A CLASS OF SINGULAR FOURTH-ORDER THREE-POINT BOUNDARY VALUE PROBLEMS
新概念英语第一册教材简介
新概念英语第一册教材简介The New Concept English book consists of 144 lessons。
with each odd-numbered lesson being the main text and panied by ns。
while the even-___ related to the us lesson。
This unique approach ___.In terms of tenses。
the book follows a strong hierarchy and pattern。
It includes the present continuous tense in Lessons 31-34.the future tense using "be going to" in Lessons 37-40.the present simple tense in Lessons 51-56.the past simple tense in Lessons 67-76.the present perfect tense in Lessons 83-90.and the future tense using "will" in Lessons 91-96.Lessons 117-118 cover the past continuous tense。
while Lessons 119-120 focus on the past perfect tense.Apart from these tenses and sentence structures。
the remaining 68 lessons cover us language and grammar points。
It is ___ the key points of each lesson.For example。
singular point数学
singular point数学Singular Point: Exploring the Mathematics Behind ItIntroductionIn the vast field of mathematics, singular points play a pivotal role in various branches such as calculus, differential equations, and complex analysis. These unique points have fascinated mathematicians for centuries, capturing their attention and driving their exploration. In this article, we will delve into the concept of singular points, examining their characteristics, applications, and significance in the realm of mathematics.Defining Singular PointsA singular point can be defined as a point within a mathematical function or equation where certain properties exhibit exceptional behavior, distinct from the surrounding points. It is a point of interest that usually stands out due to its peculiar properties, making it a key component in understanding the overall behavior of a mathematical system.Characteristics of Singular PointsSingular points possess several distinct characteristics that set them apart from regular points in a mathematical function or equation. Firstly, at a singular point, the function or equation may become undefined or exhibit infinitely large values. This erratic behavior can be attributed to the fact that singular points often represent critical points where the derivative of a function becomes zero or undetermined.Furthermore, singular points can be classified into various categories based on their behavior. For instance, isolated singular points are those that are distinct from any nearby points. On the other hand, non-isolated singular points are surrounded by an infinite number of nearby singular points, forming intricate patterns in the mathematical landscape.Applications of Singular PointsSingular points find wide-ranging applications in diverse fields of mathematics and beyond. In physics, for instance, singular points play a crucial role in understanding the behavior of physical phenomena. One such example is the presence of singularities in black holes, where the laws of physics break down. By studying the singular points in these extreme cosmic objects, scientists can gain valuable insights into the nature of space, time, and gravity.Moreover, singular points have significant implications in engineering and optimization. In control theory, for instance, the presence of singular points can help engineers understand the stability and controllability of complex systems. By identifying and analyzing these points, engineers can develop strategies to ensure the optimal performance and efficiency of various technological systems.Significance of Singular Points in MathematicsMathematically, singular points hold immense significance as they often reveal valuable information about the behavior and solutions of equations and functions. By studying the properties of singular points, mathematicians can gain insights into the nature of a mathematical system and its underlying structure.Singular points have a direct impact on the overall solution space of equations. The presence of singular points can lead to the emergence of multiple solutions or bifurcations, where the behavior of a system changes abruptly. Understanding and characterizing these singular points through rigorous mathematical analysis are fundamental in unraveling the complexities of a wide range of mathematical phenomena.ConclusionIn conclusion, singular points are fascinating and fundamental components of mathematics with applications in various fields. These unique points display exceptional behavior, which often leads to important insights and breakthroughs in understanding equations, functions, and complex systems. By exploring the characteristics, applications, and significance of singular points, mathematicians can continue to push the boundaries of mathematical knowledge and uncover new frontiers in this ever-evolving discipline.。
高中英语 Unit 4 Law and order Period Three Task,Projec
高中英语 Unit 4 Law and order Period Three Task，Project and Self assessment同步精练牛津译林版选修10时间：50分钟Ⅰ.用所给词的适当形式填空1．You should find out if the police and the detective have completed their________(investigate)．2．A man in our city was found guilty of________(commit) fraud.3．Could I trouble you________(turn) down the radio a little?4．Silence is requested in this area while the examinations________(give)．5．Would you mind________(shut) the door?6．All of this is further complicated by the legal situation________(regard) cybercrime.7．Many companies are________(will) to report cases of cybercrime because they are afraid of losing customers.8．Any employee________(find)leaking information will lose his or her job.Ⅱ.完成句子1．You must find a________(目击者)the traffic accident.2．Different kinds of crimes must be ________(报告给)the police.3．The suspect must ____________(接受审判)．4．The police investigate the crimes and____________(收集证据)．5．He was found____________(犯有……的罪行) murder.Ⅲ.单项填空1．In________most countries，a university degree can give you________ flying start in life.A．the；a B．the；/C．/；/ D．/；a2. I'd rather________rudely to her yesterday.A．you not speak B．your not speakingC．you didn't speak D．you hadn't spoken3．Do you have any seats________on the flight for Mexico leaving at 3：16 pm?A．available B．accessibleC．acceptable D．adaptable4．It is not just the size of the Olympic Games________makes them unique，but________they mean to us.A．which；that B．that；whatC．that；because D．that；that5．—Has Sam finished his homework today?—I have no idea.He________ it this morning.A．did B．has doneC．was doing D．had done6．I like________in the autumn when the weather is clear and bright.A．this B．that C．it D．one7．________has been announced，we shall have our final exams next month.A．That B．As C．It D．What8．With modern equipment，many mysteries have________to light in recent years.A．bought B．come C．thrown D．appeared9. The effect of the medicine on this kind of disease remains________.A．seen B．to be seenC．seeing D．to see10．—Does anybody want an extra ticket to go to the movies?—Whom would you rather________with you，Li Hua or me?A．to go B．have goneC．have to go D．have go11．As a result of the earthquake，twothirds of the buildings in the area________.A．need repairing B．needs repairingC．needs to be repaired D．need to repair12. In order to be in touch with you conveniently，I shall inform you byemail________.A．when you are necessaryB．when it was necessaryC．when necessaryD．when being necessary13．As a result of heavy snow，the highway has been closed up until further________.A．news B．knowledgeC．notice D．message14. A story goes________Elizabeth I of England liked nothing more than beingsurrounded by clever and qualified noblemen at court.A．when B．where C．what D．that15．—I know a little about gardening.Could I make some suggestions?—________.A．Go right ahead B．Take it easyC．You will make it D．Don't mention itⅣ.任务型读写A busy life can be personally satisfying，but it may make you feel too tired to achieve the inner peace that will connect you with your true happiness.Begin with simplifying your life and working towards a more peaceful state of mind.Recognize the differences between the things you need and the things you want.Our culture provides us with the message that materials will make our lives better.The reality is that most of these things will complicate our lives without bringing true happiness.Free yourself—learn to be satisfied with fewer materials and greater simplicity.If you let someone else define your life，you're missing the chance to follow your own desires.Your inner life is weakened when you are limited by conformity.Why do you give up your freedom and allow all of your decisions to be defined by what others think you “should” do? Think for yourself.Let your passions be your guide.Life is full of opportunities to earn money，give services.Learn new skills and make new friends.Some of us want them all and fill up our timetable with all kinds of activities.Rushing from one activity to another leaves you with no time to slow down.No matter how worthy you think your activities are，rethink them.Keep the ones that are most important and leave out the ones that are adding to the pace of your life with little return.Life is forever changing，and you will never reach a point of simplicity and endless happiness.But each moment you spend on the path to simplicity does have the possibility to bring happiness to your life.peaceful__2__.Free yourself from dependence on__3__ Distingushing things you need from things you want.Learning to be__4__with fewer materials and greater simplicity.Think for yourselfNever missing the chance to__5__. Never being affected by what others thinkyou“__6__”do.Letting your passions be your guide.续表Rethink all the activities Leaving time to__7__rather than fill up everyday with activities.Keeping the activities that are __8__.__9__ Each effort to simplify your life may__10__youachieve happiness.Ⅴ.书面表达某大学教授称，高学历者的贫穷意味着耻辱和失败，并对大学生提出要求，“当你40岁时，没有4000万的身价不要来见我，也别说是我的学生。
线性代数英文专业词汇
92
the Gram-Schmidt process
正交化过程
93
reducing a matrix to the diagonal form
对角化矩阵
94
orthonormal basis
标准正交基
95
orthogonal transformation
正交变换
96linear transformation线性变换
矩阵mxn
38
the determinant of matrix A
方阵A的行列式
39
operations on Matrices
矩阵的运算
40
a transposed matrix
转置矩阵
41
an inverse matrix
逆矩阵
42
an conjugate matrix
共轭矩阵
43
an diagonal matrix
《线性代数》英文专业词汇
序号
英文
中 文
1
Linear Algebra
线性代数
2
determinant
行列式
3
row
行
4
column
列
5
element
元素
6
diagonal
对角线
7
principal diagona
主对角线
8
auxiliary diagonal
次对角线
9
transposed determinant
78
augmented matrix
增广矩阵
79
general solution
英语单词初一
初一英语单词上册一、初一英语单词上册Unit 1my pron. 我的name n. 名字is v. 是name's = name is 名字是clock n. 钟I pron. 我的am v. 是I'm = I am 我是nice adj. 好的；令人愉快的to part. 用于与动词原形一起构成动词不定式meet v. 遇见；相逢you pron. 你；你们what pron. & adj. 什么what's = what is 是什么your pron. 你的；你们的hello interj. （表示问候）喂hi interj. （表示问候）嗨his pron. 他的and conj. 和；又；而且her pron. 她的question n. 问题；难题；询问；疑问answer n. 回答；答复；答案look v. 看；望；看起来first adj. 第一的first name 名字last adj. 最后的；上一个的last name 姓氏boy n. 男孩girl n. 女孩zero num. 零one num. 一two num. 二three num. 三four num. 四five num. 五six num. 六seven num. 七eight num. 八nine num. 九telephone n. 电话number n. 数；数字telephone number 电话号码phone n. 电话phone number 电话号码it pron. 它it's = it is 它是card n. 卡；卡片ID card 身份证family n. 家；家庭family name 姓氏二、初一英语单词上册Unit 2 this pron. & adj. 这；这个pencil n. 铅笔pen n. 钢笔book n. 书eraser n. 橡皮；铅笔擦；黑板擦ruler n. 尺；直尺case n. 箱；盒；橱pencil case 铅笔盒；文具盒backpack n. 双肩背包pencil sharpener 卷笔刀；铅笔刀dictionary n. 字典；词典that pron. & adj. 那；那个yes adv. （表示肯定）是no adv. （表示否定）不；不是not adv. （构成否定形式）不是isn't = is not 不是excuse v. 原谅；宽恕excuse me 请原谅（客套语，用于与陌生人搭话、打断别人说话等场合）thank v. 感谢OK interj. 好；不错in prep. 用（表示方法，媒介，工具等）English n. 英语；英文a art. 一个（只，把，台……）how adv. （指程度）多么；何等；怎样do v. & aux. 做；干；构成否定句、疑问句的助动词spell v. 拼写baseball n. 棒球watch n. 手表computer n. 电脑；电子计算机game n. 游戏computer game 电子游戏key n. 钥匙notebook n. 笔记本ring n. 环；戒指call v. 打电话at prep. 在……（里面或附近）；在……（点、刻）；以in prep. 在……里面the art. 表示特指的人、物、事或群体lost v. 遗失found v. 找回lost and found 失物招领please interj. （祈使句中用作请求的客套话）请school n. 学校a set of 一套；一副of prep. （属于）……r三、初一英语单词上册Unit 3sister n. 姐；妹mother n. 妈妈；母亲father n. 爸爸；父亲parent n. 父亲或母亲brother n. 兄；弟grandmother n. 祖母；外祖母grandfather n. 祖父；外祖父friend n. 朋友grandparent n. 祖父（母）；外祖父（母）those pron. & adj. 那些are v. 是that's 那是these pron. & adj. 这些she pron. 她he pron. 他he's = he is 他是aunt n. 姨母；姑母；伯母；婶母；舅母son n. 儿子cousin n. 堂（表）兄弟；堂（表）姐妹daughter n. 女儿uncle n. 叔；伯；舅；姨夫；姑父picture n. 照片；图片dear adj. 亲爱的（冠于信函中的称谓，以示礼貌）for prep. 为了（表示目的或原因）thanks for 为……而感谢photo n. 照片；相片here adv. 这里；在这里四、初一英语单词上册Unit 4where adv. 在哪里（疑问副词）where's = where is 在哪儿table n. 桌子bed n. 床dresser n. 梳妆台bookcase n. 书橱；书柜sofa n. 沙发chair n. 椅子drawer n. 抽屉plant n. 植物under prep. 在……下they pron. 他们they're = they are 他们是on prep. 在……上don't = do not 不know v. 知道；了解bag n. 书包；提包；袋子math n. 数学alarm clock 闹钟CD abbr. 光盘video n. 录像；视频tape n. 录音带video tape 录像带hat n. 帽子take v. 拿走；带到thing n. 东西；物to prep. 朝；向；至；达mom n. 妈妈（非正式用语）can modal v. 能；可以；会bring v. 拿来；取来；带来some adj. & pron. 一些；若干need v. 需要floor n. 地板；地面room n. 房间TV abbr. 电视；电视机desk n. 书桌；课桌五、初一英语单词上册Unit 5 have v. 有soccer n. 英式足球ball n. 球soccer ball 英式足球tennis n. 网球racket n. 球拍（网球、羽毛球的）tennis racket 网球拍ping-pong n. 乒乓球volleyball n. 排球basketball n. 篮球bat n. 球拍（乒乓球等的）does v. & aux. 做；干；构成否定句、疑问句的助动词（动词do的第三人称单数形式doesn't = does not 不let v. 允许；让us pron. 我们（we的宾格）let's = let us 让我们；让咱们play v. 玩；打（球）well interj. 喔；噢；唔；这个sound v. 听起来good adj. 良好的；令人满意的sport n. 运动we pron. 我们many adj. 大量的club n. 社团；俱乐部more pron. 更多的；更大的class n. 班级；（一节）课interesting adj. 有趣的；令人感兴趣的boring adj. 无聊的；令人生厌的fun adj. 令人愉快的difficult adj. 困难的relaxing adj. 轻松的watch v. 观看；注视watch TV 看电视has v. （have的第三人单数形式）有great adj. 美妙的；大的collection n. 收藏品；收集物but conj. 但是play sports 参加体育运动或比赛only adv. 只；仅仅them pron. （they的宾格）他（她，它）们every adj. 每一；每个day n. 天；日间；白天；一日六、初一英语单词上册Unit 6like v. 喜欢banana n. 香蕉hamburger n. 汉堡包tomato n. 西红柿broccoli n. 花椰菜French fries 炸马铃薯条；薯条orange n. 橙子ice n. 冰cream n. 奶油；乳脂ice cream 冰淇淋salad n. 沙拉strawberry n. 草莓pear n. 梨have v. 吃；饮oh interj. 啊；噢；呀（表示惊讶等）countable noun 可数名词uncountable noun 不可数名词food n. 食物egg n. 蛋；鸡蛋apple n. 苹果carrot n. 胡萝卜chicken n. 鸡；鸡肉breakfast n. 早餐lunch n. 午餐dinner n. 晚餐；正餐fruit n. 水果vegetable n. 蔬菜；植物runner n. 奔跑者eat v. 吃well adv. 好；对；满意地run v. 跑；奔跑star n. 星星；明星lot adv. 许多；很多lots of 大量；许多healthy adj. 健康的；强健的dessert n. （饭后的）甜食list n. 清单复习Unit 1 to 6furniture n. 家具（总称）people n. 人；人民an art. （元音前）一个（只，把，台……）blank n. 空白conversation n. 交谈；谈话other pron. & adj. 另外的人（物）；其他的also adv. 也；亦；并且七、初一英语单词上册Unit 7how much （价钱）多少pants n. （pl.)裤子sock n. 短袜shirt n. 男衬衣；衬衫T-shirt n. T恤衫shorts n. （pl.)短裤sweater n. 毛衣shoe n. 鞋skirt n. 裙子sale n. 出售；廉价销售dollar n. 元（美国、加拿大等国的货币单位，符号为$）color n. 色；颜色black adj. & n. 黑色（的）white adj. & n. 白色（的）red adj. & n. 红色（的）green adj. & n. 绿色（的）blue adj. & n. 蓝色（的）yellow adj. & n. 黄色（的）big adj. 广大的；重大的small adj. 小的；小号的short adj. 短的；矮的long adj. 长的clerk n. （银行、办公室、商店等的）职员；办事员help v. 帮助；援助want v. 需要；想要Here you are. 给你。
英语数量词单复数总结归纳
英语数量词单复数总结归纳在英语中，数量词用来表示数量或者计数。
数量词的单复数形式在使用中有一些规律和变化。
本文将总结并归纳英语数量词的单复数形式和用法。
一、基数词的单复数形式1. 基数词（cardinal numerals）是用来表示确切数量的词，比如1、2、3等。
以下是基数词的单复数形式变化规则：- 单数形式（Singular form）：除了11和12以外的基数词后面加上-th，如1 → first，2 → second。
- 复数形式（Plural form）：除了11和12以外的基数词后面加上-th，如3 → third，4 → fourth。
11 → eleventh，12 → twelfth。
例句：- I received my ____ salary today. (1st)- The meeting will be held on the ____ of November. (2nd)- They arrived at the airport on the ____ of October. (10th)二、序数词的单复数形式2. 序数词（ordinal numerals）是用来表示顺序或者次序的词，比如first（第一）、second（第二）、third（第三）等。
以下是序数词的单复数形式变化规则：- 单数形式（Singular form）：基数词的单数形式后面加上-th，如one（1）→ first（第一）、two（2）→ second（第二），除了11和12为特殊形式。
- 复数形式（Plural form）：基数词的复数形式后面加上-ths，如one → firsts、two → seconds。
例句：- Today is the ____ day of the month. (first)- She won the ____ place in the competition. (third)- They finished in the ____ and fourth places. (second)三、不规则变化的数量词3. 有一些数量词的单复数形式变化不规则，需要单独记忆。
常微分方程 双语课程常用词汇表
《常微分方程》双语课程常用词汇表acceleration n. 加速度constant acceleration 常加速度downward acceleration 向下的加速度gravitational acceleration 重力加速度total acceleration 总加速度upward acceleration 向上的加速度account（for）v. 占去algebra 代数algebraic equation 代数方程linear algebra 线性代数the fundamental theorem of algebra 代数学基本定理amount v. 总计n. 总数amplitude n. 振幅application n. 应用by repeated application of 反复应用apply v. 应用approach v. 趋近于approach zero 趋近于零approach infinity 趋近于无穷area n. 面积cross-sectional area 横截面积the horizontal cross-sectional area 水平方向的截面积arrange v. 安排、整理、排列arrangement n. 安排、整理、排列rearrangement n. 重新安排、重新整理、重新排列associate v. 联系associated a.. 相应的associated with 对应于…的associated homogeneous linear equation 相应的齐线性方程associativity n. 结合律assume v. 假设assumption n. 假设asymptote 渐近线oblique asymptote 斜渐近线[əˈbli:k]axis 数轴negative x -axis 负x 轴positive y -axis 正y 轴x -axis x 轴y -axis y 轴base n. 基be present v. 出现body 天体boundary n. 边界bounded a. 有界的unbounded a. 无界的brine 盐水calculus 微积分elementary calculus 初等微积分capacitor 电容器case 情形exceptional case 例外情形chain rule （求导的）链式法则clockwise 顺时针clockwise direction 顺时针方向counterclockwise 逆时针counterclockwise direction 逆时针方向close v. 闭closed container 封闭的容器closed interval 闭区间coefficient 系数constant coefficient 常系数leading coefficient 首项系数undetermined coefficient 待定系数variable coefficient 变系数collect v. 整理collect coefficients 整理系数column 列commute v. 交换commutative a. 交换的commutativity 交换性property of commutativity 交换性质complete a. 完备的incomplete a. 不完备的complex a. 复的complex conjugate 复共轭的complex conjugate pairs 复共轭对complex conjugate roots 复共轭根component n. 分量componentwise 分量形式composition 复合compress v. 压缩compute v. 计算concentration n. 浓度condition 条件a given initial condition 一个给定的初始条件initial condition 初始条件necessary condition 必要条件sufficient condition 充分条件the given condition 给定的条件conjugate 共轭的constant 常数arbitrary constant 任意常数constant multiple 数乘constant of integration 积分常数constant speed 常速度damping constant 阻尼常数positive constant 正的常数continuity n. 连续性discontinuity 不连续性continuous 连续的continuous function 连续函数continuous partial derivative 连续偏导数discontinuous 不连续的piecewise continuous 分段连续的convention 惯例convergence n. 收敛absolute convergence 绝对收敛uniform convergence 一致收敛coordinate 坐标coordinate axis 坐标轴polar coordinates 极坐标corresponding a. 相应的cube 立方，立方体current 电流cylinder 柱，柱面dashpot 减震器decomposition 分解partial fraction decomposition 部分分式分解defect n. 亏量defective v. 亏损的define v. 定义definition n. 定义degenerate a. 退化的denominator 分母derive v. 导出derivation n. 求导（数）derivative n. 导数[diˈrivətiv] antiderivative 原函数first derivative 一阶导数second derivative 二阶导数the highest derivative 最高阶导数determine v. 确定determinant 行列式determinant of coefficients 系数行列式operational determinant 算子行列式diagonal 对角线principal diagonal 主对角线differ v. 不同difference n. 差differentiable 可微的differentiable function 可微函数differentiability 可微性differentiability condition 可微性条件differential n. 微分differential form 微分形式differentiate v. 微分differentiate term wise 逐项微分differentiation n. 微分（运算）term-by-term differentiation 逐项微分displacement 位移distance 距离distinct 不同的distinct real roots 不同的实根distributives 分配性diverge v. 发散divide v. 划分，除subdivide 细分domain 定义域double 重，二重，双double root 二重根duplicate v. 复制、重复duplication n. 复制、重复eliminate v. 消去elimination n. 消元法、消去the method of elimination 消元法、消去法eigenvalue n. 特征值complex conjugate eigenvalue 复共轭特征值defective eigenvalue 不完备的特征值multiple eigenvalue 多重特征值zero eigenvalue 零特征值eigenvector 特征向量generalized eigenvector 广义特征向量rank generalized eigenvector r 阶广义特征向量element 元素diagonal element 对角元off-diagonal element 非对角元element wise 逐个元素地ellipse 椭圆elliptical orbit 椭圆型轨道employ v. 利用employ the technique of 利用…技术enable v. 使能够entry n. 元素equate v. 使相等equation 方程Bernoulli equation 伯努利方程Bessel’s equation 贝赛尔方程characteristic equation 特征方程cubic equation 三次方程differential equation 微分方程eigenvector equation 特征向量方程exact differential equation 恰当微分方程higher-degree equation 高次方程homogeneous equation 齐次方程Legend re’s equation 勒让德方程linear first-order equation 一阶线性方程Logistic equation 逻辑斯蒂方程natural growth equation 自然增长方程ordinary differential equation 常微分方程partial differential equation 偏微分方程quadratic equation 二次方程reducible equation 可降阶方程second-degree equation 二次方程separable differential equation 可分离变量方程simultaneous equations 联立方程组equilibrium position 平衡位置equivalent 等价的be equivalent to 等价于equivalently 等价地error 误差average error 平均误差existence 存在existence-uniqueness theorem 存在唯一性定理exponent 指数negative exponent 负指数exponential 指数(的)exponential function 指数函数matrix exponential 矩阵指数factor n. 因式,因子v. 分解因式common factor 公因式,公因子integrating factor 积分因子linear factor 一次因式irreducible quadratic factor 二次不可约因式factorization n. 因子分解field 场、域direction field 方向场first 第一的the first two… 前两（个）……flow v. 流动n. 流量inflow n. 流入(量) outflow n. 流出(量)focus 焦点following 下面的force 力external force 外力external period ice force 周期性外力frictional force 摩擦力form 形式decimal form 小数形式explicit form 显式形式implicit form 隐式形式polar form 极坐标形式the standard form 标准形式upper triangular form 上三角形式former a. 以前的the former 前者formula 公式fraction 分式,分数frequency 频率function 函数analytic function 解析函数coefficient function 系数函数complementary function 补函数component function 分量函数constant-valued function 常数值函数continuous function 连续函数piecewise continuous function 分段连续函数decreasing function 单调减函数differentiable function 可微函数n times differentiable function n 阶可微函数twice differentiable function 二阶可微函数sufficiently differentiable function 足够阶可微函数discontinuous function 不连续函数elementary function 初等函数factorial function 分式函数increasing function 单调增函数matrix-valued function 矩阵值函数position function 位置函数rational function 有理函数real-valued function 实值函数trigonometric function 三角函数unknown function 未知函数vector-valued function 向量值函数generalize (to) v. 推广generalization n. 推广graph 图象hemispherical 半球形的hold v. 成立homogeneous 齐(次)的nonhomogenous 非齐(次)的hyperbolic 双曲型的hyperbolic cosine 双曲余弦hyperbolic sine 双曲正弦hypothesis n. 假设hypotheses n. 假设(复数形式) identity 恒等式identity principle 恒等原理trigonometric identity 三角恒等式illustrate v. 说明imaginary part 虚部immaterial a. 不重要的, 不相干的imply v. 意味着, 暗示impulse 脉冲independent a. 独立的, 不相关的independent of 独立于……inductor 电感器initial 开始的, 最初的initial condition 初始条件initial position 初始位置initial population 初始人口数initial velocity 初始速度integer 整数nonnegative integer 非负整数integral 积分definite integral 定积分improper integral 非正常积分indefinite integral 不定积分integral sign 积分号integrate v. 积分integrate by parts 分部积分integration n. 积分integration of both sides 两边积分interior n. 内部in terms of 根据interval 区间closed interval 闭区间interval of real number 实数区间open interval 开区间subinterval 子区间bounded subinterval 有界子区间the ends of the interval 区间的端点the whole interval 整个区间involve v. 包含，涉及Kepl er’s laws of planetary motion 开普勒行星运动定律latter a. 后期的，末期的the latter 后者left-hand side 左边like 类似，相似like powers 同次幂like term 同类项limit 极限take the limit 取极限upper limit 上极限line 线，线条line segment 线段real line 实数轴straight line 直线tangent line 切线the line tangent (to) 与…相切的直线the entire real line 整个实轴linear 线性的linear combination 线性组合linear dependence 线性相关linear independence 线性无关nonlinear 非线性的linearly 线性地linearly dependent 线性相关的linearly independent 线性无关的linearly independent solutions 线性无关解linearity 线性性liter 升logarithm 对数logarithmic term 含有对数的项long division 长除法major semi axis 长半轴mass (物体的)质量mathematical model 数学模型mathematical modeling 数学建模matrix 矩阵augmented matrix 增广矩阵coefficient matrix 系数矩阵diagonal matrix 对角矩阵exponential matrix 指数矩阵fundamental matrix 基解矩阵identity matrix 单位矩阵inverse matrix 逆矩阵matrix addition 矩阵加法matrix multiplication 矩阵乘法nonsingular matrix 非奇异矩阵singular matrix 奇异矩阵square matrix 方阵upper triangular matrix 上三角矩阵zero matrix 零矩阵mean value theorem for integral 积分中值定理method 方法straightforward method 直接的方法minimum 最小值minus prep. 减,减去;负的minus sign 负号motion 运动free undamped motion 无阻尼自由运动simple harmonic motion 简谐运动multiply v. 乘,倍增multiplication n. 乘法multiplicity n. 重数nature 自然, 本质nilpotent 幂零的number 数complex number 复数imaginary number 虚数negative number 负数nonnegative number 非负数positive number 正数real number 实数unknown number 未知数numerator (分数的)分子operate v. 运算,作用operation n. 运算,操作elementary row operation 初等行变换operator 算子polynomial operator 多项式算子orbit 轨道order 阶first-order equation 一阶方程fourth-order equation 四阶方程of exponential order 指数阶的second-order equation 二阶方程nth-order equation n 阶方程the mixed second-order partial derivative 二阶混合偏导数the order of a differential equation 微分方程的阶origin 原点original 原来的the original equation 原方程the original form 原来的形式oscillate v. 振动oscillation n. 振动forced oscillation 强迫振动free oscillation 自由振动parabola 抛物线 [pə'ræbələ]parameter 参数variation of parameters 常数变易法parameterize v. 参数化parameterization n. 参数化particle 粒子phase angle 相角phase portrait 相图plane 平面point 点end point 端点isolated point 孤立点ordinary point 常点singular point 奇点regular singular point 正则奇点irregular singular point 非正则奇点polynomial 多项式n th-degree polynomial n 次多项式a polynomial of degree n n 次多项式a polynomial of lower degree 次数较低的多项式Taylor polynomial 泰勒多项式possible 可能的possibility 可能性power 幂power function 幂函数in powers of x x 的幂in powers of x −a x −a 的幂presence 出现, 在场preceding 前面的prime 求导符号“撇”problem 问题mathematical problem 数学问题initial value problem 初始值问题proceed v. 继续进行, 继续下去product 乘, 积dot product 点积product rule 乘法法则scalar product 点积,数积,内积property 性质proposition 命题quotient 商radius 半径radius of convergence 收敛半径rate 速率at a rate of 以…的速率at a rate proportional to 以与…成正比的速率birth rate 出生率death rate 死亡率time rate of change of (something) …关于时间的变化率interest rate 利率reactant 反应物readily 容易地real part 实部recall v. 记起,回顾rectangle 长方形, 矩形open rectangle 开矩形recurrence relation 递推关系many-term recurrence relation 多项间的递推关系two-term recurrence relation 两项间的递推关系recursion formula 递推公式reduce v. 化简, 简化, 约简reduction n. 化简, 简化, 约简reduction of order 降阶resistor 电阻器result n. 结果v. 导致(in)revolution n. 旋转right-hand side 右边root 根characteristic root 特征根complex root 复根double root 二重根equal roots 相等的根k-fold root k 重根rational root 有理根real root 实根repeated root 重根the square root 平方根triple root 三重根rotation n. 旋转counterclockwise rotation 逆时针旋转routine 例行的; 平凡的a routine matter 平凡的情形row 行scalar 纯量(的), 数量(的), 标量(的)series 级数binomial series 二项式级数geometric series 几何级数harmonic series 调和级数infinite series 无穷级数power series 幂级数convergent power series 收敛的幂级数power series representation 幂级数表示power series in x x的幂级数power series in x −a x −a 的幂级数power series solution 幂级数解Taylor series 泰勒级数set 集合show v. 证明side 边left-hand side 左边right-hand side 右边simple 简单的simplify v. 简化, 化简simplification n. 简化, 化简singularity 奇异性slope 斜率slope field 斜率场smooth 光滑的piecewise smooth 逐段光滑的solute n. 溶质，溶解物solution n. 解explicit solution 显式解implicit solution 隐式解infinitely many solutions 无穷多解negative-valued solution 负值解period ice solution 周期解positive-valued solution 正值解singular solution 奇解solution curve 解曲线the (a) genera l solution 通解the particular solution 特解solve v. 解solvent n. 溶剂some 某个some open interval 某个开区间spring 弹簧spring constant 弹性系数step 步骤finitely many steps 有限多步stretch 拉伸subject(to) a. 易受…的ad.在…条件下subscript 下标even subscript 偶下标odd subscript 奇下标substitute v. 代入substitution n. 代入direct substitution 直接代入back substitution 回代subtract v. 减去subtraction n. 减去suffice v. 足够sufficient n. 足够的, 充分的sufficient condition 充分条件sum n. 和sum zero 总和为零summand 被加数summation 求和(法), 累加, 加法the index of summation 求和的指标the sum of…and … …与…的和superposition 叠加symmetry 对称symmetric form 对称形式system 方程组,系统first-order system 一阶方程组higher-order system 高阶方程组two-dimensional system 二维系统upper triangular system 上三角方程组take 取, 实施take the Laplace transform 取拉普拉斯变换take the limit 取极限tangent 正切(的),切线(的)be tangent to 与…相切time 时间per unit of time 单位时间time lag 时滞tank 箱, 柜, 罐water tank 水箱term 项constant term 常数项termwise addition 逐项相加term by term 逐项the first term 第一项the first few terms 前几项the genera l term 通项, 一般项the leading term 首项terminology 术语trajectory 轨道, 轨迹transform v. 转化n. 变换Laplace transform 拉普拉斯变换inverse Laplace transform 拉普拉斯反变换transformation n. 变换,转化transpose v. , n. 转置,移项triangle 三角(形)right triangle 直角三角形triple 三重的, 三次的, 三倍的triple eigenvalue 三重特征根trivial 平凡的, 不重要的trivial case 平凡情况nontrivial 非平凡的tuple 组n -tuple n 元组unique 唯一的uniqueness 唯一性unique solution 唯一解unknown 未知的the unknown 未知量value 值numerical value 数值absolute value 绝对值variable 变量dependent variable 因变量independent variable 自变量variable of integration 积分变量vector 向量acceleration vector 加速度向量column vector 列向量constant vector 常数向量position vector 位置向量radius vector 向径, 矢径row vector 行向量solution vector 解向量unit vector 单位向量verify v. 证明vanish 等于零vanish identically 恒等于零variable 变量dependent variable 因变量independent variable 自变量separation of variable 变量分离voltage 电压volume 列Wronskian 伏朗斯基行列式yield 产生zero 零nonzero 非零。
三年级上册英语第四单元句子
三年级上册英语第四单元句子The Fourth Unit Sentences of Grade Three English in the First SemesterIn the fourth unit of the English textbook for the first semester of Grade Three, students are introduced to various sentences and their structures. These sentences aim to enhance students' understanding of basic grammar rules and expand their vocabulary. Let's take a closer look at the sentences covered in this unit.1. This is my sister.In this sentence, students learn to introduce a family member using the possessive pronoun "my." They also practice using the verb "is" to describe someone or something.2. That is his cat.This sentence focuses on using the possessive pronoun "his" to indicate ownership. Students learn to identify and describe objects or animals belonging to others.3. These are my books.Through this sentence, students learn to use the plural form of the verb "to be" by adding an "s" to the end of the verb. They practice describing multiple objects or possessions.4. Those are her toys.Similar to the previous sentence, this sentence emphasizes using the plural form of the verb "to be" to describe possessions belonging to someone else.5. I like ice cream.In this sentence, students learn to express their preferences using the verb "like." They practice stating their likes and dislikes regarding different things.6. She likes to sing.Through this sentence, students learn to use the verb "to like" in the third-person singular form. They practice describing the preferences of someone else.7. He can swim.This sentence introduces the concept of using the modal verb "can" to express abilities. Students practice stating what someone can do.8. We can run fast.Similar to the previous sentence, this sentence emphasizes using the modal verb "can" to express abilities, but in the first-person plural form. Students practice describing the abilities of a group.9. They can jump high.This sentence expands on the use of the modal verb "can" to express abilities, but in the third-person plural form. Students practice describing the abilities of multiple individuals.10. Do you like bananas?In this sentence, students learn to form questions using the auxiliary verb "do." They practice asking about someone's preferences.11. Does he like apples?Similar to the previous sentence, this sentence focuses on forming questions using the auxiliary verb "does." Students practice asking about someone else's preferences.12. Can you swim?Through this sentence, students learn to form questions using the modal verb "can." They practice asking about someone's abilities.These are the sentences covered in the fourth unit of the Grade Three English textbook. By studying and practicing these sentences, students will develop a solid foundation in English grammar and vocabulary. They will be able to introduce familymembers, describe possessions, express preferences, talk about abilities, and form questions. This unit lays the groundwork for further language learning and will help students communicate effectively in everyday situations.。
必修4第三单元知识点总结
必修4第三单元知识点总结第一节：The Structure of the Universe1. The size of the Universe- The Universe is vast and expanding, consisting of billions of galaxies, each containing billions of stars.- It is difficult to comprehend the size of the Universe due to its immense scale.2. Galaxies- Galaxies are massive systems of stars, dust, and gas held together by gravity.- The Milky Way is the galaxy that contains our solar system.3. Stars- Stars are massive, luminous spheres of plasma that emit light and heat.- The life cycle of a star includes formation, main sequence, red giant, and white dwarf stages.4. The Big Bang Theory- The Big Bang Theory posits that the Universe began as a singular point and has been expanding ever since.- This theory has been supported by evidence such as the cosmic microwave background radiation.5. The Universe’s age and fate- The Universe is estimated to be around 13.8 billion years old.- There are different theories about the ultimate fate of the Universe, such as the Big Freeze and the Big Crunch.第二节：The Origins of the Universe1. Theories of the Universe’s origins- Theories of the Universe’s origins include the Big Bang Theory and the Steady State Theory.2. Evidence for the Big Bang- Evidence that supports the Big Bang Theory includes the redshift of distant galaxies, the cosmic microwave background radiation, and the abundance of light elements.3. The role of gravity in the formation of the Universe- Gravity played a key role in the formation of structures in the early Universe, such as galaxies and clusters of galaxies.4. The formation of light elements- Light elements like hydrogen and helium were formed in the early Universe during the process of nucleosynthesis.5. Dark matter and dark energy- Dark matter and dark energy are mysterious components of the Universe that make up a large percentage of its content.第三节：The Solar System and Planets1. The formation of the Solar System- The Solar System formed from a cloud of gas and dust called the solar nebula, with the Sun forming at its center and planets forming from the leftover material.2. Composition and structure of the Sun- The Sun is a massive ball of gas mostly composed of hydrogen and helium.- It consists of several layers, including the core, radiative zone, convective zone, photosphere, chromosphere, and corona.3. The inner planets- The inner planets of the Solar System include Mercury, Venus, Earth, and Mars.- These planets are rocky and terrestrial, with solid surfaces and relatively thin atmospheres.4. The outer planets- The outer planets of the Solar System include Jupiter, Saturn, Uranus, and Neptune.- These planets are gas giants with thick atmospheres and no solid surfaces.5. Dwarf planets and other celestial bodies- Dwarf planets like Pluto and Ceres are considered part of the Solar System, as well as other smaller objects such as asteroids, comets, and meteoroids.第四节：The Earth’s Moon1. The origin and properties of the Moon- The most widely accepted theory for the origin of the Moon is the Giant-impact hypothesis, which posits that the Moon formed from debris created by a collision between early Earth and a Mars-sized body.- The Moon is smaller and less dense than Earth and has a cratered surface with no atmosphere.2. Phases of the Moon- The Moon goes through different phases as seen from Earth, including new moon, first quarter, full moon, and last quarter, which are caused by the relative positions of the Earth, Moon, and Sun.3. Lunar eclipses and tides- Lunar eclipses occur when the Earth passes between the Sun and the Moon, causing the Earth’s shadow to fall on the Moon.- Tides on Earth are caused by the gravitational pull of the Moon, with high tides occurring on the side of the Earth facing the Moon and on the opposite side.第五节：The Earth and Its Atmosphere1. The structure of the Earth- The Earth is composed of several layers, including the inner core, outer core, mantle, and crust, with the lithosphere and asthenosphere playing key roles in the movement of tectonic plates.2. Composition and properties of the atmosphere- The Earth’s atmosphere is composed of several layers, including the troposphere, stratosphere, mesosphere, thermosphere, and exosphere.- It consists of different gases, with nitrogen and oxygen making up the majority of the atmosphere, along with trace gases and water vapor.3. The greenhouse effect- The greenhouse effect is the process by which greenhouse gases in the atmosphere trap heat from the Sun, raising the Earth’s temperature and making it suitable for life.4. Weather and climate- Weather refers to the short-term conditions of the atmosphere, including temperature, humidity, precipitation, wind, and visibility.- Climate refers to the long-term patterns of weather in a particular area.5. Natural hazards and disasters- Natural hazards such as hurricanes, tornadoes, and earthquakes can lead to natural disasters that have a significant impact on the Earth’s environment and its inhabitants.第六节：Earth’s Resources and Energy1. Renewable and nonrenewable resources- Renewable resources such as solar, wind, and hydroelectric power can be replenished naturally and are considered more sustainable than nonrenewable resources like fossil fuels.2. Fossil fuels- Fossil fuels like coal, oil, and natural gas are formed from the remains of ancient plants and animals and are a major source of energy for human civilization.3. Nuclear power- Nuclear energy is generated through the fission of uranium or plutonium atoms, producing heat that can be used to generate electricity.4. Alternative energy sources- Alternative energy sources such as solar, wind, hydroelectric, and geothermal power are being increasingly explored as cleaner and more sustainable alternatives to traditional fossil fuels.5. Energy conservation and sustainability- Energy conservation involves reducing energy usage through efficiency measures, while sustainability focuses on the long-term impact of human activity on the environment.第七节：Climate Change and Environmental Issues1. Global climate change- Climate change refers to long-term shifts in temperature and weather patterns, with global warming caused by human activities such as deforestation, burning fossil fuels, and industrialization.2. Effects of climate change- Climate change can lead to rising sea levels, extreme weather events, loss of biodiversity, and threats to human health and food security.3. Mitigation and adaptation- Mitigation involves reducing greenhouse gas emissions and transitioning to cleaner energy sources, while adaptation focuses on preparing for and addressing the impacts of climate change.4. Environmental issues- Other environmental issues such as air and water pollution, deforestation, habitat destruction, and waste management also have significant impacts on the Earth’s ecosystems and human well-being.5. Conservation and sustainable development- Conservation efforts aim to protect and preserve natural resources and wildlife, while sustainable development seeks to meet the needs of present and future generations without compromising the health of the planet.综上所述，必修4第三单元涉及了宇宙的结构与起源、太阳系与行星、地球与其大气层、地球资源与能源、气候变化与环境问题等多个方面的知识点。
英语单词表
编号 单词10001my10002name10003is10004clock10005I10006am10007nice10008to10009meet10010you10011what10012your10013hello10014hi10015his10016and10017her10018question10019answer10020look10021first10022first name 10023last10024last name10025boy10026girl10027zero10028one10029two10030three10031four10032five10033six10034seven10035eight10036nine10037telephone10038number10039telephone number 10040phone10041phone number 10042it10044IDcard(identification) 10045family10046family name10047this10048pencil10049pen10050book10051eraser10052ruler10053case10054pencil case10055backpack10056pencil sharpener 10057dictionary10058that10059yes10060no10061not10062excuse10063thank10064OK10065in10066English10067a10068how10069do10070spell10071baseball10072watch10073computer10074game10075computer game 10076key10077notebook10078ring10079call10080at10081in10082the10083lost10084found10085lost and found10087school 10088a set of 10089of10090sister 10091mother 10092father 10093parent 10094brother 10095grandmother 10096grandfather 10097friend 10098grandparent 10099those 10100are10101these 10102she10103he10104aunt10105son10106cousin 10107daughter 10108uncle 10109picture 10110dear10111for10112thanks for 10113photo 10114here10115where 10116table 10117bed10118dresser 10119bookcase 10120sofa10121chair 10122drawer 10123plant 10124under 10125they10126on10127know 10128bag10130alarm clock 10131CD(=compactdisc) 10132video10133tape10134videotape10135hat10136take10137thing10138to10139mom10140can10141bring10142some10143need10144floor10145TV（=television）10146room10147desk10148have10149soccer10150ball10151soccer ball10152tennis10153racket10154tennis racket 10155ping-pong10156volleyball10157basketball10158bat10159does10160let10161us10162play10163sound10164good10165sport10166we10167many10168club10169more10170class10171Interesting10173Fun10174Difficult10175Relaxing10176Watch10177watch TV10178like10179banana10180hamburger10181tomato10182broccoli10183french fries 10184orange10185ice10186cream10187ice cream10188salad10189strawberry 10190pear10191have10192oh10193countable noun 10194uncountable noun 10195food10196egg10197apple10198carrot10199chicken10200breakfast10201lunch10202dinner10203fruit10204vegetable10205runner10206eat10207well10208runner10209star10210lot10211lots of10212healthy10213dessert10214list10215furniture10216people10217an10218blank10219conversation 10220other10221also10222pants10223sock10224shirt10225T-shirt10226shorts10227sweater10228shoe10229skirt10230sale10231dollar10232color10233black10234white10235red10236green10237blue10238yellow10239big10240small10241short10242long10243clerk10244help10245want10246Here you are. 10247You're welcome. 10248example10249ten10250eleven10251twelve10252thirteen10253fourteen10254fifteen10255sixteen10256seventeen10257eighteen10258nineteen10259twenty10260thirty10261clothes10262store10263come10264buy10265very10266price10267each10268anybody 10269afford10270our10271see10272yourself 10273Mr.10274sell10275from10276have a look 10277on sale 10278sorry10279when10280birthday 10281month10282January 10283February 10284March10285April10286May10287June10288July10289August10290September 10291October 10292November 10293December 10294first10295second10296third10297fourth10298fifth10299sixth10300seventh 10301eighth10302ninth10303tenth10304eleventh 10305twelfth 10306thirteenth 10307fourteenth 10308fifteenth 10309sixteenth 10310seventeenth 10311eighteenth 10312nineteenth10313twentieth10314thirtieth10315date10316Happy10317Happy Birthday! 10318birth10319age10320old10321how old10322speech10323contest10324party10325trip10326basketball game 10327volleyball game 10328School Day10329art10330festival10331Chinese10332music10333year10334year(s) old 10335go10336movie10337go to a movie 10338action10339comedy10340documentary 10341thriller10342kind10343singular10344plural10345opera10346Beijing Opera 10347find10348someone10349who10350student10351scary10352funny10353sad10354exciting10355really10356often10357think10358learn10359about10361with10362favorite 10363actor10364new10365successful 10366weekend10367too10368Rush10369Mr. Bean 10370Shaolin Temple 10371guitar10372join10373dance10374swim10375sing10376chess10377paint10378speak10379can't=can not 10380kid10381our10382drum10383piano10384trumpet10385violin10386orange10387musician 10388then10389be10390rock10391band10392show10393Sunday10394pm10395Kung fu 10396may10397draw10398little10399a little 10400e-mail10401address10402why10403time10404what time 10405go to school 10406get up10408take a shower 10409usually10410o'clock10411work10412hour10413brush10414teeth10415after10416go to work 10417get to10418bus10419hotel10420all10421night10422love10423listen10424home10425morning10426go to bed 10427job10428am10429afternoon 10430evening10431homework10432do homework 10433go home 10434letter10435around10436start10437write10438tell10439me10440soon10441best10442wish10443Saturday10444survey10445subject10446science10447P.E.10448because10449description 10450word10451teacher10452who10453Mrs.10454partner10455city10456dad10457Monday10458Tuesday10459Wednesday10460Thursday10461Friday10462Saturday10463Sunday10464biology10465busy10466next10467strict10468tired10469Miss10470ask10471anybody10472dog10473around10474America10475so10476China10477before10478hobby10479today10480life10481pal10482pen pal10483Canada10484France10485Japan10486the United States 10487Australia10488Singapore10489the United Kingdom 10490country10491Sydney10492New york10493Paris10494Toronto10495Tokyo10496live10497language10498Japanese10499would10500French10501like10502dislike 10503post10504office 10505post office 10506library 10507restaurant 10508bank10509supermarket 10510St.=street 10511pay10512pay phone 10513park10514ave=avenue 10515center 10516bridge 10517mail10518there10519mear10520across 10521across from 10522next10523next to 10524between 10525front10526in front of 10527behind 10528neighborhood 10529just10530straight 10531turn10532left10533down10534right10535on the right 10536open10537market 10538clean10539quiet10540dirty10541house10542welcome 10543garden 10544district 10545enjoy10546walk10547take a walk10548through 10549beginning 10550tour 10551visit 10552place 10553fun 10554have fun 10555if10556hungry 10557arrive 10558way 10559take 10560taxi 10561airport 10562pass 10563hope 10564yours 10565koala 10566tiger 10567elephant 10568dolphin 10569panda 10570lion 10571penguin 10572girraffe 10573zoo 10574cute 10575map 10576smart 10577animal 10578box 10579kind of 10580south 10581Africa 10582bingo 10583ugly 10584clever 10585friendly 10586beautiful 10587shy 10588other 10589grass 10590sleep 10591during 10592at night 10593leaf 10594lazy10595meat10596relax10597shop10598assistant 10599shop assistant 10600doctor10601reporter 10602policeman 10603waiter10604bank clerk 10605hospital 10606now10607star10608policewoman 10609nurse10610money10611give10612get10613wear10614uniform10615sometimes 10616in 在10617dangerous 10618thief10619late10620out10621talk10622station10623TV station 10624police10625police station 10626newspaper 10627hard10628as10629at10630summer10631story10632magazine 10633young10634play10635news10636children 10637international 10638teach10639skill10640sir10641madam10642clean10643read10644on10645apartment 10646TV show 10647sure10648wait10649wait for 10650toy10651west10652activity 10653shop10654mall10655pool10656camera 10657bird10658rain10659windy10660cloudy 10661sunny10662snow10663weather 10664Moscow 10665Boston 10666cook10667study10668bad10669terrible 10670pretty 10671hot10672cold10673cool10674warm10675humid10676wacation 10677on vacation 10678take a photo 10679lie10680beach10681look at 10682group10683cool10684surprised 10685heat10686relaxed 10687winter 10688scarf10689everyone10690have a good time 10691man10692describe10693look for10694talk about 10695direction10696unit10697most10698following10699in order to 10700improve10701hair10702curly10703straight10704tall10705medium10706height10707thin10708heavy10709build10710like10711always10712captain10713team10714popular10715blonde10716goodlooking 10717bit10718a little bit 10719joke10720never10721stop10722brown10723person10724beard10725glasses10726look10727remember10728pop singer 10729singer10730not…any mor 10731say10732nobody10733would will 10734I’d = I woul 10735noodles10736beef10737mutton10738cabbage10739potato10740special10741drink10742large10743size10744bowl10745he’d= he wou 10746juice10747dumpling10748porridge10749tea10750green tea 10751rice10752soup10753onion10754fish10755Tel10756RMB10757Mon.10758Tues.10759Wed.10760Thurs.10761Fri10762reason10763menu10764was is10765did do10766went go10767visit10768test10769What about…? 10770stay10771at home10772have10773do some reading 10774practice10775regular10776irregular 10777present10778past10779mountain10780geography 10781spend10782week10783yesterday10784No.= number 10785middle10786middle school 10787most10788go shopping 10789had have10790saw see10791talk10792talk show10793wrote write 10794song10795go for a walk 10796sat sit10797down10798cat10799It is time to 10800wasn’t= was not 10801no10802anything10803suggestion 10804New York City 10805camp10806summer camp 10807museum10808guide10809central10810didn’t= did n 10811exam10812really10813rainy10814were are10815fantastic10816unfriendly 10817awful10818delicious10819expensive10820crowded10821cheap10822think of10823water10824cry10825corner10826make10827made make 10828feel10829walk10831decide10832wall10833the Great Wall 10834palace10835the Palace Museum 10836square10837Tian’an Men Squar 10838Hutung10839make10840classmate10841discuss10842report10843sex10844soap10845soap opera10846sitcom10847situation10848nothing10849ha10850stand10851mind10852king10853How about ? ... 10854fact10855in fact10856culture10857host10858agree10859agree with10860sunglasses10861belt10862wallet10863key ring10864by10865fashion10866said say10867article10868put10869idea10870color10871rule10872hallway10873classroom10874fight10875Ms10876outside10878hall10879have to10880else10881sports shoes10882gym10883Dr= doctor 医10884by10885wash10886later10887the Children’s Palac 10888no talking10889loudly10890aceessory10891snow10892order10893opinion10894order10895form10896how often10897exercise10898skateboard10899hardly10900ever10901once10902twice10903time10904surf10905Internet10906program10907high school10908result10909active10910for10911as for10912about10913junk10914junk food10915milk10916coffee10917chip10918cola10919chocolate10920drink10921health10922how many10923interviewer10924habit 10925try10926of course 10927look after 10928lifestyle 10929grade 10930better 10931same10932as10933different 10934difference 10935unhealthy 10936yuck10937maybe 10938although 10939for10940grandpa 10941a lot of 10942keep10943must10944less10945Katrina 10946matter 10947have10948cold10949have a cold 10950stomachache 10951sore10952back10953arm10954ear10955eye10956foot10957hand10958head10959leg10960mouth 10961neck10962nose10963stomach 10964tooth 10965throat 10966toothache 10967fever 10968rest10969honey 10970dentist10971should10972headache10973shouldn't10974ago10975so10976illness10977advice10978thirsty10979stress10980(be)stressed out 10981early10982problem10983way10984traditional 10985believe10986balance10987yin10988yang10989weak10990Dangshe10991Huangqi10992herb10993angry10994tofu10995medicine10996western10997everybody10998get10999few11000a few11001stay11002important11003balanced11004diet11005moment11006at the moment 11007until11008dear11009host family 11010hear11011babysit11012camp11013plan11014Tibet11015hike11016Hong Kong11017yeah11019away11020get back11021send11022postcard11023San Francisco 11024Hawaii11025bike11026ride11027sightseeing 11028fishing11029rent11030famous11031take a vacation 11032Greece11033Spain11034Europe11035something 11036lake11037the Great Lakes 11038leave11039countryside 11040nature11041forget11042a lot11043finish11044Thailand11045tourist11046Italy11047Hector11048Lambert11049Morgan11050subway11051hey11052train11053forty11054fifty11055sixty11056seventy11057eighty11058ninety11059hundred11060minute11061take11062by11063by bus11064far11066kilometer11067shower11068quick11069bicycle11070early11071mile11072stop11073transportation11074north11075North America11076part11077depend11078depend on11079river11080boat11081by boat11082must11083more11084than11085means11086car11087town11088ill11089worry11090so11091much11092lesson11093another11094concert11095whom11096calendar11097tomorrow11098the day after tomorrow 11099weekday11100invitation11101training11102chemistry11103America11104project11105match11106whole11107over11108come over11109free11110till11111Ted11112Kay11113Lisa11114Eliza11115Vince11116outgoing 11117twin11118calm11119wild11120serious11121athletic 11122note11123mean11124as11125way11126both11127hers11128physics11129however11130more than 11131in common 11132be good at 11133schoolwork 11134laugh11135for11136opposite 11137view11138interest 11139though11140necessary 11141beat11142care11143friendship 11144primary11145primary school 11146infromation 11147Tina11148Tara11149Pedro11150Isabel11151Holly11152wheel11153woman11154use11155cheese11156sick11157body11158begin11159begin with 11160swimming pool 11161excited 11162Harbin11163safe11164fast11165passenger 11166Sandy11167shake11168milk shake 11169blender 11170turn on 11171cut11172up11173cut up11174peel11175pour11176into11177yogurt11178ingredient 11179cup11180watermelon 11181teaspoon 11182amount11183instruction 11184finally 11185mix11186mix up11187popcorn 11188popper11189boil11190salt11191add11192add…to…11193sandwich 11194bread11195butter11196relish11197lettuce 11198turkey11199slice11200super11201top11202recipe11203check11204green onion 11205duck11206sauce 11207pancake 11208roll11209gift11210shark 11211aquarium 11212seal11213hang11214hang out 11215souvenir 11216win11217autogrph 11218prize 11219visitor 11220outdoor 11221octopus 11222end11223monitor 11224Chicago 11225California 11226sleep late 11227drive 11228off11229day off 11230rain11231DVD11232yard11233yard sale 11234luckily 11235umbrella 11236raincoat 11237wet11238competition 11239player 11240future 11241again 11242Laura 11243Toby11244Grace 11245Jake11246born11247record 11248hiccup 11249sneeze 11250too…to…11251golf11252Brazilian11253national 11254achievement 11255perform11256gymnast11257gold11258medal11259championship 11260golfer11261become11262call11263talented 11264loving11265creative 11266outstanding 11267kind11268unusual11269grandson 11270violinist 11271skate11272ice skating 11273champion 11274tour11275the U.S. 11276well-known 11277pianist11278could11279hum11280piece11281accordion 11282take part(in) 11283Poland11284alive11285athlete11286because of 11287Asia11288table tennis 11289university 11290major11291major in 11292management 11293number11294single11295ITTF11296Martina Hingis 11297David Beckham 11298Donna11299Charles11300Tiger Woods 11301Shirley Temple 11302Mozart11303Ronaldo11304Arthur11305Vivian11306Midori11307Chopin11308grow11309grow up11310programmer 11311computer science 11312engineer11313pilot11314professional 11315act11316move11317dream11318somewhere11319exhibition 11320artist11321part-time11322save11323at the same time 11324hold11325rich11326travel11327all over11328retire11329yet11330resolution 11331instrument 11332over11333fax11334reader11335fit11336communicate 11337lady11338foreign11339build11340exchange11341exchange student 11342Manuel11343chore11344dish11345do the dishes 11346sweep11347trash11348take out 11349make one's bed 11350make the bed 11351fold11352living room 11353meeting11354work on11355hate11356do chores 11357laundry11358do the laundry 11359snack11360teenager 11361borrow11362invite11363player11364care11365take care of 11366feed11367mine11368Rosa11369radio11370radio station 11371comfortable 11372seat11373screen11374close11375service11376quality11377theater11378cinema11379clothing 11380jeans11381trendy11382teen11383funky11384easy11385FM11386AM11387jazz11388worse11389worst11390bargain11391meal11392positive 11393negative11395loud11396talent11397talent show 11398performer 11399success11400act11401without11402together 11403musical11404distance 11405near11406farthest 11407province 11408southern 11409still11410lovely11411northern 11412-10℃11413enough11414Jason11415Danny11416Dannis11417Fido11418Jim Carrey 11419sea11420DJ11421Los Angeles 11422central11423diner11424curry11425deli11426leader11427band11428easy11429piece11430brown bread 11431forbid11432Forbidden City 11433camel11434rat11435(not)at all 11436cow11437ha11438seriously 11439hen11440lay11442will11443robot11444won't11445they'll11446everything11447paper11448fewer11449pollution11450tree11451she'll11452building11453astronaut11454rocket11455space11456space station 11457fly11458took11459moon11460I'll11461fall11462fell11463fall in love with 11464alone11465pet11466parrot11467probably11468go skating11469suit11470able11471be able to11472dress11473casually11474which11475even11476the World Cup 11477wrote11478myself11479interview11480predict11481prediction11482came11483come true11484sound11485company11486thought11487strategy11488fiction11489unpleasant11490scientist11491in the future 11492hundreds of11493already11494made11495factory11496simple11497such11498bored11499everywhere11500human11501shape11502huge11503earthquake11504snake11505possible11506electric11507toothbrush11508seem11509impossible11510housework11511rating11512Alexis11513keep out11514play11515argue11516wrong11517What's wrong? 11518style11519out of style 11520could11521call sb. up11522ticket11523surprise11524on the phone 11525What's the matter? 11526pay for11527part-time job 11528okay11529either11530bake11531bake sale11532Teen Talk11533tutor11534origanizal11535the same as 11536in style11537haircut11538except11539upset11540fail11541get on11542didn't11543couldn't11544return11545football11546until11547fit11548fit…into…11549as…as possible 11550pressure11551complain11552include11553pushy11554push11555send11556all kinds of 11557compare11558crazy11559themselves11560adult11561on the one hand 11562organized11563on the other hand 11564freedom11565Eve11566Erin11567Nicole11568Emilio11569Alice11570UFO11571barber11572barber shop 11573bathroom11574bedroom11575kitchen11576get out11577alien11578bought11579land11580got11581take off11582while11583experience11584imagine11585strange11586follow11587amazing11588kid11589scared11590climb11591jump11592shout11593rode11594train station11595ran11596run away11597anywhere11598met11599come in11600happen11601accident11602Beijing International Airport 11603plane11604heard11605modern11606kill11607Memphis11608murder11609hear about11610bright11611playground11612bell11613rang11614told11615close11616silence11617take place11618recent11619World Trade Center11620destroy11621terrorist11622meaning11623as…as…11624became11625flight11626earth11627hero11628flew11629Davy11630Martin Luther King11631Allen11632made11633anymore11634direct speech11635reported speech11636first of all11637message11638pass on11639suppose11640be supposed to11641hard-working11642do well in11643in good health11644report card11645nervous11646envelope11647semester11648disappointing11649lucky11650copy11651own11652get over11653poor11654village11655Peking University11656graduate11657volunteer11658the Ministry of Education 11659Chinese Young Pioneer 11660rural11661area11662meter11663sea level11664thin11665ate11666fortunately11667decision11668husband11669dormitory11670senior high school11671open up11672start11673influence11674return11675hometown11676Greenpeace11677care for11678border11679UNICEF11680WWF11681danger11682Lana11683Marcia11684have a great time 11685organize11686take away11687clean-up11688flower11689agent11690around the world 11691make a living 11692against11693charity11694chance11695all the time11696injured11697sincerely11698lawyer11699tonight11700mobile phone11701Andrea11702Mark11703Michael11704What's the problem? 11705fat11706window11707play football 11708consequence11709explain11710following11711Harry11712collect11713shell11714marathon11715pair11716skate11717since11718Hilltop School 11719raise11720several11721skater11722stamp11723kite11724monster11725globe11726anyone11727run out of11728store11729cake11730particularly 11731collector11732by the way11733common11734extra11735coin11736topic11737been11738be interested in 11739writer11740character11741capital11742European11743Russian11744Australian11745Jewish11746Jew11747thousand11748emperor11749foreigner11750quite11751certain11752the Olympic Games 11753far away11754miss11755Alison11756Celia11757Liam11758Ellen11759Leo11760not at all11761turn down11762yard11763right away11764task11765poster11766waitress11767brought11768solution11769line11770wait in line 11771annoy11772annoyed11773polite11774perhaps11775door11776cut in line 11777hasn't11778term11779etiquette 11780normal11781behavior 11782at first 11783Asian11784uncomfortable 11785impolite 11786allow11787keep…down 11788voice11789public11790take care 11791cough11792sneeze11793break11794break the rule 11795politely 11796smoke11797put out11798cigarette 11799criticize 11800careful11801drop11802litter11803pick11804pick…up 11805behave11806Nick11807Harris11808comment11809album11810personal 11811special11812receive11813gave11814guy11815spider11816mouse11817snake11818hamster11819turtle11820child11821pot-bellied11822pig11823advantage11824disadvantage11825perfect11826rabbit11827company11828cost11829asleep11830fall asleep11831choose11832present11833open11834later11835given11836give away11837bench11838rather than11839Sweden11840instead11841enter11842nearly11843sang11844clearly11845stage11846native11847native speaker 11848winner11849modest11850interested11851encourage11852progress11853make progress 11854hear of11855suggest11856Beijinger11857take an interest in 11858besides11859make friends with 11860statement11861mention11862Connie11863amusement11864neither11865Disneyland 11866Mickey Mouse 11867Donald Duck 11868character11869seen11870theme11871attraction 11872roller coaster 11873cruise11874board11875on board11876route11877end up11878island11879especially 11880exchange student 11881attendant11882flight attendant 11883discover11884requirement 11885guide11886tour guide 11887film11888southeast11889wonderful11890holiday11891quarter11892three quarters 11893population 11894simply11895Putonghua11896fear11897brave11898excellent11899Indian11900Night Safari 11901dark11902daytime11903wake11904wake up11905fox11906natural11907environment 11908temperature 11909all year round 11910equator。
一类具有可积系数的四阶 J-对称微分算子的本质谱
一类具有可积系数的四阶 J-对称微分算子的本质谱彭艳伟;王万义;邱洁【摘要】By using the method of direct sum decomposition for operator and quadratic comparison ,the es-sential spectrum of a class of fourth-order J-symmetric differential operator with integrable coefficients is studied .T he existent range of essential spectrum and available scope of discrete spectrum are given .In addition ,the essential spectrum of a class of second-order J-symmetric differential operator with integra-ble coefficients to fourth-order is extended .At last ,a simple example about the essential spectrum of a class of fourth-order J-symmetric differential operator with integrable coefficients is given .%利用算子直和分解的方法和二次型比较的方法，研究了一类具有可积系数的四阶 J-对称微分算子的本质谱，得到了其本质谱的存在范围，并且给出了与之相对应的离散谱的存在范围。
将具有可积系数的二阶 J-对称微分算子的本质谱推广到四阶，使其得到更广泛的应用。
最后，对于这类具有可积系数的四阶 J-对称微分算子的本质谱提供了简明的实例。
英语排序知识点总结高中
英语排序知识点总结高中I. Grammar1. Parts of Speech- Noun: a word used to identify any of a class of people, places, or things.- Pronoun: a word that can function by itself as a noun phrase and that refers either to the participants in the discourse or to someone or something mentioned elsewhere in the discourse.- Verb: a word that describes an action or state.- Adjective: a word that describes a noun or pronoun.- Adverb: a word or phrase that modifies or qualifies an adjective, verb, or other adverb. 2. Sentence Structure- Subject: the person or thing that is doing the action of the verb.- Predicate: the part of the sentence that tells us what the subject is doing.- Clause: a group of words with a subject and a verb.- Phrase: a group of words that does not have a subject and a verb.3. Tenses- Past Tense: used to describe events that have already happened.- Present Tense: used to describe events that are happening right now or that happen regularly.- Future Tense: used to describe events that have not yet happened but will happen at some point in the future.4. Agreement- Subject-Verb Agreement: the subject and verb in a sentence must agree in number.- Pronoun-Antecedent Agreement: a pronoun must agree in number and gender with its antecedent.5. Parallelism- Parallel Structure: the use of the same grammatical structure for similar items, phrases, or clauses in a sentence.II. Vocabulary1. Word Formation- Prefixes: a group of letters added to the beginning of a word to change its meaning.- Suffixes: a group of letters added to the end of a word to change its meaning.2. Synonyms and Antonyms- Synonyms: words that have similar meanings.- Antonyms: words that have opposite meanings.3. Idioms and Phrasal Verbs- Idioms: a group of words established by usage as having a meaning not deducible from those of the individual words.- Phrasal Verbs: a combination of a verb and one or more particles (prepositions or adverbs) where the particles are not necessary to the meaning of the verb, but add to it.III. Reading Comprehension1. Context Clues- Definition Clue: the meaning of the unknown word is given directly in the sentence.- Example Clue: an example is given to help the reader understand the meaning of the unknown word.- Contrast Clue: a word that is opposite in meaning to the unknown word is given in the sentence.2. Inferences- Drawing Conclusions: using information from the text to make a decision or form an opinion.- Making Predictions: using clues from the text to guess what will happen next.3. Main Ideas and Supporting Details- Main Idea: the most important idea in a paragraph or passage.- Supporting Details: the facts, reasons, examples, and other evidence that support the main idea.IV. Writing1. Essay Structure- Introduction: the first paragraph of an essay that introduces the main idea or argument. - Body: the middle part of an essay that presents the main arguments or points.- Conclusion: the final paragraph of an essay that summarizes the main points and reinforces the main idea or argument.2. Punctuation and Capitalization- Period: used at the end of a declarative sentence.- Question Mark: used at the end of an interrogative sentence.- Exclamation Mark: used to show strong feeling or emotion.3. Types of Essays- Narrative Essay: tells a story or describes an event.- Expository Essay: presents information, discusses ideas, or explains a process.- Persuasive Essay: tries to convince readers to do something or to accept the writer’s point of view.V. Speaking1. Public Speaking- Vocal Delivery: the way the voice is used to communicate the message.- Nonverbal Delivery: facial expressions, gestures, and body language used to communicate the message.- Visual Aids: images, charts, or other visual tools used to enhance the presentation.2. Debating- Argumentation: using logic, reasoning, and evidence to support a claim or position.- Rebuttal: making counter-arguments to weaken the opposing side.VI. Listening1. Active Listening- Paying Attention: being mentally and emotionally engaged in the conversation.- Asking Questions: seeking clarification or additional information.- Paraphrasing: restating what was said to ensure understanding.2. Note-taking- Summarizing: condensing information into concise and clear points.- Organizing: arranging information in a logical and easily accessible way.VII. Literature1. Literary Devices- Metaphor: a figure of speech that identifies something as being the same as an unrelated thing for rhetorical effect, thus highlighting its similarities.- Simile: a figure of speech that directly compares two things using like or as.- Personification: giving human characteristics to non-human things.2. Literary Genres- Fiction: stories or characters that come from the imagination of the author.- Poetry: writing that uses a formal or structured style and often uses rhyme and meter. - Drama: a story meant to be performed in front of an audience.3. Analysis- Characterization: the process by which the writer reveals the personality of a character. - Plot Development: the sequence of events in a story and how they are arranged. Overall, the comprehensive knowledge in high school English covers a wide range of important topics such as grammar, vocabulary, reading comprehension, writing, speaking, listening, and literature. Mastering these concepts will not only support academic success but also lay a strong foundation for effective communication and critical thinking skills.。
People's Education PEP Edition Fourth Grade Englis
04
Oral expression and communication ability cultivation
Guidance on oral expression skills
01
Basic sentence structure
Teach students how to construct simple sentences using subject
• Homework and review suggestions after class
01
Course Introduction and Teaching Objectives
Textbook content and structure
Unit Overview
Each unit in the textbook is designed to cover a specific theme, such as family, school, homes, etc. The content is organized in a logical and cultural way, allowing students to gradually build their language skills
singular的例子
SingularIntroductionIn English grammar, the term “singular” refers to a grammatical number that denotes a single person, thing, or entity. It is the opposite ofthe plural, which indicates more than one. The singular form of a noun, pronoun, verb, or adjective is used when there is only one of the respective objects or when referring to a singular individual or entity. This article will delve into the concept of singular in more detail and explore its various applications across different parts of speech.Singular NounsA singular noun is a word that represents one person, place, thing, or idea. It is the basic form of a noun and is typically used whenreferring to a single entity. Examples of singular nouns include “cat,” “house,” “bottle,” and “friend.” However, there are someexceptions where a singular noun may end in -s, such as “news” or “mathematics,” which are considered grammatically singular despitetheir plural appearance.Singular PronounsPronouns, like nouns, can also be in singular or plural form. Singular pronouns are used when referring to one person or object. Commonsingular pronouns include “he,” “she,” “it,” and “this.” For example, “He is coming to the party,” “She is the manager,” “It is raining,” and “This car is mine.” Singular pronouns are important in avoiding repetition and making sentences more concise and clear.Singular VerbsVerbs in singular form are used when the subject of a sentence is singular. This means that the verb agrees in number with the subject.For instance, in the sentence “The cat jumps,” the verb “jumps” isin singular fo rm to match the singular subject “cat.” On the otherhand, in a plural sentence such as “The cats jump,” the verb “jump” is in the plural form to correspond with the plural subject “cats.”Singular AdjectivesAdjectives describe or modify nouns, and they also have singular and plural forms. An adjective in singular form is used when the noun it modifies is singular. For example, in the phrase “a beautiful flower,” the adjective “beautiful” is in singular form to match the singular noun “flower.” In contrast, if the noun is plural, as in “beautiful flowers,” the adjective takes the plural form to agree with the noun.Singular and Plural AgreementMaintaining agreement between singular and plural forms is essential for grammatical correctness. When writing or speaking, it is important to ensure that nouns, pronouns, verbs, and adjectives are in agreement to create a coherent sentence. Failure to do so can lead to confusion or an incorrect interpretation. Let’s look at some examples to illustrate this:1.Incorrect: “The boy walk to school.” Correct: “The boy walks toschool.”2.Incorrect: “They is playing soccer.” Correct: “They are playingsoccer.”In the first example, the verb “walk” should be in the singular form “walks” to agree with the singular subject “boy.” In the second example, the pronoun “they” is plural, so the verb “is” should be changed to the plural form “are” to maintain agreement.Singular in Indefinite ArticlesThe use of indefinite articles also relates to the concept of singular. In English, the indefinite article “a” is used before singular countable nouns that begin with a consonant sound, while “an” is used before singular countable nouns beginning with a vowel sound. For example, “a dog,” “an hour,” “a book.” These articles indicatethat we are referring to one of the respective objects or entities.Singular in Countable and Uncountable NounsCountable nouns refer to objects that can be counted individually, such as “dog,” “book,” or “pen.” These nouns have both singular and plural forms. On the other hand, uncountable nouns represent substances, concepts, or phenomena that cannot be counted or divided into separate units, such as “water,” “love,” or “information.” Uncountable nouns are considered grammatically singular and are not used with the indefinite article. For instance, instead of saying “a water” or “a love,” we simply say “water” or “love.”ConclusionIn conclusion, the concept of singular plays a fundamental role in English grammar. Understanding and correctly using singular nouns, pronouns, verbs, adjectives, and articles is essential for effective communication. Maintaining agreement between singular and plural formsis crucial to ensure grammatical accuracy. By mastering the concept of singular, one can express ideas clearly and concisely in a grammatically correct manner.。
《商务英语语法》3-Determiners L(6,7)
B. some types of a
C. some type of a
D. some types of
7. Issues of price, place, promotion, and product are ______ conventional concerns in planning marketing strategies. (2004, 59)
no, some, any, etc cardinal numerals ordinal numerals
multiplicative numeral fractional numeral quantifier (phrases)
6.1 Collocation between determiners and nouns
2) Word order of three subclasses of determiners
“predeterminers + central determiners+ postdeterminers”
Discussion
1. Which of the following determiners（限定词）can be placed before both singular count nouns and plural count nouns? （2012, 52）
D. no such √源自6. Because fuel supplies are finite and many people are wasteful, we will have to install ______ solar heating device in our home. (2005, 56)
四年级下英语课文和单词
四年级下英语课文和单词全文共3篇示例，供读者参考篇1English Class - 4th GradeEnglish has always been one of my favorite subjects in school. I find it really interesting to learn a new language and get exposed to different cultures. This year in 4th grade, our English textbook is full of fun stories, poems, and activities.One of the first units we covered was about family. We learned vocabulary words like mother, father, sister, brother, grandma, grandpa, aunt, uncle, and cousin. The reading had a nice story about a kid introducing their big family. I could relate since I have a huge family too with lots of aunts, uncles, and cousins. We did an activity where we had to draw a family tree and label all the family members. It was a good way to practice the new words.Another unit focused on different occupations and community helpers. We learned words like doctor, nurse, teacher, firefighter, police officer, chef, and farmer. The readings were about kids describing what they want to be when they grow up.I'm not totally sure yet, but I think maybe a scientist could be cool. For the project, we had to dress up as a community worker and give a short presentation about what that job entails. I was a construction worker, which involved hard hats and tools.My favorite unit so far was the one about animals. We covered names of all different creatures like elephant, giraffe, monkey, kangaroo, and penguin. But we also learned adjectives to describe them, like big, small, tall, wide, heavy, and light. The readings were amazing non-fiction passages loaded with facts about exotic animals. Did you know that a giraffe's tongue is over 20 inches long? We ended up doing group projects where each group picked an animal, researched it, and then presented to the class with visuals and props. My group did the lion, so we made a diorama of the savannah and printed out lion photographs.Of course, we've learned lots of other common vocabulary too related to school supplies, food, colors, weather, and more. Some of the trickier words have been eraser, folder, lunchbox, spaghetti, broccoli, turquoise, foggy, and chilly. For colors, I kept mixing up violet and indigo. With weather words, remembering if it's gusty for wind or breezy was hard. Spelling tests on the weekly word lists are no joke!We've covered different grammatical concepts too like verb tenses, singular/plural nouns, adjectives, and basic sentence structure. I'm starting to get the hang of making simple sentences like "The brown dog ran quickly" by putting the parts of speech in order. But then we have to take it further and make them more complex and descriptive. Like "The energetic puppy excitedly chased the strays down the sunny street." Using adverbs and adjectives to extend and spice up the sentences is key.There's been a good mix of readings, worksheets, activities, games, and projects throughout the year to keep things engaging. The readings have covered all different genres like fiction stories, non-fiction articles, fables, and poems. Sometimes the passages will have a recording so we can hear the proper pronunciation. The worksheets let us practice vocabulary, grammar, comprehension, and writing. The games have included fun ways to review the words like Pictionary, Charades, and Bingo. And the projects give us a chance to get creative and apply what we've learned in a bigger way.Learning English is definitely a challenge, but I feel like I'm making good progress. There's so much vocabulary to commit to memory. And putting all the grammatical rules into practicewhen writing and speaking is tough. But overall, I'm enjoying the content and process. The variety of activities keeps me interested and motivated. I like being exposed to different texts and cultures through the stories and lessons.I've come a long way already from the basics we started with like colors, numbers, and simple phrases. Now I'm reading full narratives and non-fiction passages. I'm constructing full sentences and short paragraphs. I'm picking up vocabulary for more complex topics like science, social studies, and literature. While English is far from easy, consistency and immersion through our readings, exercises, and multimedia resources is helping it stick.I know English will continue to be an important focus through middle school and high school. The further I advance, the more valuable and applicable it will become. Who knows, maybe I'll even pursue it as a career someday through a job involving lots of writing, communication, or international relations. Either way, establishing this solid foundation in elementary school will pay dividends. I'm eager to continue expanding my skills in spelling, grammar, reading comprehension, and verbal/written expression. Kudos to ourteacher for making English class so engaging at this critical stage!篇2My Fourth Grade English ClassEnglish is one of my favorite classes this year in fourth grade.I like how we get to learn new words, read interesting stories, and practice speaking and listening. Our textbook is really cool too with lots of colorful pictures and fun activities.At the beginning of the year, we started with some basics. The first unit was all about introducing yourself and talking about your family. We learned words like sister, brother, mom, dad, grandparents and cousins. The readings were dialogues of kids telling their friends about their families. I have one younger brother named Jake, so I could relate to those readings.Some of the other early units covered topics like numbers, colors, shapes, days of the week, months of the year, and telling time. The number words were pretty easy since we had learned to count to 100 way back in kindergarten. But telling time on analog clocks was kind of tricky at first. Words like quarter, half, minute and hour were new vocabulary. By the end of that unit though, I could read a clock like a pro.Then we got into some really fun units all about animals, foods, and toys. We read folklore stories from different cultures about talking animals. My favorite was the tale of the tiger and the strawberries from Indonesia. We also learned the names of a bunch of different animals like elephant, kangaroo, zebra and alligator. For the food unit, I enjoyed bringing in labels and boxes from home to share all the different food words in English like pizza, broccoli, ice cream and chocolate. The toy unit was great because we got to bring in our favorite toys and doshow-and-tell while using words like doll, car, blocks and video games.Of course, no English class would be complete without lots of fun verb words for actions. Over the year we learned words like run, jump, skip, throw, catch, read, write, draw, listen, and many more. We'd have to listen carefully as the teacher said the word and showed an action, then we had to do it ourselves. It was a lively way to learn and practice.One of the big units towards the end of the year was about different cultures and countries around the world. We learned words for common traditions, holidays, foods, clothing and cultural items from places like Mexico, India, Egypt and China. For the reading, we'd get exposed to folktales and stories fromeach of those cultures. I thought the mythology stories about gods and goddesses from ancient Greece were really fascinating. For the culture unit, we even had to do group projects and presentations to teach the rest of the class about our assigned country.Another helpful part of English class has been all the games, songs and chants we use to practice vocabulary. Our teacher is amazing at coming up with fun, silly ways to remember words through rhymes, hand motions and cheers. Whenever we'd have indoor recess, we'd get to play vocabulary games likeSimon Says, Charades or Pictionary. Even just simple flashcard oraround-the-room drilling with a beach ball helped make practicing English feel more like play than work.Of course, with all the vocabulary words we're learning, we have to take quizzes pretty frequently. The quizzes include matching words to pictures, filling in the blanks, unscrambling letters, multiple choice, and giving short definitions. As long as I've been studying regularly, the quizzes aren't too bad. Plus, our teacher doesn't just make us memorize words but also teaches us prefixes, suffixes, root words, and how to use context clues from sentences to figure out new words.Looking back over the whole year, it's amazing how many English vocabulary words I've learned in fourth grade. Just from the topics I talked about like families, time, animals, foods, toys, actions, cultures and more, I've probably learned and worked with over 500 new English words this year! With all the readings, writing, speaking, listening, games and quizzes we've done, I really feel like my English skills have grown a ton. I can't wait to move on to fifth grade and continue my English language journey. Who knows how many more words I'll learn and how much more fluent I'll become? English is a blast!篇3My Fourth Grade English Textbook and WordsHi there! My name is Jamie and I'm in the 4th grade. I just turned 10 years old last month. Today I wanted to tell you all about the English textbook we use in my class and some of the words and lessons we've learned so far this year. Get ready, because there's a lot to cover!Our textbook is called "Exploring English" and it's pretty thick - I bet it has over 200 pages! The cover has a bunch of different scenes drawn on it, like a city, a forest, kids playing sports, and even some outer space images. I think the picturesare meant to represent all the different topics and adventures we'll explore through reading and learning English this year. Pretty cool!The very first unit was all about friends, family, and community. We learned lots of vocabulary words related to people, like sibling, cousin, neighbor, and classmate. One story was about a girl who moved to a new neighborhood and made friends with the kids next door. Another one featured extended family members coming together for a reunion. The readings taught me that your community is made up of all the people around you - not just your relatives, but also your neighbors, teachers, etc. I have a pretty big extended family myself, with grandparents, aunts, uncles, and cousins spread out in a few different states. So this unit helped me appreciate how lucky I am to have such a wide community of loved ones.Up next was a whole unit focused on animals! This was probably my favorite unit so far. We read amazing fiction stories about kids going on safaris and doing things like watching elephants at a watering hole in Africa. But we also learned a ton of facts about real creatures - their habitats, diets, behaviors, and more. I marked so many new vocabulary words to review, like species, mammal, herbivore, nocturnal, and migration. My topthree favorite animals we studied have to be cheetahs (since they're the fastest), bald eagles (our national symbol), and dolphins (because they're so smart). Honestly, every time we read about a new type of animal, I thought "This one is definitely the coolest!" I just love learning about the natural world.Then we had a unit all about seasons, weather, and climate. This one built on some of the science concepts I had learned previously about things like the water cycle and why we have seasons. But now I know way more weather-related vocab, from blizzard and drought to humid and overcast. Did you know that snow is formed when moisture in clouds freezes into ice crystals? That's so fascinating! We read all these engaging books and articles about extreme weather events, climates around the globe, and even weather myths and legends from ancient cultures. My favorite was a Native American myth about why the seasons change - it involved a colorful battle between the Winter Maker and the Summer Maker. Very creative!After that was a unit centered around community service and giving back. We learned how important it is to volunteer and support those in need. The texts taught us about food banks, disaster relief efforts, environmental conservation, and more. I discovered so many inspiring real-life examples of kids takingaction to better their communities, like starting charitable lemonade stands, organizing park clean-ups, or collecting supplies for animal shelters. Some new words I mastered include volunteer, poverty, donation, recycle, and compassion. This unit really motivated me to find ways to make a positive difference myself. My class is planning a used book drive soon to gather reading materials for a local literacy program. I can't wait!Most recently, we've been immersed in a unit all about creative arts and expression. We've analyzed poetry, learned about different styles of visual art, studied famous plays and novels, and much more. It's been amazing exploring how people use artistic outlets like writing, painting, music, and dance to express their perspectives and experiences. Some awesome new vocabulary includes metaphor, rhythm, abstract, protagonist, and intensity. My personal favorites from this unit were an illustrated book about Frida Kahlo's life and a play script that put a modern twist on a classic fairy tale. Who knew learning could be so creative and expressive?Phew, that's a whole lot of English learning we've packed into one school year already! And believe it or not, we still have a few more units to go before summer break. Coming up soon is a unit focused on inventions and discoveries. I can't wait to learnabout groundbreaking innovations throughout history and all the brilliant scientists, inventors, and thinkers who made them possible. Maybe I'll even get some inspiration for a cool invention idea of my own!Well, that's a glimpse into our 4th grade English learning journey so far. Between the engaging stories, fascinating facts, and all the new vocabulary, my brain is simply overflowing with knowledge. I know mastering literacy and language arts will open up so many doors for me in the future when it comes to communicating, thinking critically, and understanding the world around me. I'm proud of all the progress I've made so far, and I'm excited to keep exploring and discovering through the pages of our English textbook. The adventure continues!。
英语中数词-基数词序数词
Special usage above "four"
Referring to a group of more than four things
Use the corresponding numeral instead of the corresponding numeral followed by "of," e.g., "There are five apples on the table."
Clear communication
Using both types of numbers in a sentence can help make the communication clearer and more precise, especially when dealing with complex or detailed information.
Numerals in English - Cardinal and Ordinal Numbers
目录
• Cardinal numeral • Ordinal number words • The Usage of Cardinal and Ordinal Numbers • Special usage of numerals
Describing order and quantity
Sometimes, people may use both cardinal and ordinal numbers together to provide more specific information about order and quantity. For example, "There were approximately 200 people in attendance, with about 50 in the first row and the rest spread throughout the remaining seats."
排列组合英文单词
排列组合英文单词Arrangement of Combinations of English WordsIntroductionIn the English language, there are countless combinations of words that can be formed through various arrangements. This article explores the concept of arranging and combining English words to create meaningful expressions and creative compositions. Without further ado, let us delve into the intriguing world of arranging and combining English words.Expressive VocabularyVocabulary serves as the building blocks of language. By combining and arranging words, we are able to express complex ideas and convey precise meaning. A rich and diverse vocabulary enhances our ability to communicate effectively. The arrangement of words allows us to convey different shades of emotion, from joy to sorrow, and everything in between.Word Placement and OrderThe placement and order of words play a crucial role in determining the grammatical correctness and clarity of a sentence. In English, the typical word order is subject-verb-object. However, by rearranging the words, the emphasis can be shifted and new meanings can be created.For example, let's consider the sentence "She ate the apple." By rearranging the words, we can say "The apple, she ate," which puts emphasis on the apple rather than the subject. This simple rearrangement demonstratesthe power of word arrangement in altering the meaning and impact of a sentence.Idioms and PhrasesIdioms and phrases are a fascinating aspect of the English language. They are expressions that have a figurative meaning, different from the literal interpretation of the words in the arrangement. Idioms and phrases add color and depth to our language, making it more vivid and captivating.For instance, the phrase "barking up the wrong tree" does not refer to a literal act of barking or a tree. It metaphorically means accusing or blaming the wrong person or thing. Through unique word arrangements, idioms and phrases provide a creative and nuanced way of communicating.Poetry and ProsePoetry and prose are literary forms that heavily rely on the arrangement and combination of words. In poetry, the arrangement of words is often structured in a specific rhythm and meter, creating a musicality that enhances the emotional impact of the words. Poets carefully select and arrange words to evoke vivid imagery and convey complex emotions.Prose, on the other hand, allows for a more flexible arrangement of words. It enables authors to craft detailed descriptions, engaging narratives, and profound character development. The careful arrangement and combination of words in prose bring stories to life, enabling readers to immerse themselves in different worlds and experiences.Creative ExpressionBeyond literature, the arrangement and combination of English words are also used for creative expression in various forms of art. Song lyrics, advertisements, slogans, and even social media captions rely on the arrangement of words to captivate an audience and convey a particular message.Consider famous advertising slogans such as Nike's "Just Do It" or McDonald's "I'm Lovin' It." These concise and catchy phrases utilize a clever arrangement of words to leave a lasting impression on consumers. The arrangement of words becomes a powerful tool for marketers to communicate their brand's message effectively.ConclusionThe arrangement and combination of English words form the bedrock of communication and creative expression. From everyday conversations to timeless literary works, words arranged in different ways shape our understanding of the world and enable us to connect with others.Whether in poetry or prose, idioms or slogans, the arrangement of words carries immense power. It is through this arrangement that we can capture emotions, paint vivid pictures, and leave a lasting impact on the minds of those who read or hear our words. Let us continue to explore the endless possibilities of arranging and combining English words to unlock new levels of communication and creativity.。
subject-verb_agreement课件
e.g.
The pair of shoes is worn out. 这双鞋破了。 The shoes are worn out. 鞋子破了。
Grammatical agreement
1.8 Some nouns ending with –s express a singular meaning, such as news, physics, economics, the United States, Arabian Nights, etc.
2.4 indefinite quantity + noun, such as part of, a lot of, one of, a number of, plenty of, etc., the verb form depends on the noun.
Eg. A part of the textbooks have arrived. A part of the apple has been eaten up .
Notional agreement
2.5 Nouns expressing time, money, distance, etc are used as a subject, the verb takes a singular form.
Ten miles is a good distance. 十英里是一个相当的距离。
2.3 some nouns phrases, such as bread and butter, knife and fork, law and order, are used as the subject, the verb takes a singular form.
Notional agreement
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1
Introduction
Le t 0 < η < 1. T he pu rpose of this pap e r is to stud y th e e xiste nc e of n ontrivial solu tion to the follow in g n online ar fou rth -ord er th ree- p oin t b oun dary valu e p roble m ( u (4) ( t) = f ( t, u ( t) , u� ( t ) , u � � ( t) , u� � � ( t)) , a .e. t ∈ [0 , 1] , (P) u � � (0) = A , u( η ) = B , u � ( η ) = C, u � � (1) = D. In m ech anic s, the fou rth-ord er bou n dary valu e proble ms c an mod el th e de fle ction of some e lastic b e ams. Problem (P) is very intere stin g b ecau se it is a mu lti- point b ou nd ary valu e prob le m in b eam eq uations. Th ere are quite a f ew pap ers con ce rn ed w ith th e existen ce of solu tion to p roblem (P) (see [1-4]). The se pap ers re qu ire d th at f ( t, u 0 , u1 , u 2 , u 3 ) = f ( t, u 0 , u2 ) is a c ontinuou s fu nc tion . In th is pap er, we c onside r prob lem (P) with all ord er d erivative s of u nk nown fun ction .
2
Main Results
In 1989, A garwal [5] prop osed a line ar growth c ond ition of con stan t ty pe |f ( t, u 0 , u1 , u 2 , u 3 ) | ≤ a0 | u0 | + a1 | u 1 | + a 2 | u 2 | + a3 |u 3 | + a4 ,
wh ere ai , 0 ≤ i ≤ 4 , are n onn egative con stants, and c onside red the e xistenc e of solution to anoth er fou rth- order b oun dary valu e p roblem . In 2008, H opkin s an d Kosm atov [6] stu died th e followin g line ar growth con dition of fun ction typ e
An n. of D iff. Eqs . 26:4(2010) , 477-483
A CLASS OF SINGULAR FOURTH-ORDER THREE-POINT BOUNDARY VALUE PROBLEMS
Qingliu Yao
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477
478
A NN. OF DIFF. EQ S.
| f (t, u 0 , u 1 , u2 ) | ≤ a0 ( t ) | u0 | + a1 ( t ) | u1 | + a2 ( t ) | u2 | + a3 ( t ) ,