347\241\200.md" "b/docs/markdowns/\350\256\241\347\256\227\346\234\272\345\237\272\347\241\200.md" new file mode 100644 index 0000000..9c80531 --- /dev/null +++ "b/docs/markdowns/\350\256\241\347\256\227\346\234\272\345\237\272\347\241\200.md" @@ -0,0 +1,66 @@ +--- +title: 计算机基础速成 +tags: 基础速成 +date: 2024-12-20 17:11:05 + +--- + +# 计算机基础 + +世界上第一台电子计算机ENIAC 1946年诞生于美国 + +四代主要元器件: + +1. 电子管 +2. 晶体管 +3. 中小规模集成电路 +4. 大规模或超大规模集成电路 + +第二代存储器为磁芯磁盘磁带 + +第二代出现高级程序、第三代出现操作系统和会话式语言 + +# 计算机辅助系统 + +CAD计算机辅助设计 + +CAM计算机辅助制造 + +CBE计算机辅助教育 + +CAI计算机辅助教学 + +CMI计算机管理教学 + +CAT计算机辅助测试 + +CIMS计算机集成制作系统 + +CAE计算机辅助工程 + +计算机特点:运算速度快、计算精度高、储存容量大、具有逻辑判断能力、工作自动化、通用性强(速精储逻自通) + +计算机的发展趋势:巨型机、微型机、网络化、智能化(巨微网智) + +位bit是计算机存储数据的最小单位 + +字节B是计算机存储数据的基本单位 + +1B=8bit 1KB=1024B 1MB=1024KB + +1GB=1024MB 1TB=1024GB + +ASCII 美国标准信息交换代码 共128个字符 + +不可打印字符33个 + +ASCII码表示:运算符号、控制符号、英文标点符号、十进制0~9 + +7位,存储1个字节 最高位为0(标) + +8位,存储1个字节 最高位为1(拓展) + +(0~9 48~47)(A~Z 65~90) (a~z 97~122) + +空格<数字<大写字母<小写字母 + diff --git "a/docs/markdowns/\351\253\230\347\255\211\346\225\260\345\255\246.md" "b/docs/markdowns/\351\253\230\347\255\211\346\225\260\345\255\246.md" index f2f8c77..437e1be 100644 --- "a/docs/markdowns/\351\253\230\347\255\211\346\225\260\345\255\246.md" +++ "b/docs/markdowns/\351\253\230\347\255\211\346\225\260\345\255\246.md" @@ -112,7 +112,7 @@ cos是邻边比斜边 特殊值及图像 -![image-20240807215332157](https://s2.loli.net/2024/08/08/6FgbuIApzlsZPBR.png) +image-20240807215332157 ### tanx @@ -120,21 +120,21 @@ tanx是对边比邻边 特殊值及基本情况 -![image-20240807215650531](https://s2.loli.net/2024/08/08/2bFtBzsmMc97Uue.png) +image-20240807215650531 tanx图像 -![image-20240807215829893](https://s2.loli.net/2024/08/08/k48lKhpgneX5rf6.png) +image-20240807215829893 ### 三角函数公式 image-20240807220724828 -![image-20240807220702872](https://s2.loli.net/2024/08/08/97u3aUbAtPIEWcY.png) +image-20240807220702872 ### 和差化积 -![image-20240807220545556](https://s2.loli.net/2024/08/08/Orvl9RXb4CS7zD8.png) +image-20240807220545556 ### tan公式 @@ -146,35 +146,35 @@ tanx图像 #### arctanx图像 -![image-20240807221236827](https://s2.loli.net/2024/08/08/uBn7i3lOSTAv1VC.png) +image-20240807221236827 #### 特殊值 arcsin、arccos、arctan与sin、cos、tan相同 -![image-20240807221540546](https://s2.loli.net/2024/08/08/qgpbce8rVv6yTBR.png) +image-20240807221540546 # 因式分解 -提公因式 +## 提公因式 image-20240808204732462 -公式法 +## 公式法 image-20240808205149676 -十字相乘法 +## 十字相乘法 image-20240808205424908 -找根法 +## 找根法 -![image-20240808210315474](https://s2.loli.net/2024/08/08/WhAK1UyF9Gp37cf.png) +image-20240808210315474 # 常见不等式解法 -![image-20240808212741215](https://s2.loli.net/2024/08/08/cL72k4FCrRptEM5.png) +image-20240808212741215 ## 分式不等式 @@ -301,7 +301,7 @@ arcsin、arccos、arctan与sin、cos、tan相同 常见有界:sin、cos、arctan -![image-20240813210845806](https://s2.loli.net/2024/08/13/B1FADLPHrjKeEoI.png) +image-20240813210845806 0乘有界=0 @@ -313,7 +313,7 @@ arcsin、arccos、arctan与sin、cos、tan相同 ## 第二重要极限 -![image-20240814210457482](https://s2.loli.net/2024/08/14/VxGYN25lqQf4X6e.png) +image-20240814210457482 image-20240814211811921 @@ -418,23 +418,23 @@ f(x0) = 左极限 = 右极限 = 连续 常用公式 -![image-20240920220853858](https://s2.loli.net/2024/09/24/SOU8daiqyoNpbCQ.png) +image-20240920220853858 -![image-20240920220944107](https://s2.loli.net/2024/09/24/leNopjiVMhrXzsH.png) +image-20240920220944107 例题 -![image-20240920221140608](https://s2.loli.net/2024/09/24/vSl61NBcF2yd5KH.png) +image-20240920221140608 导数相乘和导数相加减不同 -![image-20240920221403043](https://s2.loli.net/2024/09/24/dtLjJCI8xgm34yH.png) +image-20240920221403043 -![image-20240920221707297](https://s2.loli.net/2024/09/24/vWmpXe5uGjA8Fob.png) +image-20240920221707297 导数相除 -![image-20240920221810272](https://s2.loli.net/2024/09/20/AktVQRm9n4TJFgO.png) +image-20240920221810272 ## 复合函数求导 @@ -446,11 +446,11 @@ f(x0) = 左极限 = 右极限 = 连续 复合函数乘法求导 -![image-20240921205725441](https://s2.loli.net/2024/09/24/sOvwZDrBPoRNUEa.png) +image-20240921205725441 ## 幂指式求导 -![image-20240921210927100](https://s2.loli.net/2024/09/24/cI6xitPAuvo8lSV.png) +image-20240921210927100 计算完成后,改写为原式子 @@ -458,13 +458,13 @@ f(x0) = 左极限 = 右极限 = 连续 例: -![image-20240921212319313](https://s2.loli.net/2024/09/21/TCALpuhKOk28FZD.png) +image-20240921212319313 ## 隐函数求导 隐函数的二阶导直接对一阶导再次求导即可 -![image-20240924205027272](https://s2.loli.net/2024/09/24/Yxl6LuU83FkQIgs.png) +image-20240924205027272 方法 @@ -472,9 +472,9 @@ f(x0) = 左极限 = 右极限 = 连续 例题 -![image-20240924211306480](https://s2.loli.net/2024/09/24/7LW4Nvy8Y6QjVga.png) +image-20240924211306480 -![image-20240924212123558](https://s2.loli.net/2024/09/24/zyGMQWkBXZg1dmj.png) +image-20240924212123558 ![image-20240924213334439](https://s2.loli.net/2024/09/24/NCn6P5wgLmBG4KH.png) @@ -564,7 +564,7 @@ Cxx的求解方式 ## 微分计算 -![image-20241028215055400](https://s2.loli.net/2024/10/28/mZsqjYRKFE3xudH.png) +image-20241028215055400 ![image-20241028215221699](https://s2.loli.net/2024/10/28/YgEIyqJT9RaWf75.png) @@ -1048,3 +1048,250 @@ Cxx的求解方式 ### 齐次式 +解法:换元 + +image-20241129152238603 + +### 伯努利方程 + +解法 + +image-20241129154824038 + +image-20241129154929242 + +## 二阶微分方程 + +### 右侧为0求通解 + +解法 + +image-20241130211023114 + +### 右侧为0求特解 + +特解就是在通解的基础上把xy的值带入求出c1,c2,然后回带即可 + +image-20241130220656082 + +### 右侧不为0求通解(第一类) + +image-20241130223640020 + +根据类型设特解形式 + +image-20241130223609211 + +求出y*对其求导就可以得到原式带入解出其他结果值 + +### 右侧不为0求通解(第二类) + +解法,有点乱 + +总结下来就几步:找出A+bi,先求`y*`,所以要求出对左侧求导为0的结果,带入公式,算出r和a+bi之间的关系,根据关系算出`y*`的公式,求导回带到之前的式子里的二阶导计算,算出真正的`y*`,接着算出Y,带入式子计算即可 + +image-20241130231630467 + +### 右侧不为0求特解 + +在之前通解的情况下,解出c1c2带回原式即可 + +## 求解关于变限积分的等式 + +解法 + +对其求导计算求微分方程即可 + +# 二重积分 + +## 基本概念与性质 + +概念 + +image-20241201151158437 + +性质 + +image-20241201152820335 + +image-20241201153102293 + +## 比大小 + +image-20241201153258192 + +## 估值定理 + +image-20241201153531386 + +## 圆的表达式 + +image-20241201161852983 + +## 椭圆表达式 + +image-20241201162003774 + +## 直角坐标系下的计算公式 + +将二重积分化为定积分来计算 + +公式 + +image-20241201165504629 + +image-20241201165732355 + +image-20241201170014292 + +### 解法 + +image-20241201170940881 + +## 超越积分顺序选择 + +题型,根据对应的x或y确定是哪个型,然后和基本的二重积分一样画图来写 + +image-20241201194700389 + +## 交换积分次序 + +x型与y型的顺序交换 + +image-20241201210102993 + +根据题目已知条件确定类型,然后画图确定范围 + +## 极坐标系的二重积分 + +极坐标如下图所示 + +image-20241201212222125 + +### 极坐标的三角关系 + +image-20241201212531854 + +在极坐标下:x平方+y平方=r平方 + +### 二重积分计算 + +解法 + +image-20241201213357114 + +上下限的确定方法 + +image-20241201214042472 + +半径r的取值范围 + +image-20241201220202398 + +常见的积分图像 + +image-20241201220756013 + +image-20241201221128351 + +image-20241201221347282 + +## 二重积分对称性 + +条件,偶倍奇零,画图,看关于哪个轴对称,然后看对应函数的奇偶性来算 + +image-20241201232156107 + +注:若D对称,首选对称性 + +# 多元函数微分学 + +## 基本概念 + +image-20241202151422828 + +## 定义域 + +image-20241202152756449 + +## 二元函数对应法则 + +解法 + +image-20241202160223137 + +例题 + +image-20241202160541099 + +## 二元函数极限 + +image-20241202161011693 + +例题 + +image-20241202162143839 + +## 一阶偏导 + +关于哪个函数的变化 + +image-20241202163418074 + +写法 + +image-20241202164445756 + +计算方法 + +image-20241202164635347 + +例题 + +dz/dy 就对y求导,x看作常数,反之同理 + +image-20241202165039465 + +## 全微分 + +解法 + +image-20241203192400808 + +## 可微与偏导的关系 + +image-20241203193519444 + +## 二阶偏导 + +一般来说就是正常对x或y求两次导就行,也有特殊的,如下图所示 + +image-20241203195612113 + +## 二元隐函数一阶偏导 + +image-20241203200811459 + +例题 + +image-20241203201540622 + +## 二元隐函数二阶偏导 + +image-20241203202228376 + +## 链式法则 + +从外向里,层层求导 + +链式法则:将每层函数关系罗列 + +## 具体复合函数求导 + +直接对给出条件带入 + +## 抽象复合函数求导 + +解法 + +image-20241203203841533 diff --git "a/public/markdowns/\350\213\261\350\257\255\350\257\255\346\263\225.md" "b/public/markdowns/\350\213\261\350\257\255\350\257\255\346\263\225.md" index 78e9d7c..6bfb46f 100644 --- "a/public/markdowns/\350\213\261\350\257\255\350\257\255\346\263\225.md" +++ "b/public/markdowns/\350\213\261\350\257\255\350\257\255\346\263\225.md" @@ -8,706 +8,807 @@ categories: description: 英语语法 --- -语序和五种基本句型 -=== -## 英语的五种基本句式 -- 主语:主体 -- 谓语:主体执行的动作 -- 系动词:连系作用的动词,连接前面的主语和后面的表语 -- 表语:描述主语的性质、特点、位置 -- 宾语:动作承受者 -- 间接宾语:通常是人 -- 直接宾语:通常是物 -- 宾语补语:补充宾语,补充宾语的信息 + -1. 主 + 谓 -2. 主 + 系 + 表 -3. 主 + 谓 + 表 -4. 主 + 谓 + 间接宾语 + 直接宾语 -5. 主 + 谓 + 宾语 + 宾语补语 +# 单词速记 -### 句式一 +source 源头 -Subject(主语) + Verb(谓语) +growth 成长 -The universe remains:宇宙长存 +all things 万物 -The universe + remains +resource 资源 -### 句式二 +cost .n:费用 .v:花费 -主语 + 系动词 + 表语 +resident citizens 居民 -The food is delicious:这个食物很好吃 +uniform 校服 制服 统一的 清一色的 -The food + is + delicious +catch a cold 感冒 -### 句式三 +fail in 在某方面失败 -主语 + 谓语 + 宾语 +succeded in 在某方面成功 -He took his bag and left:他拿着书包离开了 +# 句子成分 -### 句式四 +在英语中,有八大句子成分,分别是:主语、谓语、宾语、表语、定语、补足语、同位语和状语。 -主语 + 谓语 + 间接宾语 + 直接宾语 +其中主要的成分是主、谓、宾,次要的成分是表语、定语、补足语、状语和同位语 -Her father bought her a dictionary:她爸爸给她买了一本词典 +谓语分为Vt和Vi,分别为及物动词和不及物动词 -### 句式五 +## 主语 -主语 + 动词 + 宾语 + 补语 +是一个句子所要说明的人和事物,是一句的主体。(一般位于句首) -We made him our monitor:我们选他当班长 +作主语的有:名词、代词、数词、不定式、动名词和主语从句 -总结:Nothing is impossible to a willing heart!有志者事竟成! +动作的发出者是主语 -# be动词的形式和用法 +the + .adj(表示一类人或一类物)---考点 -## be动词的形式 +the + .adj(表示一类人)的话[此时如果它作为主语,那么就是主语从句,此时谓语动词就需要变为复数] -be,is,am,are,was,were,being,been +the + .adj(表示一类物)的话[谓语动词就要用到单数的形式] -is,am,are:一般现在时 +形容词没有单复数 -was,were:过去时,was使用在单数主语的后面,were使用在复数主语的后面 +It is + adj. + for sb(可省略) + to do -being,been:being是be动词的现在分词,been是be动词的过去分词 +with就远原则,主谓一致 -1. The man is back. 译:那个男人回来了 -2. They are back. 译:他们回来了 -3. He was back. 译:他(之前就回来了)回来了 -4. They were back. 译:他们(之前就回来了)回来了 -5. They have been back. 译:他们(已经)回来了 +be going to do :将要做某事,将来时 -## be动词的用法 +not only xxx but also xxx、eithor or、neithor nor就近原则,主谓一致 -后面接名词、形容词、地点副词或短语作补足语 +动词不能做主语,出现多个动词要么变成非谓语,要么变成从句 -be动词连接主语及补足语成分 +## 谓语 -1. The man is a teacher. --> a teacher作为补足语,补充说明前面的teacher -2. Mary's new dresses are colorful. --> 第一个is是连接主语和后面的补足语成分 -3. My mother was in the kitchen. --> in the kitchen,说明了主语的位置,be动词连接主语 +说明主语的动作或状态。常用动词或动词词组担任,放在主语后面,通常有简单谓语和复合谓语。 -练习: +简单谓语:由单个动词或动词词组充当谓语 -1. 他们是老师(they,teachers) +复合谓语:由情态动词或者其他助动词+动词构成,或由系动词+表语构成,系动词单独不做谓语 - they are teachers. +1. You should clean the house.(情态动词+动词) +2. You look beautiful today.(系动词+表语) +3. My brother is reading a book. (助动词+动词) +4. He has finished homework.(助动词+动词) -2. 他以前是一名老师(he, a teacher,before) +burst into laughter(突然大笑) - he was a teacher before. +burst into tears(突然大哭) -3. 他已经当了3年的老师(for 3 years) +and but or并列连词,前后连接的东西要一样,如果前面是个句子,后面就需要是个句子 - he has been a teacher for 3 years. +祈使句谓语把动词原形放在开头,省略主语you -# Be动词的否定、提问、回答 +非谓语有ing、to do、done形式 -在am,is,are,was,were后面加not. +## 宾语 -缩略式am not,isn't,aren't,wasn't,weren't +表示动作的对象,是动作的承受者。宾语一般放在动词或动词短语之后。介词后也会跟宾语。 -## 使用be动词提问和回答 +refused to do sth:拒绝做某事 -- Is he a teacher? -- Yes he is / No,he isn't +cooperate with sb:与某人合作 +succeed in:在某方面取得成功 +介词后面要加动词的ing -- Are you a teacher? -- Yes,I am / No,I am not. +**双宾语和宾补** +宾补:宾语补足语,只补充说明宾语的动作、身份、状态 +I bought my mother a gift. +主 谓 宾 宾 +We made him a teacher. +主 谓 宾 宾补 -- Were they teachers? -- Yes,they were / No,they weren't +区别 -# 代词的主格和宾格 +双宾:mother !=a gift两者中间无联系 -## 主格代词 +宾补:两者之间有联系,him可以是teacher -主格代词一般用于主语的位置上 +be to do:将来时 -I,he,she,it,you,we,they +pay attention to:注意 -I:我 +## 定语 -he:他 +单词作定语时通常放在它所修饰的名词之前,短语和从句作定语时则放在它所修饰的名词之后 -she:她 +a || an || the adj. n.句型 -it:它 +## 状语 -you:你/你们 +状语用来修饰动词、形容词、副词或者是全句,说明方式、因果、条件、时间、地点、让步、方向、程度、目的等 -we:我/我们 +so that 如此,以至于 -they:他们 +managed to do:设法做某事 -1. I am a teacher. -2. He is a teacher -3. You are teachers +because + 句子 -## 宾格代词 +because of + 词或者短语、ing -me,him,her,it,you,us,them +## 补语 -意思与上述主格代词相同 +英语有些及物动词,除了要有宾语之外,还要加上宾语补足语,才能使句子的意义更加完整。它起补充说明宾语要干什么,怎么样的作用 -1. He likes me. -2. We like her. -3. I like them. +in good order:井然有序 -# 名词性/形容词性物主代词 +broken in:闯入 -## 形容词性物主代词 +break up:分手 -不可单独,需要形容后面的词 +break out:爆发 -单数形式: +break down:出故障 -- my:我的 -- your:你的 -- his:他的 -- her:她的 -- its:它的 -- one's:某人的 +sometimes 有时候 -复数形式: +some times 几次 -- our:我们的 -- your:你们的 -- their:他们的 +some time 一些时间 +sometime某个时候 +## 表语 -1. This is my book. -2. We love our motherland. -3. Those are your socks. +放在系动词之后。是用来说明主语的性质、特征、状态与身份。表达主语具体情况。 -## 名词性物主代词 +不可数:little 几乎没有;a little 有一点 -本身就含有了名词的概念,后面不能再接名词 +可数:few 几乎没有;a few 有一点 -单数形式: +## 同位语 -- mine -- yours -- his -- hers -- its -- one's:某人的 +同位语是在名词或代词之后并列名词或代词或名词短语对前者加以说明的成分,近乎于后置定语。 -复数形式: +# 名词 -- ours:我们的 -- yours:你们的 -- theirs:他们的 +## 特殊规则 +名词+s是复数,动词+s是单数 +大多数情况,元音字母用an,辅音字母用a -1. The book is ours -2. The apple is hers +少数情况:universe -> a -image-20240505143118850 +- an + - hour + - honest + - honor -# 反身代词 +do 后面需要用动词的原型 -单数形式 +## 可数名词规则变化 -- myself:我自己 -- yourselft:你自己 -- herself:她自己 -- himself:他自己 -- itself:它自己 +一般可数名词直接在词尾+s -复数形式 +看到s、x、ch、sh结尾,加es -- yourselves:你们自己 -- ourselves:我们自己 -- themselves:他们自己 +一般情况下o结尾,有生命加es,无生命加s -作用: +以f或者fe,变ves -- 做宾语 -- 做同谓语 +看到元音+y,直接加s;看到辅音+y,变ies -# 实意动词 +专有名词直接加s -动作有实际意义的动词称为实意动词 +如果是合成词(由多个单词组成的词),比如Englishman,可以被拆分成English man,那么就让表示人的单词变为复数,说明让man变为复数,也就是说变为Englishmen -## 实意动词的特征 +germ 细菌 萌芽 -实意动词 +## 可数名词不规则变化 -- come:来 -- read:读 -- go:去 -- watch:看 -- play:玩 -- fly:飞 +1. 元音变化 + - woman women + - tooth teeth + - wife wives +2. 词尾变化 + - child children + - ox oxen +3. 单复数同形 + - sheep + - Japanese + - Chinese + - fish + - deer +4. 只有复数形式的名词 + - scissors(剪刀) + - trousers(裤子) -单三形式:一般现在时,主语是第三人称单数,需要使用动词的单三形式,在动词后面加入s、es、或将最后的y改成res +## 名词所有格 -1. He comes from Shenyang. -2. She is reading story books. -3. They went to America yesterday. - - 这里的went是由go的过去形式产生的 -4. We have watched the game for three times. -5. My mother will fly back to China next month. +名词所有格表示所有的关系意为“........的” -## 实意动词的否定/提问/回答 +- 有生命 + - 单数名词后+'s + - 以s结尾的复数 + ' +- 无生命 + - 名词A + of +名词B -使用助动词进行否定 +A+B's + n(单数) + v(单数) -在助动词do does did后面加not +A's+B's+n(复数) + v(复数) -do、does:一般现在时,do一般使用在非第三人称单数的上面,而does使用在第三人称单数上 +people -> 人 变为单复数同型 -did:一般过去时 +people -> 名族|部落 a people || two peoples -do not/don't +borrow 别人借给自己(借入) -does not/doesn't +lend 自己借给别人(借出) -did not/didn't +# 冠词 -1. I don't go to school by bus/我不坐公共汽车去学校 -2. She doesn't watch TV everyday/她每天都不看电商 -3. They didn't swim last night/昨天晚上他们没有游泳 +a/an(不定冠词):第一次出现 -使用助动词进行提问 +the(定冠词):上文提到过 -- He often plays golf. - - Does he often play golf? - - Yes,he does / No,he doesn't -- They go to school by bus. - - Do they go to school by bus? - - Yes,they do / No,they don't -- Sam had breakfast yesterday. - - Did Sam have breakfast yesterday?(这里的had需要变为原型) - - Yes,he did / No,he didn't +the:这个,那个 -# 使用疑问词进行提问和回答 +a/an(元音字母结尾使用):一个,一种 -使用疑问词进行提问 +a/an 是表示:数量“一” -- when:什么时候 -- where:哪 -- who:谁 -- what:什么 -- how:怎么 -- how long:多长时间 -- how far:多远 -- how often:多长时间一次 -- why:为什么 +a/an也是表示一类人或一类事物 -He bought three books yesterday. +a用于以辅音音素开头的单词前 -谁买的:Who bought three books yesterday? +an用于以元音因素开头的单词前 -买了什么:What did he buy yesterday? +辅音(特殊):a boy a dog a university -什么时候买的:When did he buy three book? +元音(特殊):an apple an hour -1. They have been in China for three years. +不定冠词(a/an)一般是泛指,定冠词(the)一般是特指 - How long have they been in China?(将have提到主语的前面) +## 定冠词(the) -2. It is about 4 kilometers from Beijing to Xi'an. +1.表示特指某些人或事物 +2.用于序数词前 +3.用于乐器名词前 +4.用于最高级前 +5.用于世上独一无二的事物面前 +6.用于姓氏复数前,表示“一家人” +7.用于形容词前,表示“一类人” - How far is it from Beijing to Xi'an? +the a of b -3. They come to visit me once a week. +## 不加the的情况(零冠词) - How often do they come to visit me?(这里的do是因为原句中不存在助动词,所以借出一个并让主语后面的动词变为原型) +在表示三餐、球类运动、游戏等的名词前 +(1) have breakfast/lunch/dinner +(2) play basketball/footbal +(3) play games -4. She came late,because she missed the bus. +在国名、城市、地名、人名等专有名词前 +China +Shanghai +Beijing +Tom - Why did she come late?(这里的come是变为了原型,did是过去时) +在不可数名词前 +I want to eat rice.我想吃米饭 +I want to drink a cup of tea.我想喝杯茶 -# 名词 +在节假日、季节、星期等名词前 -名词分两类: +Today is Sunday.今天是星期天 +National Day falls on October 1st.国庆节是在10月1号 +Spring is very warm.春天非常温暖 -1. 可数名词(countable noun) +在称呼语、官职、头衔等名词前 - 指数得过来的概念 +Uncle Sam -2. 不可数名称(uncountable noun) +共有是A+B's + 单数 - 无法计算的数量或抽象概念 +各有A's+B's + 复数 -- 可数名词:apple,pencil,student -- 不可数名称:salt,coffee,water,history,love +# 动词 -两个或两个以上的名词,需要变为复数 +表示状态或动作的词叫动词 -可数名词有单数和复数之分: +实义动词 +表示行为、动作或状态的词,具有实在的意义,又称为行为动词。如:play,,give,listen -- apple-apples -- pencil-pencils -- tomato-tomatoes +助动词 -不可数名称无复数,只用单数表征: +帮助实义动词构成各种时态的动词,如:do,does, did,will -- salt-salt -- coffee-coffee -- water-water +情态动词 +表示说话人情感和态度的词,后面接实义动词原型。如:如:can,may,must,need -名称变复数的规则 +系动词 -1. 一般末尾加上后缀-s,friend->friends -2. 以s、z、x、ch、sh结尾的词,在该词末尾加上后缀-es,bus -> buses -3. 辅音字母+y结尾的名词,将y改为i,再加-es,candy->candies -4. 以-o结尾的名词,如果不是外来词或缩写,就加-es,tomato->tomatoes,hippo(河马)->hippos[河马这个单词较长,所以被省略了很多,只加s] +用来帮助说明主语“是什么”或“怎么样”的动词,如:be,look,smell,taste, sound,feel,become, get -元音字母:a、e、i、o、u +## 动词的基本形式 -辅音字母:其他都是辅音字母 +动词原形 .v +第三人称单数现在式 .v+s -外来词:不是英语词汇 +现在分词 .v+ing +过去式 .v+ed +过去分词 .v+ed -缩写词:将一段长词汇简略就是缩写词 +## 三单变复数规则 +- 一般动词,词尾直接十s; +- 以s/x/o/ch/sh 词尾+es; +- 以辅音字母十y结尾的动词,词尾变y为i+es. +- a,e,I,ou 是元音字母,其他都是辅音字母 +- 特殊变化 -可数名词前可以加a(an)或量词 +## 动词现在分词 -- apple - - an apple(以元音字母开头的单词用an表示一个) - - apples - - a box of apples -- tomato - - a tomato - - tomatoes - - a bag of tomatoes +一般动词,词尾直接+ing; +以不发音e结尾动词,去e+ing; +以辅元辅结尾动词,双写词尾辅音字母+ing +以-ie结尾的动词,变ie为y再加ing -不可数名称前不可加a(an).没有复数,但前面可以加量词 +lie 表示说谎时的过去式或过去分词 lied lied -- coffee - - a cup of coffee +lie 表示躺的过去式或过去分词 lay(下蛋) lain -# 指示代词和不定代词 +tie 做名词表示领带,动词的ing表示系 -- 指示代词:标识人或事物的代词,用来替代前面已提到过的名称 +## 动词过去式和过去分词 -- this:这个 +一般动词,词尾直接+ed; +以e结尾动词,词尾+d; +以辅音字母十y结尾的动词,词尾变y为i+ed. +以辅元辅结尾的动词,双写词尾辅音字母十ed - these:这些 +leave 的过去式 left - that:那个 +lose 的过去式 lost - those:那些 +go 的过去式 went -- 不定代词:指代不确定的人或事物。 +go 的过去分词 gone -- one:一个 +run 的过去式 ran - the other:另外一个 +run 的过去分词 run - some:一些 +come 的过去式 came - any :一些 +come 的过去分词 come - something:某物/事 +fly 的过去式 flew - nothing:什么都没有 +fly 的过去分词 flown -- No one knows where he is.(没有一个人知道他在哪,这里的one不明确) -- x // 中缀表达式转后缀表达式并计算public static String computedInfixResult(List list){    // 初始化两个栈,数栈和结果栈    Stack stack1 = new Stack();    Stack stack2 = new Stack();    for (String val : list) {        if (val.matches("\\d+")){            // 数字载入数栈            stack1.push(val);       }        else{            // 不为数栈            // 则为运算符或小括号            // 判断结果栈是否为空,为空或为小括号就直接加入            if(stack2.isEmpty() || stack2.peek().equals("(")){                stack2.push(val);           } else if (priority(val) == -1) {                // 为小括号,则直接压入栈中                if (val.equals("("))                    stack2.push(val);                else{                    // 右括号                    while (true){                        if (stack2.peek().equals("(")){                            // 当比较后不为(时,进行循环,依次弹出每一个顶上的数据                            stack2.pop();                            break;                       }else {                            // 存入其它运算符                            stack1.push(stack2.pop());                       }                   }               }           } else if (priority(val) >= priority(stack2.peek())){                // 如果新的运算符优先级大于栈顶运算符的优先级的话                stack1.push(stack2.pop());                // 当结果栈不为空时,比较优先级                while (!stack2.isEmpty()){                    if (priority(val) >= priority(stack2.peek())){                        stack2.push(val);                   }else break;               }           }       }   }    while (!stack2.isEmpty()){        stack1.push(stack2.pop());   }    StringBuilder res = new StringBuilder();    int size = stack1.size();    for (int i = 0; i < size; i++) {        res.append(stack1.pop() + " ");   }    return String.valueOf(res.reverse());}​// 返回运算符的优先级,自定,返回的数字越大优先级越高public static int priority(String operation){    if (operation.equals("*") || operation.equals("/")){        return 1;   } else if (operation.equals("+") || operation.equals("-")) {        return 0;   }else{        return  -1;     // 假定的表达式只有加减乘除   }}​​// 将中缀表达式转成对应的Listpublic static List toInfixExpressionList(String s){    // 定义List,存放中缀表达式对应的内容    List ls = new ArrayList<>();    int i = 0;  // 指针,用于遍历表达式中的字符串    String str; // 多位数拼接    char c; // 遍历每一个字符,放入到c中    do{        // 如果c不是数字,就加入到ls        if ((c = s.charAt(i)) < 48 || (c = s.charAt(i)) > 57){            ls.add("" + c); // 不为数字,说明是运算符,直接加入            i++;    // 指针后移       }else{            // 如果是数字,需要考虑多位数的情况            str = "";   // 每一次都需要重置该字符串            while (i < s.length() && (c=s.charAt(i)) >= 48            && (c=s.charAt(i)) <= 57){                // 48 - 57 -> 0 ==> 9                str += c;   // 对数字进行拼接                i++;           }            ls.add(str);       }   }while (i < s.length());    return ls;}java +see 的过去式 saw -# 形容词 +see 的过去分词 seen -形容词通常形容人或事物的状态,性质,大小等,通常用在名词前,be动词后 +swim 的过去式 swam -- beautiful-the beautiful girl -- The girl is beautiful +swim 的过去分词 swum -The + 形容词 = 复数名词,表示一类。后面的动词使用复数 +buy 的过去式、过去分词 bought -- old-the old -- young-the young -- The old need more care than the young +## 双写规则 -# 副词 +**辅元辅,结尾重读** + +let letting -副词可以修饰动词,形容词,其他副词以及其他结构 +run running -- He runs fast -- She is very beautiful -- They work very hard +swim swimming -副词的位置: +shop shopping -1. 根据情况,放在助动词之后,实意动词之前或之后 -2. 形容词之前,其他副词之前或之后 -3. 多个助动词时,副词一般放在第一个助动词后 +**辅元辅,结尾不重读** -- He speaks very fast -- They have already left -- They have already been repaired +listen listening -常用的频度副词(always,usually,often,sometimes,never)的位置通常放在一般动词前面,be动词后面,助动词和实意动词之间。 +visit visiting -- They always come early. -- Sam often writes homework at 7:00. +**我想要不wxy** -# 不定量表达法 +know knowing -- some:一些 -- any:一些 -- most:大多数 -- every:每一个 -- all:所有的 +grow growing -**some,any都表示"一些",some主要用于肯定句,希望得到肯定回答时,也可用在疑问句中,any主要用在否定和疑问句中。** +mix mixing -- I'd been expecting some letters the whole morning,but there weren't any for me +buy buying -**most作形容词时表示大部分的,后面接复数名词** +play playing -- Most people here are from China. +其他情况 +quit **quitting** 停止;放弃 +quiz **quizzing** 小测试 +equip equipping 装备 +forget forgetting 忘记 +regret regretting 后悔;遗憾 +begin beginning 开始 +permit permitting 允许 +admit admitting 承认 +forbid forbidding 禁止 +prefer preferring 宁愿;更喜欢 +refer referring 涉及;参考;查阅 +occur occurring 发生 -**every表示"每一个,所有"后面接单数名词** +![image-20241218140936382](https://s2.loli.net/2024/12/18/nqDayo8XeW3vVYs.png) -- Every one likes the film +# 介词 -**all表示"所有",后面接可数名词复数,不可数名词单数。** +介词是英语中很活跃的词,也是介词 prep.(preposition) -- All the cars are parked in the parking lot. -- All the coffee is served on time. +位置:一般置于名词之前 +它常和名词或名词性词语构成介词短语 +beside 在...旁边 -- both:表示两者都,可作形容词,代词,副词 -- either:是两者之一 -- neither:是两者都不 +into 在里面 -1. **Both** his eyes were serverly burned. -2. There are trees on **either** side of the street. -3. **Neither** answer is correct. +out of 在外面 +among 在...中间(三个及以上) +past 通过 -- many:修饰可数名词,表示“许多” -- much修饰不可数名词,表示“许多” -- a lot of[lots of],plenty of 均可修饰可数和不可数名词 +across 穿过 通过 -many books、much water +along 沿着 -a lot of/ lots of books / water +through 通过(从内部通过) +**at + 较短的时间 < 1 day(日出日落)** +**on + 日期(具体时间) / 星期 / 节日 = 1 day(具体时间)** -- a few:为肯定含义“几个” -- few:为否定含义“没几个” +**in + 周 / 年 / 季节 / 早中晚 > 1 day(较长时间)** -以上两个词均可和**可数名词**连用 +in 在...里面 -- A few books are put into the box. -- Few books are put into the box +on 在...上面(接触表面) +under 在...下面 +behind 在...后面 -- a little为肯定含义“一点儿” -- little为否定含义“没多点” +in front of 在...前面 -以上两个词均可和**不可数名词**连用 +above 在...上面(不接触表面,不一定在正上方) -- There is a little water in the bottle -- There is little water in the bottle +below 在...下面(不接触表面) +between 在...中间(两者) +next to 挨着,在...旁边 -none和no one的意思相同,主要作代词,翻译为“一个也不,一点也不”,用法稍有区别 +image-20241218164254699 -1. none**可以**接of短语,动词可用单数也可用复数 -2. no one**不能**接of短语,动词只能用单数 +at用于表示一个较小的场合 +in表示在较大的地方;在...的里面 +on表示在...之上,强调与某物体有接触 +under强调在某物的下方,完全覆盖两物体表面可以接触也可以不接触 +between表示两者之间 +behind表示在...后面 +in front of表示在...前面 +up表示往上 down表示往下 +near表示有一定距离,只是对于说话者来说是在附近 -- No one knows the answer -- None of us have(has) arrived +# 连词 +## 并列连词 +前后语法地位一致 -# There/Here be句型 +**表示并列关系 and** -There/Here + (be) 根据上下文,有多种翻译方法,可以翻译成“有”,“这是”,be动词根据后面的名词有单复数变化 +and(和,并且) +I like blue and black. +Tom and Jerry are good friends. +and:用来连接并列的词、词组或句子 -- There is a book on the bookshelf. -- There are some books on the bookshelf. -- Here is the bus stop. -- Here are your books. +**表示选择关系 or** +or(表示“或"“否则”,表示选择或转折) +Which do you like better, apples or pears?(在疑问句中表示选择) -# 一般现在时和现在进行时 +He doesn't like milk or juice.(在否定句中表示并列) -一般现在时,表示通常性、规律性、习惯性的状态或者动作。主语是单数第三人称时,动词有单三的变化,主语是非第三人称单数时,动词变为原形 +Get up,or you'll be late. -1. They often get up at 7:00. -2. He often gets up at 7:00 +and通常用在肯定句中,而or通常用在否定句疑问句中 -一般现在时,动词的单三变化: +**拓展** -1. 在动词尾直接加s +eithor or、neither nor、not only but also就近原则 - 如:play-plays +Study hard, or your math will be worse. +(努力学习,否则你的数学成绩将会很差) +Study hard,and your math will be better +(努力学习,那么你的数学成绩将会很好) -2. 以字母s、x、ch或o结尾的动词加-es,如:guess-guesses +and和or都可以在祈使句中使用 -3. 以辅音字母+y结尾的动词,先变y为i,再加-es,如:study-studies +“and +句子" 通常是比较好的结果,意思是"...那么就会" +‘or+句子" 则表示不愉快不理想的结果,意思是"...否则就会" -- 一般现在时否定和疑问句用do,does帮助构成 - 1. He doesn't like the car.(does用在单三上,do用于非单三) - 2. Does he like the car ? - - Yes,he does./No he doesn't +or 用于疑问或否定句,and用于肯定句 +**表示转折关系 but** +but(但是,可是) -现在进行时表示现在正在进行或发生的动作。句子通常有now等时间副词呼应,基本构成形式为**be + doing** +**表示因果关系 so** -1. They are watching TV. -2. He is watching TV. -3. I am watching TV. +because(因为) +so(所以) +because 和 so不能同时出现在句子里 -动词现在分词的变化规则: +## 从属连词 -1. 一般情况下,直接在动词后加-ing,如:work - working -2. 动词以不发音的 -e 结尾,要去e加Ing,如:take - taking -3. 重读闭音节的动词,要双写词尾字母,再加 -ing,如:cut - cutting -4. 以-ie结尾的动词,变y再加-ing,如:lie - lying +引导从句 +# 代词 +image-20241219154845508 -现在进行时变否定句和疑问句时,将be动词否定或提前 +## 人称代词 -1. They aren't watching TV. - - Are they watching TV? -2. He isn't watching TV. - - Is he watching TV? -3. Am I watching TV? - - Yes,you are / No,you aren't. +为了避免重复,用来代替前面所提到的人或者物等的代词 +它有两个选择:主格和宾格 -# 一般过去时和过去进行时 +主格 发出动作,宾格 动作承受者 -一般过去时表示过去某个时间里发生的动作或状态;过去习惯性、经常性的行为 +主格:在句子中作主语(一般用在动词前)。 -- 基本结构:主语+动词过去式+其他,一般动词在动词后面加ed,还有一些不规律动词不规则变化 +宾格:在句子中作宾语。(动作的承受者,多用于动词、介词后) -- play-played、come-came - 1. He worked very hard last night. - 2. They came here by car. +## 物主代词 -动词一般过去时变化规则: +形容词性物主代词(形容词) -1. 一般在动词后加-ed。如:play-played -2. 在以字母e结尾的动词后,只加-d。如:like-liked -3. 在以"辅音字母+y"结尾的动词后,改y为i,再加-ed。如:supply-supplied -4. 在以重读闭音节结尾且末尾只有一个辅音字母的动词后,双写最后一个辅音字母,再加-ed。如:plan-planned +名词性物主代词(名词) + +## 代词总结 + +主 宾 形容词性物主代词 名词性物主代词 + +image-20241219162428109 + +# 反身代词 +表示反射或者强调的代词,表示某某自己;当主语和宾语为同一物时,表反射;当其位置在名词、代词之后,或位于句尾,表强调。 +我 -- myself -过去进行时表示在过去某一时刻或某一时间内进行或发生的动作。 +你 -- yourself -其形式为was / were + doing +他/她/它 -- himself/herself/itself -1. They were waiting for you. -2. He was talking with his friends just now. +我们 -- ourselves -# 将来时 +你们 -- yourselves -一般将来时表示将来某一时刻的动作或状态,或将来某一段时间内经常发生的动作或状态。常常和表示将来的时间状语连用。 +他们 -- themselves -- tomorrow(明天) -- next week(下周) -- int the future(将来) +# 指示代词 +用来指代或标记人或物的代词 +有4大家族: +this(这个) +that(那个) +these(这些) +those(那些) +this和that后接的谓语动词为单数形式, +these和those后接的谓语动词为复数形式。 -”助动词will或shall + 动词原形“,表示将来发生的事情。 +this和these常用来指代空间上较近的人或物,that和those常用来指代空间上较远的人或物 -1. They will go to Shanghai by ship tomorrow. -2. We shall leave for Shanghai in next month. +Tips:打电话时,用this指代自己;如果要问对方是谁,通常用that. +# 数词 +## 考点 -"be going to + 动词原形"用来表示近期或事先考虑过的将要发生的动作以及已有迹象表明必将发生某事,意为“打算;就要”。 +①表示概述/不确定的数字,+s:hundreds of 成百上千、dozensof/scores of很多 +②表示确定的数字,不+s:threehundred、threedozen +③“基数词+连字符+名词"可以构成复合形容词,表示数量,此时名词应用单数形式。 +a two-dayaftivity(=two daysactivity)为期两天的活动 +a three-hour drive (=three hoursdrive)三小时的车程 +an-hour trip (=an hour’s trip)一小时的旅途 +a?n→中间是缺了→形容词 +①in one’s twenties +in the1820s/1820's +everytwohours=every secondhour“每两小时/每隔一小时” +The second time第二次a second/third/forthtime又一次;再一次 +③“名词+基数词"可以表示书页、房间、住所等的编号及邮政编码,电话等,此时首字母常大写。另外表示编号时也可用“the+序数词+名词”,此时首字母不用大写 -- They are going to play football this afternoon -- She is going to learn French next year. +在英语当中我们的数词分为基数词和序数词两类。 +**基数词**就是我们平时熟知的数字数量而**序数词**则表示次序 +描述数量的多少称为基数词 +13~19 后缀+teen -“be doing”表示位置转移的动词。如:go,come,leave,start,arrive,可用现在进行时表示将来时。 +20~99 整10位:后缀+ty -1. They are leaving for Japen. -2. She is arriving tomorrow. +非整十数:整十位数 + 个位数,例如21,twenty one -# 完成时 +100~999 整百位数:后 + hundred +非整百位数:整百+整十+个位数 例如121 one hundred and twenty one + +注意13、15、18的基数词构成 +13:thirteen +15:fifteen +18:eighteen + +非整十位数:整十位和个位数之间需要有连线符 +22: twenty-two +非整百位数中:百位数和十位数之间用and连接 +122:one hundred and twenty-two + +序数词:表示次序的数词称为序数词,在汉语中表示“第几” + +4~19 +基数词后缀+th表示“第” + +20~99 +整十位数:变y为 ie+th; +非整十位数:个位数用序数词 + +百位以上 +结尾处变为序数词即可 + +1-20的序数词如下图所示 + +image-20241219204009524 + +# 形容词 -现在完成时(have + p.p.[过去分词]),动作过去发生,已经完成,对现在造成影响或后果,动作可能还会持续,可使用的时间状语为:already(已经) 和 yet(还) +形容词在句中用来修饰和描述名词和代词 +形容词是表示人或事物性质、状态和特征的词,一般表示.....的 -1. They have already arrived in Shanghai. -2. She has played soccer for 3 hours.(这里的has是根据单三的形式发生变化) -3. She hasn't finished the homework yet. +形容词在句中一般放在名词之前; +形容词在句中也可放在am,is,are,was,were之后 +形容词的同级、比较级和最高级:多数形容词都可以用于比较、说明事物间的等级、程度差别。 +形容词比较构成 +a.大部分形容词:词尾加er或est + +b.以e结尾的形容词:词尾加r或st + +c.以重读闭音节结尾,且结尾只有一个辅音字母的形容词:双写这个辅音字母,再加er或est + +d.以辅音字母+y结尾的形容词:变y为i,再加er或est + +e.两个或两个以上音节的形容词:+比较级的原级 + +**不规则变化的形容词** + +原型-比较级-最高级 + +many-more-most + +much-more-most + +few-fewer-fewest + +little-less-least + +用法小贴士: +many与few用与可数名词前, +much与little用于不可数名词前 + +## 比较级的用法 + +形容词比较级+than+对比成分:表示“..比...更. + +e.g.篮球比排球大 +A basketball is bigger than a volleyball. + +同级比较:形容词的原级也同样可以用于比较 +肯定:as +形容词原级+as表示.......样 +e.g. He is as tall as his brother. + +否定:not as+形容词原级+as表示“不如" +e.g.The vase is not as good as this. + +the + 形容词最高级+(名词)+比较范围:表示“..最..” -> 三者及以上 + +The older the wiser. +人老智多,姜还是老的辣 +Blood is thicker than water. +血浓于水 +Two heads are better than one. +人多智广/三个臭皮匠顶个诸葛亮 +East or west, home is the best +金窝银窝不如自己的草窝 +Experience is the best teacher. +实践出真知 +He knows most speaks least. +大智若愚 + +# 副词 +副词独白:简写为adv -过去完成时(had + .p.p),表示句中的动作发生在过去之前,即过去的过去,已经完成,对过去造成了一定的影响或后果 +是表示时间、场所、状态、频率、疑问及程度等的词。 -1. They had arrived in Shanghai. -2. She had played soccer for 3 hours. -3. They hadn't finished the work yet. +一般是由相应的形容词加ly构成的。 +副词是可以用来修饰词,词组或整个句子。 +副词位于形容词/副词的前面,动词的后面 +形容词变副词 +1 直接在形容词后加 ly +如:quiet quietly slow slowly +2 以辅音字母加y结尾的形容词,要先将y变成i,然后再加ly +如:happy happily busy busily +3有些形容词和副词形式完全相同,如:hard,early -# 动词用法 +时间副词 then, next, already, finally, today, soon. +频率副词 often, usually, never, frequently, always +疑问副词 how, when, where, why.. -动词根据功能分为四类 +# 一般将来时 -- 实意动词(Notional Verb) -- 系动词(Link Verb) -- 助动词(Auxiliary Verb) -- 情态动词(model Verb) +I am going to do something. +I am going to wash car/clothes tomorrow +be going to do -> 一般将来时 -1. 动词有数量和时态的变化,时态通常有三大时态:现在,过去和将来时 -2. 根据动作进行的状态可分为:一般时,进行时和完成时 -3. 使用动词时通常将(1)和(2)结合。例如:一般现在时,过去进行时 +一般将来时表示单纯的将来事实。 +主语后通常有助动词will + 动词原形构成以及对应be动词+going to+动词原形 -- He goes to school every day. -- He went to hospital last night. +主语 + be going to +动词原形+…=肯定句 +主语+be not going to +动词原形+ ..=否定句 +be +主语+going to+动词原形=一般疑问句 -image-20240508192138589 +一般将来时状语 -# 情态动词 +in+将来时间 +in 2020、in 2025、in the future -1. can/could 表示能力,用be able to代替can/could 现在/过去的能力客观可能性(can的可能性大),表示请求和允许 +next+时间 +next Monday、next year、next week +不规则 +tomorrow、from now on、soon -- He can/could/is able to swim. -- He can/could come tomorrow. -- Can/could I stay here? +be going to +一般指已经计划好的事情,强调某个意图,是经过事先考虑好的 +will +指主语本身愿意做的事情,没有经过事先考虑,而是在说话的当时临时想到的 -1. may/might 表示可能性,may的可能性大,在请求、允许中might更委婉 +be going to +表示近期眼下就要发生的事情。 -口语中常用的回答: +will -- Yes,please. -- No,you can't/mustn't(禁止,不准) +表示的将来时间则较远一些 +will +主语猜测或希望等内心活动,想得到肯定的、将会发生的事情 -1. He may/might come here by bus. -2. May/might join you? - - Yes,please/No,you can't/No,you mustn't diff --git "a/public/markdowns/\350\256\241\347\256\227\346\234\272\345\237\272\347\241\200.md" "b/public/markdowns/\350\256\241\347\256\227\346\234\272\345\237\272\347\241\200.md" new file mode 100644 index 0000000..9c80531 --- /dev/null +++ "b/public/markdowns/\350\256\241\347\256\227\346\234\272\345\237\272\347\241\200.md" @@ -0,0 +1,66 @@ +--- +title: 计算机基础速成 +tags: 基础速成 +date: 2024-12-20 17:11:05 + +--- + +# 计算机基础 + +世界上第一台电子计算机ENIAC 1946年诞生于美国 + +四代主要元器件: + +1. 电子管 +2. 晶体管 +3. 中小规模集成电路 +4. 大规模或超大规模集成电路 + +第二代存储器为磁芯磁盘磁带 + +第二代出现高级程序、第三代出现操作系统和会话式语言 + +# 计算机辅助系统 + +CAD计算机辅助设计 + +CAM计算机辅助制造 + +CBE计算机辅助教育 + +CAI计算机辅助教学 + +CMI计算机管理教学 + +CAT计算机辅助测试 + +CIMS计算机集成制作系统 + +CAE计算机辅助工程 + +计算机特点:运算速度快、计算精度高、储存容量大、具有逻辑判断能力、工作自动化、通用性强(速精储逻自通) + +计算机的发展趋势:巨型机、微型机、网络化、智能化(巨微网智) + +位bit是计算机存储数据的最小单位 + +字节B是计算机存储数据的基本单位 + +1B=8bit 1KB=1024B 1MB=1024KB + +1GB=1024MB 1TB=1024GB + +ASCII 美国标准信息交换代码 共128个字符 + +不可打印字符33个 + +ASCII码表示:运算符号、控制符号、英文标点符号、十进制0~9 + +7位,存储1个字节 最高位为0(标) + +8位,存储1个字节 最高位为1(拓展) + +(0~9 48~47)(A~Z 65~90) (a~z 97~122) + +空格<数字<大写字母<小写字母 + diff --git "a/public/markdowns/\351\253\230\347\255\211\346\225\260\345\255\246.md" "b/public/markdowns/\351\253\230\347\255\211\346\225\260\345\255\246.md" index a437d14..437e1be 100644 --- "a/public/markdowns/\351\253\230\347\255\211\346\225\260\345\255\246.md" +++ "b/public/markdowns/\351\253\230\347\255\211\346\225\260\345\255\246.md" @@ -301,7 +301,7 @@ arcsin、arccos、arctan与sin、cos、tan相同 常见有界:sin、cos、arctan -![image-20240813210845806](https://s2.loli.net/2024/08/13/B1FADLPHrjKeEoI.png) +image-20240813210845806 0乘有界=0 @@ -313,7 +313,7 @@ arcsin、arccos、arctan与sin、cos、tan相同 ## 第二重要极限 -![image-20240814210457482](https://s2.loli.net/2024/08/14/VxGYN25lqQf4X6e.png) +image-20240814210457482 image-20240814211811921 @@ -418,23 +418,23 @@ f(x0) = 左极限 = 右极限 = 连续 常用公式 -![image-20240920220853858](https://s2.loli.net/2024/09/24/SOU8daiqyoNpbCQ.png) +image-20240920220853858 -![image-20240920220944107](https://s2.loli.net/2024/09/24/leNopjiVMhrXzsH.png) +image-20240920220944107 例题 -![image-20240920221140608](https://s2.loli.net/2024/09/24/vSl61NBcF2yd5KH.png) +image-20240920221140608 导数相乘和导数相加减不同 -![image-20240920221403043](https://s2.loli.net/2024/09/24/dtLjJCI8xgm34yH.png) +image-20240920221403043 -![image-20240920221707297](https://s2.loli.net/2024/09/24/vWmpXe5uGjA8Fob.png) +image-20240920221707297 导数相除 -![image-20240920221810272](https://s2.loli.net/2024/09/20/AktVQRm9n4TJFgO.png) +image-20240920221810272 ## 复合函数求导 @@ -446,11 +446,11 @@ f(x0) = 左极限 = 右极限 = 连续 复合函数乘法求导 -![image-20240921205725441](https://s2.loli.net/2024/09/24/sOvwZDrBPoRNUEa.png) +image-20240921205725441 ## 幂指式求导 -![image-20240921210927100](https://s2.loli.net/2024/09/24/cI6xitPAuvo8lSV.png) +image-20240921210927100 计算完成后,改写为原式子 @@ -458,13 +458,13 @@ f(x0) = 左极限 = 右极限 = 连续 例: -![image-20240921212319313](https://s2.loli.net/2024/09/21/TCALpuhKOk28FZD.png) +image-20240921212319313 ## 隐函数求导 隐函数的二阶导直接对一阶导再次求导即可 -![image-20240924205027272](https://s2.loli.net/2024/09/24/Yxl6LuU83FkQIgs.png) +image-20240924205027272 方法 @@ -472,9 +472,9 @@ f(x0) = 左极限 = 右极限 = 连续 例题 -![image-20240924211306480](https://s2.loli.net/2024/09/24/7LW4Nvy8Y6QjVga.png) +image-20240924211306480 -![image-20240924212123558](https://s2.loli.net/2024/09/24/zyGMQWkBXZg1dmj.png) +image-20240924212123558 ![image-20240924213334439](https://s2.loli.net/2024/09/24/NCn6P5wgLmBG4KH.png) @@ -564,7 +564,7 @@ Cxx的求解方式 ## 微分计算 -![image-20241028215055400](https://s2.loli.net/2024/10/28/mZsqjYRKFE3xudH.png) +image-20241028215055400 ![image-20241028215221699](https://s2.loli.net/2024/10/28/YgEIyqJT9RaWf75.png) @@ -1234,3 +1234,64 @@ x型与y型的顺序交换 ## 一阶偏导 +关于哪个函数的变化 + +image-20241202163418074 + +写法 + +image-20241202164445756 + +计算方法 + +image-20241202164635347 + +例题 + +dz/dy 就对y求导,x看作常数,反之同理 + +image-20241202165039465 + +## 全微分 + +解法 + +image-20241203192400808 + +## 可微与偏导的关系 + +image-20241203193519444 + +## 二阶偏导 + +一般来说就是正常对x或y求两次导就行,也有特殊的,如下图所示 + +image-20241203195612113 + +## 二元隐函数一阶偏导 + +image-20241203200811459 + +例题 + +image-20241203201540622 + +## 二元隐函数二阶偏导 + +image-20241203202228376 + +## 链式法则 + +从外向里,层层求导 + +链式法则:将每层函数关系罗列 + +## 具体复合函数求导 + +直接对给出条件带入 + +## 抽象复合函数求导 + +解法 + +image-20241203203841533 diff --git a/src/components/Content.vue b/src/components/Content.vue index 711ae7a..12ec981 100644 --- a/src/components/Content.vue +++ b/src/components/Content.vue @@ -44,9 +44,15 @@ export default { setup() { const route = useRoute(); const store = useStore(); + const date = JSON.parse(sessionStorage.getItem("markdownFiles")).find( + (item) => item.title === route.params.title + ).date; const article = ref({ title: route.params.title || "无标题", - date: route.params.date || "未知日期", + date: + new Date(date).toLocaleDateString("zh-CN", { + timeZone: "Asia/Shanghai", + }) || "未知日期", content: "", }); const titles = ref([]); diff --git a/src/components/RSSGenerator.vue b/src/components/RSSGenerator.vue index bcbbee2..16c6a26 100644 --- a/src/components/RSSGenerator.vue +++ b/src/components/RSSGenerator.vue @@ -1,6 +1,6 @@ @@ -63,9 +63,9 @@ const generateRSS = () => {