第一篇：词汇学复习要点总结
词汇学复习要点总结
1.Word definition: A word is defined by the association of a given sense with a given group of sounds capable of a given grammatical use.[ P 2]
2.The development of English vocabulary[P 3]
(1)The Old English: 449-1100,(2)Middle English: 1100-1500
(3)Modern English: 1500-present
3.Classification of English Words[P 9]
(1)By origin: native words and loan words
(2)By level of usage: common words;literal words;colloquial words;slang words;technical words
(3)By notion: function words and content words
4.Function words & content words[P 17]
Function words are often short words such as determiners, conjunctions, prepositions, auxiliaries, and so forth.Functions words behave like grammatical signals or functional markers, expressing the kinds of connection between content words.5.Morpheme definition[P 21]
The morpheme is the smallest meaningful linguistic unit of language, not divisible or analyzable into smaller forms.6.Allomorphs[P 22]
An allomorph is any of the variant forms of a morpheme as conditioned by position or adjoining sounds.7.Classification of morphemes[P 23]
A.Free morphemes and bound morphemes
B.Roots and affixes
8.区分Inflectional affixes 和Derivational affixes[P 25]
9.Definition of root stem and base [P 33]
(1)Root: A root is a form which is not further analyzable, either in terms of derivational or inflectional morphology.(2)A stem is of concern only when dealing with inflectional morphology….Inflectional(but not derivational)affixes are added to it: it is the part of the word-form which remains when all inflectional affixes have been removed.(3)A base is any form to which affixes if any kind can be added;it may also be defined as”a form to which a rule of word-formation is applied”.10.Differences of root, stem and base [P 33]
(1)Any root or stem can be termed a base.But a base differs from a root, in that the former is a derivationally analyzable form to which derivational affixes are added, while the latter is a form which permits no further analysis.(2)A base is also different from a stem since both derivational and inflectional affixes can be attached to a base, whereas only inflectional affixes can be added to a stem.11.Definition of derivation [P 42]
Derivation may be defined as a process of forming new words by the addition of a word element, such as a prefix, suffix or combining form, to an already existing word.12.Classifications of prefixes [P 44](给定前缀须知意思，连线题)
(1)“negative” prefixes: un-, non-, in-, dis-, a-
(2)“reversative or privative” prefixes: un-, de-, dis-
(3)“pejorative” prefixes: mis-, mal-, pseudo-
(4)“prefixes of degree or size”: arch-, super-, out-, sub-, over-, under-, hyper-, ultra-, mini-
(5)Prefixes of attitude: co-, counter-, anti-, pro-
(6)“locative” prefixes: super-, sub-, inter-, trans-
(7)Prefixes of time and order: fore-, pre-, post-, ex-, re-
(8)“number” prefixes: uni-/mono-, bi-/di-, tri-, multi-/poly-
(9)A miscellaneous catalogue: auto-, neo-, pan-, proto-, semi-, vice-
13.Classifications of suffixes [P 49]
(1)According to the word-class o the word they form
(2)According to the kind of base
14.Differences between initialisms and acronyms [P 72]
Initialism is a type of shortening, using the first letters of words to form a proper name, a technical term, or a phrase;an initialism is pronounced letter by letter.Acronyms are words formed from the initial letters of the name of an organization or a scientific term, etc.Acronyms differ from initialisms in that they are pronounced as words rather than as sequences of letters.15.Clipping [P 75]
The process of clipping involves the deletion of one or more syllables from a word, which is also available in its full form.16.Blending [P 77]
Blending is the process of word-formation in which a new word is formed by combining the meanings and sounds of two words, one of which is not in its full form or both of which are not in their full forms.17.Conventionality [P 93]
Most English words are conventional, arbitrary symbols;consequently, there is no intrinsic relation between the sound-symbol and its sense.A more convincing evidence of the conventional and arbitrary nature of the connection between sound-symbol and meaning can be illustrated by a set of homophones.18.Lexical meaning [P 97] 填空
Lexical meaning may be subdivided into denotative meaning, connotative meaning, social meaning and affective meaning.19.Two process leading to polysemy [P 111]
There are two important process in the development of word meaning: radiation and concatenation.20.Types of homonyms 对其进行区分[P 115]
(1)Perfect homonyms: Words identical in sound and spelling but different in meaning are called perfect homonyms.E.g.lie, page, base.(2)Homophones: Words identical in sound but different in spelling and meaning are called homophones.E.g.bear/bare, dear/ deer, air/heir, pair/pear.(3)Homographs: Words identical in spelling but different in sound and meaning are called homographs.E.g.lead, sow, tear.21.文体效果
Polysemic and homonymous words are stylistically useful to achieve humor or irony, or to heighten dramatic effect.[P 121]
Synonyms, therefore, are extremely valuable stylistically in helping to avoid monotonous repetition and in achieving precision.[P 133]
22.Definition and types of antonym 需举例[P 136]
Definition: the term antonym is used for “oppositeness of meaning”;words that are opposite are antonyms.Types:
(1)On the basis of semantic contrastContraries: Contraries or contrary terms display a type of semantic ○
contrast, illustrated by such pairs as rich and poor, heavy and light.Complementaries: Complementaries or contradictories represent a type ○
of binary semantic opposition.The assertion of one of the items implies the denial of the other;an entity cannot be both at once.E.g.alive and dead, single and married present and absent.Conversives: Another important type of binary opposition.E.g.lend and ○
borrow, husband and wife, employer and employee, above and below.(2)On the basis of morphological structureRoot antonyms: E.g.deep and shallow, love and hate, up and down.○Derivational antonyms: Words with the same roots having negative affixes.○
E.g.happy and unhappy, possible and impossible, loyal and disloyal, prewar and postwar, harmful and harmless.23.简答 Two types of contexts [P 152]
The meanings of words, especially those of polysemous words may be viewed as determined either by linguistic(or verbal)contexts or extra-linguistic(or nonverbal)contexts.(1)Linguistic context: The three main types of linguistic context are the lexical,grammatical, and verbal context in its broad sense.(2)Extra-linguistic context/ Context of situation
（不会答，求高人解答)
24.Linguistic cause 简答[P 172]
Change of meaning is frequently brought about by two tendencies in a linguistic system: towards ellipsis and towards analogy.25.Four Tendencies in Semantic Change 连线题[P 176]
A.Restriction of meaning(specialization);
B.Extension of meaning(generalization);
C.Degeneration of meaning(pejoration);
D.Elevation of meaning(amelioration).26.The common categories of metonymy 连线题[P 187]
A.Sign for the person or thing signified: e.g.from the cradle to the grave;the Cross;bloodshed;crown, scepter, throne.B.Container for its contents;the place for the people occupying it: e.g.the bottle;wardrobe;the town;the chair.C.The abstract for the concrete: e.g.a beauty;the pride;authority or authorities;the management;the press.D.The concrete for the abstract: e.g.tongue;name;seat;the floor;brain;ear.E.A part for the whole and vice versa: for a part to indicate the whole, we have following examples: a sail;hand;head.The whole may be named for a part, e.g.the smiling year;the army;a country.F.The material for the thing made: silver;nickel;plastic;nylons;marble;rubbers.27.填空题 [P 191]
To sum up, an idiom may be defined as a combination of two or more words which are usually structurally fixed and semantically opaque, and function as a single unit of meaning.It is an established form, one that has been accepted by traditional usage.As such, the component words, word order and meaning of each idiom should be learned as a whole.
第二篇：词汇学知识点总结
词汇学期末复习
1.In brief, a word may be defined as a fundamental unit of speech and minimum free form;with a unity of sound and meaning(both lexical and grammatical meaning), capable of performing a given syntactic function.2.The morpheme(词素)is the smallest meaningful linguistic unit of language, not divisible or analyzable into smaller forms.Example: One morpheme: nation Two morphemes: nation-al Three morphemes: nation-al-ize Four morphemes: de-nation-al-ize 3.An allomorph(词素变体)is any of the variant forms of a morpheme as conditioned by position or adjoining sounds.For example: go: went, gone-ion/-tion/-sion/-ation are the positional variants of the same suffix.4.Inflectional affixes(曲折词缀)
Affixes attached to the end of words to indicate grammatical relationships are inflectional, thus known as inflectional morphemes.For example: cats, walked, walking, John’s book„ 5.Derivational affixes(派生词缀)
Affixes added to other morphemes to create new words.They can be further divided into prefixes and suffixes.For example: re＋write, mini＋car, work＋er 6.Connotative meaning(内涵意义)
In contrast to denotative meaning, connotative meaning refers to the overtones or associations which a word suggests or implies.Mother(a female parent)is often associated with ‘love’, ‘care’, ‘tenderness’, ‘forgiving’, etc.Home(a dwelling place)may suggest ‘family, warmth, safety, love, convenience’, etc 7.Stylistic meaning(文体意义)
Words may have stylistic features, which make them appropriate for different contexts.Examples: male parent, father, daddy ；
residence, home, pad 8.Affective meaning(情感意义)
Affective meaning indicates the speaker’s attitude towards the person or thing in question.Words that have emotive values may fall into two categories:
Appreciative or commendatory(褒义): words of positive overtones used to show appreciation or approval.eg: love, cherish, prize, admire, worship, charm.Pejorative or derogatory(贬义): words of negative connotations imply disapproval, contempt or criticism.eg : hate, vicious.9.Collocative meaning(搭配意义)
Collocative meaning consists of the associations a word acquires in its collocation.In other words, it is that part of the word meaning suggested by the words before or after the word in discussion.eg:pretty: girl, woman, flower, etc.handsome: boy, man, car, etc.10.a)Radiation辐射型：
It is the semantic process in which the primary meaning stands at the centre and the secondary meaning radiates out of it.Though all the secondary meanings are independent of one another, they can all be traced back to the primary meaning.face
head
11.b)Concatenation 连锁型:
It is the semantic process in which the meaning of a word moves gradually away from its primary meaning in succession so that the present meaning seems to have no connection to the primary meaning.E.g.candidate：
1)white-roped 2)office seeker in white gowns 3)a person who seeks an office 4)a person proposed for a place, award, etc.12.Linguistic context can be subdivided into lexical context and grammatical context.a)lexical context: refers to the lexemes that co-occur with the word in question.The meaning of the word is often affected and defined by the neighbouring lexemes.E.g“paper” : a term paper，today’s paper ；“do ” : do one’s teeth: brush，do fish: cook.13.b)grammatical context: In some cases, the meanings of a polysemant may be influenced by the structure in which it occurs.E.g.“become”
become + adj./n., means‘begin to be’
become + pron./n., means ‘suit, befit’
become + of, means ‘happen to, often in a bad way’ 1.Causes of changes in word meaning 1)historical cause :It often happens that though a word retain its original form, its meaning has changed because the object it denotes has changed, this is the historical cause of semantic change.eg.pencil(from Latin word meaning)—a little tail or a fine brush, like our Chinese pen
when it was made of wood and graphite石墨，it was still called a “pencil”
2)Social cause : Change in word meaning results from a constant verbal traffic between common words and various technical words.eg.hot and cold have changed their meaning in the field of politics, as in “cold war”,” hot war” and “hot line”
3)Foreign influences : The influence of foreign words is a particularly important cause.eg.stool: any kind of seat for one person including a king’s seat
The French word chair was adopted to denote a more comfortable piece of furniture.4)Linguistic cause
Towards ellipsis 省略
a general---a general officer;uniform—uniform dress
Towards analogy 类推
Energetic(精力旺盛)—formerly meant “to operate, effect” as in “the most energetic chemicals”, now energetic means “of , having or showing energy, vigorous, forceful” as if it had been derived from energy 5)Psychological cause 1）Euphemism（委婉词）：
It refers that the word changed after people use mild, agreeable language when speaking of an unpleasant or embarrassing fact and of taboo subjects as sex and the excretive processes of the body such as death can be used as '' go west''.2）Grandiloquence（夸张）：
It refers to the use of long, important-sounding words for effect.The desire to upgrade or raise the social status of a position, occupation, or institution by changing its common name to one felt to confer greater dignity or importance is another psychological factor in the change of word meaning.In a sense, it is a form of euphemism.e.g.''hair stylist'' was upgraded as ''hairologist'' for barbers.3）Cynicism（挖苦语）：
It refers that the desire to sneer(冷笑)and to be sarcastic(讽刺)cause the semantic change.e.g.sanctimonious(假装神圣)means ''devoted, holy or scared'' and now means ''pretending to be very holy or pious''.2.The difference between suffixation and conversion The difference between suffixation and conversion is whether the addition of an affix is needed.Suffixation is the formation of new words by adding suffixes to stems , and mainly change the word class.They may also add attached meaning to the stem.eg: hard harden,attract attractive.Conversion is a word-formation whereby a word of a certain word-class is shifted into a word of another without the addition of an affix.It is also called zero derivation(零位派生).eg:Verb-noun conversion : a three-year wait.It is a good buy.3.The fundamental features / the character of the basic word stock基本词汇
All national character 全民性:The basic word stock denote the most common things and phenomena of the world around us , which are indispensable to all the people who speak the language.eg: rain, head,brother.Stability稳定性: They are likely to remain relatively unchanged.Productivity 能产性:They are mostly root words, means they can form new words with other roots and affixes.eg.postman, chairman, workman.Polysemy : They often possess more than one meaning.Collocability 搭配性: many of them have many set expressions, proverbial sayings and so on.eg,heart: a heart of gold, learn by heart.4..The characteristics /features of compounds 1)Phonological features e.g.Compound
Free phrase
a ’fat cat
a fat ’cat
’greenhouse
green ’house
a ’dark horse
a dark ’horse
2)Semantic features : ‘one-wordness’: every compound should express a single idea just as one word;the elements are inseparable and the change of the element would result in the loss of the original identity.3)Grammatical features :Tend to fill a single grammatical slot in a sentence.e.g.He bad-mouthed me.In adjective-plus-noun compounds, the adjective element cannot take inflectional suffixes.e.g.hot line, red tape 5.homonymy
第三篇：诗歌总结 复习要点
诗歌鉴赏答题模式归类
一、题型意识（拿到题目，先作题型判断）
诗歌鉴赏四大题型： 形象题 语言题 技巧题 主旨题
二、审题意识（问什么答什么，怎么问怎么答）
抓住题干的审题点，勾画出来，体会其所示该题的信息区源、回答思路、回答角度，甚至答案。
三、术语意识
答案的精准建立在正确识别并使用诗歌鉴赏相关术语的基础上，积累必备的鉴赏术语是至关重要的。务必梳理成体系，强化记忆。
四、套路意识 牢牢掌握经典题型的回答套路，事半功倍。
第一种类型 形象题 分析人物形象
1.提问方式：这首诗塑造了一个的什么样的人物形象？ 2.提问变体：这首词体现了某某什么样的人生态度？你怎么看待某某形象？ 3.解答分析： 概括形象特点公式：外在形象+内在品性+基本身份 4.答题步骤：
①概括形象特点； 总 ②找出并描摹诗歌形象； 分 ③揭示作者情感。总 注意：有手法点手法
5.答题示例： 寻陆鸿渐不遇 皎然
移家虽带郭，野径入桑麻。近种篱边菊，秋来未著花。扣门无犬吠，欲去问西家。报道山中去，归来每日斜。
注：带郭，意即靠近外城。
诗中的陆鸿渐是一个怎样的人物形象？请简要分析。
答案：诗中的陆鸿渐是一个寄情山水、不以尘事为念的高人逸士形象。（步骤一）前四句通过对幽僻、高雅的隐居之地的景物描写，表现了陆鸿渐的高洁不俗。最后两句通过西邻对陆鸿渐行踪的叙述，侧面烘托（点手法）了陆鸿渐的潇洒疏放。（步骤二）作者通过陆鸿渐这一形象的塑造表现了对隐逸生活的向往和追求。（步骤三）分析物象 物象：托物言志诗中的意象简称物象。答题步骤： ①物象特点（外+内）②联系诗歌描绘分析 ③体现出什么“志”
答题示例： 画菊
花开不并百花从，独立疏篱趣未穷。宁可枝头抱香死，何曾吹落北风中。请分析菊花的形象。
诗人刻画了菊花独立寒秋，傲霜开放的傲岸高洁形象。（步骤一）菊花独立疏篱，不求虚荣，不屑与“百花”为伍；宁可带着清香枯死枝头，绝不向北风屈服飘零落地。（步骤二）这里的菊花正是诗人的自我写照，它坚持节操、傲然不屈的顽强精神，体现了诗人的耿耿忠心、铮铮铁骨的高风亮节。（步骤三）分析意境
1.提问方式：这首诗营造了一种怎样的意境？
2.提问变体：这首诗描绘了一幅怎样的画面？表达了诗人怎样的思想感情？ 3.解答分析：所谓意境，包括景、情、境三个方面。答题时三方面缺一不可。4.答题步骤：
①描绘诗中展现的图景画面。考生应抓住诗中的主要景物，用自己的语言再现画面。②概括景物所营造的氛围特点。一般用两个双音节词即可，例如孤寂冷清、恬静优美、雄浑壮阔、萧瑟凄凉等，注意要能准确地体现景物的特点和情调。
③分析作者的思想感情。切忌空洞，要答具体。比如光答“表达了作者感伤的情怀”是不行的，应答出为什么而“感伤”。
5.答题示例： 绝句二首(其一)杜甫
迟日江山丽，春风花草香。泥融飞燕子，沙暖睡鸳鸯。
注此诗写于诗人经过“一岁四行役”的奔波流离之后，暂时定居成都草堂时。此诗描绘了怎样的景物？表达了诗人怎样的感情？请简要分析。
答：此诗描绘了一派美丽的初春景象：春天阳光普照，四野青绿，江水映日，春风送来花草的馨香，泥融土湿，燕子正繁忙地衔泥筑巢，日丽沙暖，鸳鸯在沙洲上静睡不动。(步骤一)这是一幅明净绚丽的春景图。(步骤二)表现了诗人结束奔波流离生活安定后愉悦闲适的心境。(步骤三)第二种类型 语言题 语言风格题
1.提问方式：这首诗在语言上有何特色？
2.提问变体：请分析这首诗的语言风格。谈谈此诗的语言艺术。
3.解答分析：这种题型不是要求揣摩个别字词运用的巧妙，而是要品味整首诗表现出来的语言风格。能用来答题的词一般有：清新自然、朴实无华、华美绚丽、明白晓畅、多用口语、委婉含蓄、雄浑豪放、笔调婉约、简练生动„„
4.答题步骤：(1)用一两个词准确点明语言特色。(2)用诗中有关语句具体分析这种特色。(3)指出表现了作者怎样的感情。5.答题示例： 春怨
打起黄莺儿，莫教枝上啼。啼时惊妾梦，不得到辽西。请分析此诗的语言特色。
答：此诗语言特点是清新自然，口语化，(步骤一)“黄莺儿”是儿化音，显出女子的纯真娇憨。“啼时惊妾梦，不得到辽西”用质朴的语言表明了打黄莺是因为它惊扰了自己思
念丈夫的美梦。(步骤二)这样非常自然地表现了女子对丈夫的思念之情。(步骤三)炼字题 1.提问方式：这一联中最生动传神的是什么字？为什么？ 2.提问变体：某字历来为人称道，你认为它好在哪里？ 3.解答分析：答题时不能把该字孤立起来谈，得放在句中，结合全诗的意境情感来分析。4.答题步骤：(1)解释该字在句中的含义。(2)展开联想把该字放入原句中描述景象。(3)点出该字烘托了怎样的意境，或表达了怎样的感情，有什么效果。5.答题示例： 南浦别·白居易
南浦凄凄别，西风袅袅秋。一看肠一断，好去莫回头。
前人认为，“看”字看似平常，实际上非常传神，它能真切透露出抒情主人公的形象。你同意这种说法吗？为什么？
答：同意。看，在诗中指回望。(步骤一)离人孤独地走了，还频频回望，每一次回望，都令自己肝肠寸断。此字让我们仿佛看到抒情主人公泪眼朦胧，想看又不敢看的形象。(步骤二)只一“看”字，就淋漓尽致地（步骤四）表现了离别的酸楚。(步骤三)一词领全诗型 1.提问方式：某词是全诗的关键，为什么？
2.解答分析：古诗非常讲究构思，往往一个字或一个词就构成全诗的线索，全诗的感情基调、全诗的思想，抓住这个词命题往往可以以小见大，考出考生对全诗的把握程度。3.答题步骤：(1)该词对突出主旨所起的作用。(2)从该词在诗中结构上所起的作用考虑。4.答题示例： 春夜洛城·闻笛李白
谁家玉笛暗飞声，散入春风满洛城。此夜曲中闻折柳，何人不起故园情？ “折柳”二字是全诗的关键，“折柳”寓意是什么？你是否同意“关键”之说，为什么？(2002年高考题)答：“折柳”的寓意是“惜别怀远”，而诗歌的主旨正是思乡之情。(步骤一)这种思乡之情是从听到“折柳”曲的笛声引起的。(步骤二)可见“折柳”是全诗的关键。
第三种类型 技巧题
1.提问方式：这首诗用了怎样的表现手法？
2.提问变体：请分析这首诗的表现技巧(或艺术手法，或手法)。诗人是怎样抒发自己的情感的？有何效果？ 3.解答分析：要准确答题，必须熟悉常用的一些表现手法：表现手法分抒情手法、描写手法、修辞手法三大类。
抒情手法有直抒胸臆和间接抒情两种。间接抒情又分借景抒情、托物言志、叙事抒情、用典抒情（借古讽今）。
描写手法主要有：(1)衬托，分正衬和反衬。反衬又有动静衬（以动衬静、以静衬动），如“明月松间照，清泉石上流”；声寂衬（以声衬静），如“日出惊山鸟，时鸣春涧中”；以乐景衬哀情，如“映阶碧草自春色，隔叶黄鹂空好音”等。(2)联想和想像，又叫虚实结合。(3)对比。(4)白描。如“春种一粒粟，秋收万颗籽。田野无闲田，农夫皆饿死”。（5）观察角度的变化。远近高低，视听触嗅、声光色态。
修辞手法常见的有：(1)比兴。如“关关雎鸠，在河之洲。窈窕淑女，君子好逑”。先言它物引起所咏之物。(2)比喻。(3)拟人。(4)夸张。(5)双关。如“东边日出西边雨，道是
无晴却有晴”，“晴”暗指感情的“情”。(6)设问（7）反问（8）借代（9）对偶。4.答题步骤：(1)准确指出用了何种手法。(2)结合诗句阐释这种手法的具体运用。(3)此手法传达出诗人怎样的感情。（4）有什么效果。5.答题示例： 早行 陈与义
露侵驼褐晓寒轻，星斗阑干分外明。寂寞小桥和梦过，稻田深处草虫鸣。
此诗主要用了什么表现手法？有何效果？
答：主要用了反衬手法。(步骤一)天未放亮，星斗纵横，分外明亮，反衬夜色之暗；“草虫鸣”反衬出环境的寂静。(步骤二)两处反衬都突出了（步骤四）诗人出行之早，心中由飘泊引起的孤独寂寞。(步骤三)
第四种类型 主旨题
1、提问方式： 评价诗作的思想感情，或概括诗歌的主题思想
2、提问变体：请分析某句诗的思想感情或内涵，阐述诗歌所表达的观点、态度、主张，就某个人对诗歌的评价谈谈你的看法等。
3、解答分析：在具体操作中，我们往往用“描绘了„„的景物，塑造了„„的形象，抒发了诗人„„的情感，歌颂了„„的品质，批判了„„的观点”等句式。
4、答题步骤：
①点明作者的情感，诗歌的主旨。（情感主旨结论公式：情感具体内涵+情感基调）总 ②进行有理有据的简要阐释，它包括：“译一译”，对能体现诗歌主旨的诗句进行文学化的翻译描绘、概括说明；“引一引”，特别重要的诗句、关键词、意象要特别的点出来专门阐释；“点一点”，语言技巧、结构章法的使用及其作用（点一点即可，不展开）。分 注意：用总分的结构安排答题层次。
5.答题示例： 江间作四首（其三）潘大临①
西山通虎穴②，赤壁隐龙宫。形胜三分国，波流万世功。沙明拳宿鹭③，天阔退飞鸿。最羡渔竿客，归船雨打篷。
„注‟①潘大临（约1057～1106)：字邠老，黄州（今湖北黄冈）人，善诗文。曾随苏轼同游赤壁。②西山：在湖北鄂州西，山幽僻深邃．③拳宿鹭：指白鹭睡眠时一腿蜷缩的样子。从全诗看，作者向往一种什么样的生活？请简要分析。答：向往一种隐逸的生活。（步骤一）诗的前两联，作者从眼前之景，转入怀古，遥想当年赤壁之战时的人事，而今安在，从而发出了“波流万世功”的感叹。诗的后两联，作者赞叹宿鹭、飞鸿的闲适，接着又仿佛看到了渔翁的扁舟，联系到“波流万世功”的感叹，于是提出“最羡渔竿客”，想驾一叶小舟在烟雨朦胧中归去！(步骤二
第四篇：高等数学复习要点总结
高等数学复习要点总结
★高等数学复习要点总结 希望有参考作用★ 张宇
下面是我给一个朋友写的，大概是今年4月份写的，发给同学们做个参考：
我把高数的东西整理了一下，按照这个复习，保证可以串起来，同时别忘了把基本功打好！高等数学
1）洛必达法则求极限，最常用，要熟练；
2）无穷小代换求极限，在解题中非常有用，几个等价公式要倒背如流；
3）求含参数的极限，关键是把握常量变量的关系，求解过程体现你极限计算的基本功； 4）1的∞次方的极限是重点，多练几个题；
5）函数连续计算中要会对点进行修改定义、补充定义，看看书上怎么写的，给你说句话你体会一下，“连续的概念是逐点概念”，所以问题就是围绕特殊点展开的，这是数学思想了；
6）闭区间连续函数性质四定理非常重要，把它们背下来，然后结合例题搞定；
7）记住趋向不同，结果就大不一样的极限；
8）两个重要极限、两个基本极限把它们的推倒过程多写写，记住；关键还是刚才的要点，一个是用e的抬头法，一个是注意“趋向不同，结果就大不一样的极限”，还有注意lnx的定义域>0;
9）要注意存在与任意的关系，存在就是说只要有一个符合就成立，任意是说只要有一个不符合就不成立，你体会体会。例题：无穷大无穷小有界变量无界变量；
10）注意夹逼定理的条件很强，不要漏掉要点；
11）“见根号差，用有理化”！！这是思维定势，很管用；
第二章
1）导数的概念非常重要！！一定会在解答题（主观题）中让你展现出你对它的理解是透彻的，所以这里不要用什么特殊化思想，就是严格按照定义来演算推理；
2）导数公式倒背如流的要求不算过分吧 呵呵；
3）连续可导的要求一个弱一个强，只要改变条件的强弱就会有截然不同的做法，你做题的时候一定要总结一下，回顾一下，看看条件的强弱问题，然后在每个题上标记出来，便于以后再复习；
4）由于有些函数求导会出现x在分母上出现，所以要知道：即使不是分段函数，有时也要用定义去求导，而且乘积中某个因子在某点不可导，但乘积在该点也可能可导；
5）中值定理的难点在于构造辅助函数，构造函数是根据题目的要求来的，除了陈文灯等人写的方法外，关键是多看例题，熟练了，自然就会了（我上次给同学们说的是“微分方程法”和“凑”法，这两个掌握了就足够了）；
6）函数性态部分是基本功，一定要耐心的按照函数作图的几大步骤认真做几个题，这样就可以把函数的各种性态串起来了，方法：抄例题，然后背下来，自己默一遍；
7）三个式子的不等事，即A 8）能用微分中值定理的，一般用积分中值定理也可以搞定，你也试试吧，体会一下数学思想和定理的联系，是有好处的；
9）这部分的经济应用题不难，关键是仔细一些，对弹性等概念理解好，你经济学的好的多了，我就不说了：）；
第三章
1）一元函数积分是高等数学中最重要的部分之一，一元函数的积分不学扎实，后面的多元函数的积分就是空中楼阁，要熟练掌握各种积分方法和几种常见的积分类型，如有理函数，三角函数的有理式和简单无理函数的积分；
2）给你说几个准公式： ； ；，作题时相当有用的哦，关键是反过来用你要有意识；
3）这里特别提醒注意积分限函数，一句话：“积分限x在积分过程中是常量，在积分完毕后是变量”，这是核心的东西，抓住它就不会迷失方向；
4）旋转体的体积看来是一定要考了，当然是重点，关键：一个是公式记清，应该是绕x轴还是y轴都要搞的清清楚楚，另一个就是体会移图和移轴的不同，这里要用到积分的计算，是体现基本功的地方；
5）积分在经济中的应用也是重重之重，记清概念，把握公式，清醒审题，仔细答题，搞定；
6）广义积分关键是计算，不是证明！！记住重点；
7）广义积分中积分函数是加减函数时不能将加减函数拆开分别积分，应将加减函数整体积分。积分上下限代入积分函数若无意义，则理解为取极限，你做做这个题就明白了：I=.作者： ypcworld2005-10-12 12:47回复此发言
------------------高等数学复习要点总结
8）其实广义积分和定积分的概念很容易搞清，一句话：定积分存在有两个必要条件，即积分区间有限，被积函数有界。破坏了积分区间有限，引出无穷区间上的广义积分，破坏了被积函数有界，引出无界函数的广义积分。
9）把握住上面的这句话，就可以不晕了，看出来了吧，基本概念非常清楚的人才能学好；
10）定积分是一个数！！这是一个经常命题的地方，好记吗？那就记住吧；
11）不定积分去根号时不用考虑绝对值，而定积分去根号时则要考虑绝对值！！这个好错，一定要记住，会的可不要错哦，不然就惨喽；
12）经验一个：三角有理函数式的积分，若有理函数式分母为，则可以通过分子分母同时乘上一个式子，使分母变为积的形式，另外，还可以直接变形为积的形式来求解
13）被积函数只要是可以看成两个不同类函数的积，就要优先考虑分步积分法，经验哦：）；
14）这里提一下，对于选择题中的抽象函数问题，我个人的认识是：将复杂的形式化成简单的形式，比如对抽象复合函数做变量替换，与其说是一种技巧方法，不如说是一条普遍的规律，任何事物都有由繁到简的趋势，这是可以上升到哲学层面的认识问题，（哈哈，这是英语学多了，not so much„as„用了一下）；
15）一个经验：如果在一个函数或者积分等中的函数，当它是同一个x的函数时，比如f(x)g(x)的形式，可以对其中的任何一个进行放大缩小或者变形，而另一个可以不动，这样的处理往往是需要的，很有用，当你作不下去时，想想我说的这个
你自己做题和总结时，也应该有意识的做这样一些归纳。自己的东西才最管用的。
三角函数公式大全
发表日期：2007-1-28 13:15:39 文章分类：技术八卦来源：转载自从数学论坛上找到了这个列表，非常的全面，但是网页排版稍微有点不方便，故转载于此：
诱导公式
sin(-a)=-sin(a)
cos(-a)=cos(a)
sin(pi/2-a)=cos(a)
cos(pi/2-a)=sin(a)
sin(pi/2+a)=cos(a)
cos(pi/2+a)=-sin(a)
sin(pi-a)=sin(a)
cos(pi-a)=-cos(a)
sin(pi+a)=-sin(a)
cos(pi+a)=-cos(a)
tgA=tanA=sinA/cosA
两角和与差的三角函数
sin(a+b)=sin(a)cos(b)+cos(α)sin(b)
cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
sin(a-b)=sin(a)cos(b)-cos(a)sin(b)
cos(a-b)=cos(a)cos(b)+sin(a)sin(b)
tan(a+b)=(tan(a)+tan(b))/(1-tan(a)tan(b))
tan(a-b)=(tan(a)-tan(b))/(1+tan(a)tan(b))
三角函数和差化积公式
sin(a)+sin(b)=2sin((a+b)/2)cos((a-b)/2)
sin(a)-sin(b)=2cos((a+b)/2)sin((a-b)/2)
cos(a)+cos(b)=2cos((a+b)/2)cos((a-b)/2)
cos(a)-cos(b)=-2sin((a+b)/2)sin((a-b)/2)
积化和差公式
sin(a)sin(b)=-1/2*[cos(a+b)-cos(a-b)]
cos(a)cos(b)=1/2*[cos(a+b)+cos(a-b)]
sin(a)cos(b)=1/2*[sin(a+b)+sin(a-b)]
二倍角公式
sin(2a)=2sin(a)cos(a)
cos(2a)=cos^2(a)-sin^2(a)=2cos^2(a)-1=1-2sin^2(a)
半角公式
sin^2(a/2)=(1-cos(a))/2
cos^2(a/2)=(1+cos(a))/2
tan(a/2)=(1-cos(a))/sin(a)=sin(a)/(1+cos(a))
万能公式
sin(a)=(2tan(a/2))/(1+tan^2(a/2))
cos(a)=(1-tan^2(a/2))/(1+tan^2(a/2))
tan(a)=(2tan(a/2))/(1-tan^2(a/2))
其它公式
a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c)[其中，tan(c)=b/a] a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c)[其中，tan(c)=a/b] 1+sin(a)=(sin(a/2)+cos(a/2))^2
1-sin(a)=(sin(a/2)-cos(a/2))^2
其他非重点三角函数
csc(a)=1/sin(a)
sec(a)=1/cos(a)
双曲函数
sinh(a)=(e^a-e^(-a))/2
cosh(a)=(e^a+e^(-a))/2
tgh(a)=sinh(a)/cosh(a)
第五篇：词汇学心得体会
词汇学感想
转眼间，词汇学这门课程，我已学了一学期。回想刚开学时，对这门课充满了抱怨与怀疑。“不就是单词么，有必要开设一门课程吗，我从小学就开始背单词，难道还不会吗？还有什么好学的”我相信很多人开始都抱有这样的想法。但上了两节课之后，我才发现里面别有洞天。首先是老师很幽默，知识渊博，各种搞笑的段子，会让你不知不觉爱上这么课。老师经常会用些重庆方言把单词谐音，这样便于记忆，虽然老师经常说些我们听不懂的东西，但毫无疑问，你会发现，原来英语可以这样学。
从这门课中，我学习到，一个很简单的单词，经过派生，复合，转化，可以演变成成千上万的单词，多么富有魔力的事情。同时也让我看到，自己要学的还很多，要走的路还很长。就拿最近学的单词的缩略来说，以往在平时生活中，其实是经常看到譬如
VIP.OPEC 这样的缩写单词，只是我从来不会想他具体有哪些单词组成，为什么要这样写。而这么课却教我以后在生活中留心观察。又比如 ：Like 这个单词，放在以前，他就是一个动词呀，还有什么疑问，现在我才知道，他还可以做名词，形容词等我想，我最大的收获，不是新认识了多少个单词，新知道了多少个词性，最重要的是，我学会了把一个很小很简单的东西深入思考，留心生活，你会发现，英语早已充次于我们的生活当中，把他作为你的生命组成部分，而不仅仅是专业。
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