501.Math.Word.Problems

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(完整word版)数学建模麻将问题

B 题麻将问题摘要麻将,又名麻雀牌，三种基础花色的名字叫做“万、条、筒".在中国麻将竞赛规则下,本题主要通过玩家和牌情况，推断其牌型即为“见万就和”的极致牌型问题.至于问题一，玩家牌型的问题。

我们在尽量简化麻将模型与本题的契合度的情况下,在去除掉麻将繁琐的牌数及规则以后，运用集合及逐步分析的方法，借鉴常微分方程中picard 逐步逼近法的证明方法，通过引理及定理的证明，从而建立了非常简单的C B A +=的集合模型，并在我们模型的条件下找到了适合的5种解。

9}6,7,8,9,9,1,2,3,4,5,,1,{11=C ； 8}6,6,6,6,7,1,2,3,4,5,,1,{12=C ；,9,9,9},4,5,6,7,8{2,3,4,4,43=C ;,6,7,8},4,5,6,6,6{2,3,4,4,44=C ;}8,7,7,7,7,6,5,4,3,3,3,3,2{5=C 。

至于问题二：玩家牌型的唯一性问题，在借鉴了问题一中得数学模型及牌型解得情况下，通过麻将规则及本题的和牌规则验证了5组解得合理性及可实现性，我们得到了玩家唯一的牌型9}6,7,8,9,9,1,2,3,4,5,,1,{11=C ，即满足题意的玩家牌型是唯一的，术语：九莲宝灯.关键词:九莲宝灯,见万就和，数学建模麻将问题，逐步分析法。

一、问题重述一个麻将玩家手中的牌，使得他摸到或吃到任何一张“万”牌都和。

问这个玩家手里是什么牌？要求给出算法，并考虑唯一性的问题。

不能光给答案。

根据中国麻将竞赛规则，筛选出来一定的牌，然后通过集合的笛卡尔积，根据和牌的牌型，整理出可能的排列组合，然后对相关的组合进行验证,得出玩家手中的牌。

通过反证法，证明牌型的唯一性问题。

二、模型假设●模型和牌的规则是建立在中国麻将竞赛规则的标准之上的。

●通过相关资料的证明，本题中的相关数据与字牌及花牌没有联系，故模型中不考虑东南西北中发白及花牌的影响,只考虑91 万、条、筒。

2023美赛数学建模f题

2023美赛数学建模f题Title: Mathematical Modeling Approach to the 2023 MCM/ICM Problem FAbstract:In this article, we will delve into problem F of the 2023 Mathematical Contest in Modeling (MCM) and Interdisciplinary Contest in Modeling (ICM). The problem description revolves around a real-world scenario that involves optimizing bus routes for a transportation system. We will discuss the problem statement, analyze the given data, propose a mathematical model, and provide a detailed solution approach to address the problem. The goal is to optimize the bus routes to minimize the total waiting time for passengers while considering various constraints.Introduction:Problem F of the 2023 MCM/ICM focuses on the optimization of bus routes to reduce waiting time for passengers. The scenario provided involves a public transportation system in a city with multiple bus stops and a given number of buses. The task is to determine the optimal routes for the buses, considering various factors such as passenger demand, travel time, and capacity constraints.Problem Statement:The problem statement requires us to optimize the bus routes to minimize the total waiting time for passengers. The optimization should be based on the given data, which includes the number of buses, the locations of bus stops, the number of passengers at each stop, the travel time between stops, and the bus capacity.Data Analysis:To solve the problem, we need to analyze the given data and understand the key factors that impact the waiting time for passengers. This includes examining the passenger demand at each stop, the travel time between stops, and the capacity of the buses.Mathematical Model:To develop a mathematical model, we need to define the decision variables, objective function, and constraints. In this case, the decision variables could be the routes for each bus, the number of passengers picked up and dropped off at each stop, and the waiting time for each passenger. The objective function could be the total waiting time for all passengers, which we aim to minimize.Solution Approach:To solve the problem, we propose a multi-objective optimization approach that combines both route optimization and passenger allocation. The algorithm includes the following steps:1. Initial Route Generation: Generate initial routes for each bus based on a heuristic algorithm, such as the nearest neighbor algorithm or a genetic algorithm.2. Passenger Allocation: Allocate passengers to buses and stops based on the given demand, capacity constraints, and travel time. This can be done using techniques like integer linear programming or heuristics.3. Route Optimization: Optimize the routes for each bus using techniques like the Traveling Salesman Problem or the Vehicle Routing Problem, considering factors such as travel time, passenger demand, and bus capacity.4. Waiting Time Calculation: Calculate the waiting time for each passenger based on the allocated bus routes and the travel time between stops.5. Performance Evaluation: Evaluate the performance of the optimized routes by calculating the total waiting time for all passengers. Compare the results with the initial routes and identify areas for further improvement.Conclusion:In this article, we have explored problem F of the 2023 MCM/ICM, which focuses on optimizing bus routes to minimize the waiting time for passengers. We have discussedthe problem statement, analyzed the given data, proposed a mathematical model, and provided a detailed solution approach. By implementing the proposed algorithm, transportation authorities can optimize bus routes, reduce waiting time, and improve the efficiency of the public transportation system.。

python软件编程等级考试(一级)编程实操题02精品word程序填空阅读填空程序试题

python软件编程等级考试(一级)编程实操题02精品word程序填空阅读填空程序试题一、程序填空1．完善程序实现以下功能并保存。

输入一元二次方程的系数a，b，c的值，求解一元二次方程 ax2+bx+c=0(a≠0)#请不要更改源程序的结构，删除原题里的①、②。

填写正确的代码，使程序完善import matha=float(input("请输入方程系数a(!=0):"))b=float(input("请输入方程系数b:"))c=float(input("请输入方程系数c:"))delta=b*b-4*a*cif delta>________:x1=(-b+math.sqrt(delta))/(2*a)x2=(-b-math.sqrt(delta))/(2*a)print("方程有两个不同的解"，x1，x2)elif delta==0:x1=________print("方程有两个相同的解"，x1)else:print("方程无解")input("运行完毕，请按回车键退出...")2．请在空格处填写正确的代码，使程序完善。

实现功能：绘制y=x2-2x+ 1的图像#加载numpy模块并限简洁的别名为npimport numpy as np#加载matplotlib.pyplot模块并限简洁的别名为pltimport matplotlib.pyplot as plt#x在-7到9之间,每隔0.1取一个点x=np.arange(-7,9,0.1)_____ = x**2-2*x+1plt.plot(x,________)plt.title('y=x*x-2*x+1')plt.xlabel('x')plt.ylabel('y')plt._________3．阅读程序。

Problems

1008 求分数序列和Time Limit:1000MS Memory Limit:65536KTotal Submit:535 Accepted:284Description有一个分数序列2/1，3/2，5/3，8/5，13/8，21/13，…… ，求这个分数序列的前n项之和。

Input输入有一行：正整数n（0≤n≤500）。

Output输出有一行：分数序列中前n项的和，要求精确到小数点后4位。

Sample Input99Sample Output160.4849Sample Result:Hint为避免溢出错误，在程序中的中间变量尽可能都使用double类型。

1009 质数判定Time Limit:1000MS Memory Limit:65536KTotal Submit:577 Accepted:293Description质数被定义为一个不能除了1和它本身整除的正整数。

你的任务就是要编写一个程序，判定任意一个大于等于2的正整数是否是质数。

Input输入只有一行，即要判定的这个正整数a（2≤a≤200）。

Output输出只有一行，若a是质数，输出“Y”，否则输出“N”。

Sample Input53Sample OutputYSample Result:Source杨珂1010 棋盘上的距离Time Limit:1000MS Memory Limit:65536KTotal Submit:602 Accepted:181Description国际象棋的棋盘是黑白相间的8 * 8的方格，棋子放在格子中间。

如下图所示：王、后、车、象的走子规则如下：∙王：横、直、斜都可以走，但每步限走一格。

∙后：横、直、斜都可以走，每步格数不受限制。

∙车：横、竖均可以走，不能斜走，格数不限。

∙象：只能斜走，格数不限。

写一个程序，给定起始位置和目标位置，计算王、后、车、象从起始位置走到目标位置所需的最少步数。

∙Input∙第一行是测试数据的组数t（0≤t≤20）。

（完整版）英文数学题（1）

（完整版）英文数学题（1）1、In 2004, 16 June falls on a Wednesday. On what day of the week will 16 June fall in 2010?2、In a magic square the sum of the numbers in each row, in each diagonal and in each column are equal. In this magic square the value of x is:3、If half of a number is 30, then three-quarters of that number is____.4、The sum of the digits of the following product999×5555、Three positive integers have a sum of 28. The greatest possible product that these integers can have is_____.6、Jack was trying to tessellate regular pentagons. He managed the following figure.The size of angle .a. is______.7、If the area of the shaded region of the regular hexagon in the diagram below is 36 cm2, the area of the whole hexagon in cm2 is_____.8、In what follows, □and Δare different numbers.When 503 is divided by □the remainder is 20.When 503 is divided by Δ the remainder is 20.When 493 is divided by □x Δthe remainder is_____.9、A lady, her brother, her son and her daughter (all related by birth) played volleyball. The worst player's twin (who is one of the four players) and thebest player are of opposite sex.The worst player and the best player are of the same age.Who cannot be the worst player(s)?A) brother only B) daughter onlyC) son and daughter only D) lady and daughter onlyE) lady only10、If you continue the given number pattern, in what row and in what position in that row will the number 320 be?1 -------------- row 12 3 -------------- row 24 5 6 -------------- row 37 8 9 10 -------------- row 4The answers are given in the order of row ; position.参考答案：1、Wednesday2、123、454、27（求数位上上的数字之和）5、28=9+9+10，因此答案为8106、36度7、1088、503-20=483 483=3×7×23＝21×23，因此□x Δ＝483，因此此题余数是10.9、D 10、25，201、Did you know? In the decimal number system (base 10) ten different digits, 0 to 9, are used to write all the numbers. In the binary number system (base 2) two different digits are used, i.e. 0 and 1.Which one of the following numbers is not a valid number in theoctal number system (base 8)?A) 128 B) 127 C) 126 D) 125 E) 1243、The number of diagonals that can be drawn in a regular polygon with twenty sides (icosagon) is_____.4、If a and b are integers, 10Ä3=1,152Ä7=3, and then 379Ä6 is equal to_____.5、Two numbers are in the ratio 2 : 3. When 4 is added to each number the ratio changes to 5 : 7.The sum of the two original numbers is____.6、The greatest number of Mondays which can occur in 45 consecutive days is____7、Saul plays a video game in which he scores 4 for a hit and lost 6 for a miss. After 20 rounds his score is 30. The number of times he has missed is____.8、Three girls A, B and C run in a 100 m race. When A finishes,B is 10 m behind A and when B finishesC is 20 m behind B. How far in metres was C from A when A finished?(Let’s assume all the athletes run at a constant speed)9、The areas of the faces of a rectangulabox are 84 cm2 , 70 cm2and 30 cm2.The volume of the box in cm3 is____.10、You have 3 weights: 1 kg, 3 kg and 9 kg as well as an equal arm balance, as shown. How many different weight objects can you weigh with these three?[Remember the weights may be placed on either side]参考答案：1、A 考察我们学过的简单的进制问题，显然8进制中没有8出现2、B 用排除法3、170 找规律，公式为n×（n-3）÷24、1 定义新运算，就是求379÷6的余数。

数学专业英语第2章课后答案

2.12.比:ratio 比例:proportion 利率:interest rate 速率:speed 除:divide 除法:division 商:quotient 同类量:like quantity 项:term 线段:line segment 角:angle 长度:length 宽:width高度:height 维数:dimension 单位:unit 分数:fraction 百分数:percentage3.(1)一条线段和一个角的比没有意义,他们不是相同类型的量.(2)比较式通过说明一个量是另一个量的多少倍做出的,并且这两个量必须依据相同的单位.(5)为了解一个方程,我们必须移项,直到未知项独自处在方程的一边,这样就可以使它等于另一边的某量.4.(1)Measuring the length of a desk, is actually comparing the length of the desk to that of a ruler.(3)Ratio is different from the measurement, it has no units. The ratio of the length and the width of the same book does not vary when the measurement unit changes.(5)60 percent of students in a school are female students, which mean that 60 students out of every 100 students are female students.2.22.初等几何:elementary geometry 三角学:trigonometry 余弦定理:Law of cosines 勾股定理/毕达哥拉斯定理:Gou-Gu theorem/Pythagoras theorem 角:angle 锐角:acute angle 直角:right angle 同终边的角:conterminal angles 仰角:angle of elevation 俯角:angle of depression 全等:congruence 夹角:included angle 三角形:triangle 三角函数:trigonometric function直角边:leg 斜边:hypotenuse 对边:opposite side 临边:adjacent side 始边:initial side 解三角形:solve a triangle 互相依赖:mutually dependent 表示成:be denoted as 定义为:be defined as3.(1)Trigonometric function of the acute angle shows the mutually dependent relations between each sides and acute angle of the right triangle.(3)If two sides and the included angle of an oblique triangle areknown, then the unknown sides and angles can be found by using the law of cosines.(5)Knowing the length of two sides and the measure of the included angle can determine the shape and size of the triangle. In other words, the two triangles made by these data are congruent.4.(1)如果一个角的顶点在一个笛卡尔坐标系的原点并且它的始边沿着x轴正方向，这个角被称为处于标准位置.(3)仰角和俯角是以一条以水平线为参考位置来测量的,如果正被观测的物体在观测者的上方,那么由水平线和视线所形成的角叫做仰角.如果正被观测的物体在观测者的下方,那么由水平线和视线所形成的的角叫做俯角.(5)如果我们知道一个三角形的两条边的长度和对着其中一条边的角度,我们如何解这个三角形呢?这个问题有一点困难来回答,因为所给的信息可能确定两个三角形,一个三角形或者一个也确定不了.2.32.素数:prime 合数:composite 质因数:prime factor/prime divisor 公倍数:common multiple 正素因子: positive prime divisor 除法算式:division equation 最大公因数:greatest common divisor(G.C.D) 最小公倍数: lowest common multiple(L.C.M) 整除:divide by 整除性:divisibility 过程:process 证明:proof 分类:classification 剩余:remainder辗转相除法:Euclidean algorithm 有限集:finite set 无限的:infinitely 可数的countable 终止:terminate 与矛盾:contrary to3.(1)We need to study by which integers an integer is divisible, that is , what factor it has. Specially, it is sometime required that an integer is expressed as the product of its prime factors.(3)The number 1 is neither a prime nor a composite number;A composite number in addition to being divisible by 1 and itself, can also be divisible by some prime number.(5)The number of the primes bounded above by any given finite integer N can be found by using the method of the sieve Eratosthenes.4.(1)数论中一个重要的问题是哥德巴赫猜想,它是关于偶数作为两个奇素数和的表示.(3)一个数,形如2p-1的素数被称为梅森素数.求出5个这样的数.(5)任意给定的整数m和素数p,p的仅有的正因子是p和1,因此仅有的可能的p和m的正公因子是p和1.因此,我们有结论:如果p是一个素数,m是任意整数,那么p整除m,要么(p,m)=1.2.42.集:set 子集:subset 真子集:proper subset 全集:universe 补集:complement 抽象集:abstract set 并集:union 交集:intersection 元素:element/member 组成:comprise/constitute包含:contain 术语:terminology 概念:concept 上有界:bounded above 上界:upper bound 最小的上界:least upper bound 完备性公理:completeness axiom3.(1)Set theory has become one of the common theoretical foundation and the important tools in many branches of mathematics.(3)Set S itself is the improper subset of S; if set T is a subset of S but not S, then T is called a proper subset of S.(5)The subset T of set S can often be denoted by {x}, that is, T consists of those elements x for which P(x) holds.(7)This example makes the following question become clear, that is, why may two straight lines in the space neither intersect nor parallel.4.(1)设N是所有自然数的集合,如果S是所有偶数的集合,那么它在N中的补集是所有奇数的集合.(3)一个非空集合S称为由上界的,如果存在一个数c具有属性:x<=c对于所有S中的x.这样一个数字c被称为S的上界.(5)从任意两个对象x和y，我们可以形成序列（x，y），它被称为一个有序对，除非x=y，否则它当然不同于（y，x）.如果S和T是任意集合，我们用S*T表示所有有序对（x,y),其中x术语S，y属于T.在R.笛卡尔展示了如何通过实轴和它自己的笛卡尔积来描述平面的点之后，集合S*T被称为S和T的笛卡尔积.2.52.竖直线:vertical line 水平线:horizontal line 数对:pairs of numbers 有序对:ordered pairs 纵坐标:ordinate 横坐标:abscissas 一一对应:one-to-one 对应点:corresponding points圆锥曲线:conic sections 非空图形:non vacuous graph 直立圆锥:right circular cone 定值角:constant angle 母线:generating line 双曲线:hyperbola 抛物线:parabola 椭圆:ellipse退化的:degenerate 非退化的:nondegenerate任意的:arbitrarily 相容的:consistent 在几何上:geometrically 二次方程:quadratic equation 判别式:discriminant 行列式:determinant3.(1)In the planar rectangular coordinate system, one can set up aone-to-one correspondence between points and ordered pairs of numbers and also a one-to-one correspondence between conic sections and quadratic equation.(3)The symbol can be used to denote the set of ordered pairs（x，y）such that the ordinate is equal to the cube of the abscissa.（5）According to the values of the discriminate，the non-degenerate graph of Equation （iii） maybe known to be a parabola， a hyperbolaor an ellipse.4.（1）在例1，我们既用了图形，也用了代数的代入法解一个方程组（其中一个方程式二次的，另一个是线性的）。

(完整word版)概率论与数理统计(英文)

3. Random Variables3.1 Definition of Random VariablesIn engineering or scientific problems, we are not only interested in the probability of events, but also interested in some variables depending on sample points. （定义在样本点上的变量）For example, we maybe interested in the life of bulbs produced by a certain company, or the weight of cows in a certain farm, etc. These ideas lead to the definition of random variables.1. random variable definitionHere are some examples.Example 3.1.1 A fair die is tossed. The number X shown is a random variable, it takes values in the set {1,2,6}.Example 3.1.2The life t of a bulb selected at random from bulbs produced by company A is a random variable, it takes values in the interval (0,) .Since the outcomes of a random experiment can not be predicted in advance, the exact value of a random variable can not be predicted before the experiment, we can only discuss the probability that it takes somevalue or the values in some subset of R.2. Distribution function Definition3.1.2 Let X be a random variable on the sample space S . Then the function()()F X P X x =≤. R x ∈is called the distribution function of XNote The distribution function ()F X is defined on real numbers, not on sample space.Example 3.1.3 Let X be the number we get from tossing a fair die. Then the distribution function of X is (Figure 3.1.1)0,1;(),1,1,2,,5;61, 6.if x n F x if n x n n if x <⎧⎪⎪=≤<+=⎨⎪≥⎪⎩Figure 3.1.1 The distribution function in Example 3.1.3 3. PropertiesThe distribution function ()F x of a random variable X has the following properties :(1) ()F x is non-decreasing.SolutionBy definition,1(2000)(2000)10.6321P X F e -≤==-=.(10003000)(3000)(1000)P X P X P X <≤=≤-≤1.50.5(3000)(1000)(1)(1)0.3834F F e e --=-=---= Question ： What are the probabilities (2000)P X < and (2000)P X =? SolutionLet 1X be the total number shown, then the events 1{}X k = contains 1k - sample points, 2,3,4,5k =. Thus11()36k P X k -==, 2,3,4,5k = And512{1}{}k X X k ==-==so 525(1)()18k P X P X k ==-===∑ 13(1)1(1)18P X P X ==-=-=Thus0,1;5()(),11;181, 1.x F x P X x x x <-⎧⎪⎪=≤=-≤<⎨⎪≥⎪⎩Figure 3.1.2 The distribution function in Example 3.1.5The distribution function of random variables is a connection between probability and calculus. By means of distribution function, the main tools in calculus, such as series, integrals are used to solve probability and statistics problems.3.2 Discrete Random Variables 离散型随机变量In this book, we study two kinds of random variables. ,,}n aAssume a discrete random variable X takes values from the set 12{,,,}n X a a a =. Let()n n P X a p ==,1,2,.n = (3.2.1) Then we have 0n p ≥, 1,2,,n = 1n n p=∑.the probability distribution of the discrete random variable X (概率分布)注意随机变量X 的分布所满足的条件(1) P i ≥0(2) P 1+P 2+…+P n =1离散型分布函数And the distribution function of X is given by()()n n a xF x P X x p ≤=≤=∑ (3.2.2)Solutionn=3, p=1/2X p r01/813/823/831/8two-point distribution(两点分布)某学生参加考试得5分的概率是p, X表示他首次得5分的考试次数，求X的分布。

(完整word版)数学建模最佳阵容问题附程序代码

最佳阵容问题摘要本文针对女子体操团体赛中最佳出场阵容的问题.我们通过对赛程规定和已知数据的分析，合理的列出了目标函数和约束条件，特别对第二问的目标函数使用中心极限定理使目标函数简化.建立了以0—1整数规划为核心的数学模型,针对第一问分别使用贪心算法和0-1规划确定全能运动员。

使用lingo对模型进行求解.最后很好的给出了不同情况下出场阵容的最佳方案，由概率知识可容易的求出夺冠概率（0)和得分期望（224。

6）,有90％的把握可战胜平均成绩为222。

7249的对手。

得出下面的具体结果.关键词贪心算法 0-1规划中心极限法一、问题分析每个队至多允许10名运动员参赛，每个项目可以有6名选手参加，每个运动员只能四项全参加或只参加单项比赛这两类中的一类，参加单项比赛的每个运动员至多只能参加三个单项.每个队应有4人参加全能比赛，其余运动员可参加单项比赛。

问题一：1. 每个选手的各单项得分按最悲观估算，排出一个出场阵容,使该队团体总分尽可能高。

2. 每个选手的各单项得分按均值估算，排出一个出场阵容，使该队团体总分尽可能高。

需要先确定4个全能运动员，考虑使用贪心算法确定,然后再使用1个0—1变量进行0-1整型规划，使用lingo求解确定剩余6个人的出场阵容。

但贪心算法只能找到局部最优解,于是考虑使用2个0-1变量也可用lingo进行求解，可以使结果更加优化。

问题二:1.求出一个出场阵容使该队总分不少于236.2分的概率最大,以该阵容出战,其夺冠的前景如何，得分期望值又如何。

2。

按以上阵容出战,它有90％的把握战胜得分为多少的对手。

要使一个出场阵容夺冠的概率最大，也可使用问题一的0—1整型规划，但此时发现目标函数过于复杂，使用lingo无法实现.于是考虑对目标函数进行合理的化简，由于各场比赛之间可以看作是相互独立的事件服从正态分布，因此我们选择使用中心极限定理对目标函数进行简化，之后再使用lingo进行求解即可。

(完整word版)标准测试函数 (1)

几种基准测试函数的简介(1)Sphere 函数211()n i i f x x ==∑ 30,100i n x =≤全局最优点: 0i x =，()0f x =(2) Generalized Schwefel ’s Problem 函数21()(ni i f x x ==-∑ 30,500i n x =≤全局最优点: 420.9687i x =,()12569.5f x =-(3) Rastrigr 函数231()[10cos(2)10]ni i i f x x x π==-+∑ 30, 5.12i n x =≤ 全局最优点： 0i x =，()0f x =（4）Griewank 函数24111()14000n n i i i f x x ===-+∑∏ 30,600i n x =≤ 全局最优点: 0i x =，()0f x =(5）Ackle 函数()e x n x n x f n i i n i i ++⎪⎭⎫ ⎝⎛---=∑∑==202cos 1exp ]12.0exp[20)(1125π 30,32i n x =≤ 全局最优点： 0i x =,()0f x =（6）SchwefelProblem 函数611()i nn i i i f x x x ===+∑∏ 30,10i n x =≤全局最优点： 0i x =,()0f x =(7)Step function 函数⎣⎦()∑=+=ni i x x f 1275.0)( 30,100i n x =≤ 全局最优点： 0i x =，()0f x =这几个基准函数具有不同的特点, 可以充分考察新型算法对不同类型问题的优化性能。

它们可以分为单峰函数（61,f f )，多峰函数(5432,,,f f f f ）.阶梯函数7f ,1f 是较为简单的单峰函数，选择该函数可以考察算法的收敛速度。

6f 是高维单峰函数可以考察算法的收敛速度和收敛精度， 7f 是个不连续的阶梯函数，可以检验算法的有效性。

【最新2018】高一英语书信建议类作文-推荐word版 (16页)

本文部分内容来自网络整理，本司不为其真实性负责，如有异议或侵权请及时联系，本司将立即删除！== 本文为word格式，下载后可方便编辑和修改！ ==高一英语书信建议类作文篇一：如何写好高中英语书信类作文【备战期末】英语书信类作文写作模板书信：【高分套路】但凡应试书信，逃不出三种段落：开头段：四大内容1、问候；2、自我介绍；3、写信背景；为什么会写这封信4、写信目的；写这封信想达到什么目的中间段：具体问题+具体分析；结尾段：客套话；口诀：开门见山说意图咨询建议123不同内容可分段感谢客气不可少期待回信成老套【经典套话】（一）开头段：灵活地去写四种内容：1、问候；How are you doing?How is everything going?1How is life treating you?2、自我介绍；I am LiHua, a 17-year-old boy currently studying in XXX middle school.I am LiHua, who...【李华同志的个人简历】由于我们在考场上的身份几乎年年都是李华，因此我们在这里有必要了解一下李华同志的一些个人情况。

当然，这位同志的个人情况是可以有我们自己人为设置的。

为了给阅卷老师留下一个好印象，我们将李华同志的个人简历概括为：一个人见人爱的好孩子。

hardworkingdiligenthelp my parents to do houseworktake part in CCTV national English speech competitionwon the second prize in CCTV national English speech competition vice monitorvice chairman of the students’ unionworked as a volunteer for the Olympic Gamesworked as a volunteer for the 21st centuryhave many foreign friends and often chat with them happily in starbark.3、写信背景（写信的缘由）I heard that ...My teacher told me...I am informed that...I learned that...我得知...I read in your newspaper/ micro-blog /website that...You said in your last letter that...4、写信目的；Now, I am writing to do sth.Now, I am writing this letter to do sth.Now, I am writing these few lines to do sth.2【七种最常见书信的―写信目的‖部分的最佳写法】自荐信：Now, I am writing to apply for the job/position.感谢信 :Now, I am writing to show/ express my heartfelt gratitude to you. 邀请信：Now, I am writing to invite you to join/enjoy/suffer/experience the....(as our guest/ judge/ instructor).建议信：Now, I am writing to give you a hand.求助信：Now, I am writing to ask you to give me a hand/ do me a favor. 道歉信 :Now, I am writing to show/ express my heartfelt apology to you. 告知信:Now, I am writing to tell you about the details.（二）中间段：具体问题（主题句）+具体分析（拓展句）【六种最常见书信的―中间段‖最佳写法】自荐信：写自己的优势写法一：There are four main reasons why I am fit for the position/job. To begin with, ... Moreover,... What's more,... Finally,...写法二：I have three main advantages. First andforemost,...Additonally,st but not least,...写法三：I have the confidence that I can handle the job.Firstly,...Secondly, ...Thirdly,...3感谢信：写对方为你所做的事Every time I （看照片、看录像、看那段时间的日记、回忆那段经历）, I just can't help thinking of you/ what you have done for me. It was so kind of you to （对方做的第一件事）. Besides, you （对方做的第二件事）, which really surprised me. Actually, I shall always remember （对方做的第三件事）, considering that,（第三件事情的意义）. Nothing will be able to erase our wonderful memories, and I will cherish them forever.邀请信：描述具体的活动内容，如活动主题、意义、地点、时间、参加者和其它事项；Here are some details for the activities. To begin with, （活动主题或活动目的，如：the theme of the contest is "human and the nature", which is undoubtedly not only entertaining but also instructive. ）Moreover, （活动的地点和时间，如it will be in room 501 from 2:00 to 5:00 on the afternoon of June 15th.） What's more,（活动人员，如：ten outstanding competitors will take part in the contest.）Finally,（其他信息，如：if you need any further information, please call me at 44876655. ）建议信：写给对方的具体建议写法一：There are several simple suggestions for you. To begin with, ... Moreover,... What's more,... Finally,...写法二：Immediate and effective measures must be put into practice. First and foremost,...Additonally,st but not least,...4写法三：The following suggestions carried out, things would probably become much better. Firstly,... Secondly,... Thirdly,...求助信：写具体需要帮助的事项Hopefully you would be so kind as to give me some suggestions/help on the following problems. To begin with,（困难一）,which has annoyed me for quite a long time. Moreover,（困难二）, for personally I lack the very basic experience on this matter. Finally,...l 常用句型：（做某事有困难）1、I have trouble in doing sth.2、I find it extremely hard for me to do sth.3、Doing sth is another terrible headache for me.l 常见困难：【生活方面】与人相处 get along well with my classmates/ the new teacher / my parents.（和我的同学/新老师/父母相处）把握时间 arrange and make good use of my everyday time for valuable things. （安排和利用每天的时间去做有意义的事情）明确目标 know the purpose of my life and the destination of my future in order to passionately live a purpose-driven life everyday. （知道我生命的目的和未来的目标，以便每天充满激情地过着―目标驱动‖的生活）【学习方面】不懂语法 have trouble in mastering the advanced grammar rules and put them into use in my speaking and writing.5篇二：高中英语作文 --建议信建议信(1)-----阐释原因；提出建议类请你代表你班同学给校长写一封信，反映一下你校食堂的几点问题，以引起学校重视，并针对问题提出两条合理建议。

(完整word版)编程经典问题

编程经典问题1.“兔子繁殖问题"，已知一对兔子，每个月可以生一对兔子，而小兔过一个月后也可生一对小兔。

即兔子的对数是:第一个月1对，第二个月2对,第三个月3对，第四个月5对，……，假设兔子的生育期是12个月,并且不死，问一年后,这对兔子有多少对活着的后代？(P45）(斐波尔系数）2.判断素数。

(P55 P68)3.猴子摘了一堆桃子，第一天吃了一半,觉得不过瘾又吃了一个；第二天吃了剩下的一半零一个；以后每天如此，到第十天,猴子一看只剩下一个了。

问最初由多少个桃子？4.求两个数的最大公约数。

（P49）5.求两个数的最小公倍数。

6.验证歌尔巴德猜想：任意一个充分大的偶数n（n 〉= 4),都可以用两个素数之和表示.（P57 P98）7.逻辑判断题：警官在老王被害现场发现ABCD四名犯罪嫌疑人,讯问中A说“我没有杀人"，B说“C是凶手”，C说“杀人者肯定是D ",D 说“C在冤枉好人”。

现已知：四人中有三人说的是真话，一人说的是假话，四名犯罪嫌疑人中有且只有一人是凶手。

请编写程序确定四个嫌疑人中哪个是凶手?(P57)8.宾馆里有100个房间，从1~100编了号.第一个服务员把所有的房间门都打开了，第二个服务员把所有编号是2的倍数的房间“相反处理”，第三个服务员把所有编号是3的倍数的房间再作“相反处理"，……,以后每个服务员都是如此。

当第三个服务员把所有编号是3的倍数的房间再作“相反处理”，……,以后每个服务员都是如此。

当第100个服务员来过后，哪几扇门是打开的.（所谓“相反处理"是：原来开着的门关上，原来关上的门打开）(P65)9.约瑟夫问题:n个人（n >= 100）围成一圈，从第一个人开始报数，数到m的人出圈，再由下一个人重新从1开始报数,数到m的人出圈；……直到所有人出圈.输出依次出出圈的人的编号。

10.围绕着山顶有10个洞，一只狐狸和一只兔子各住一个洞.狐狸总想吃掉兔子.一天兔子对狐狸说：“你想吃我有一个条件，先把洞从1~10编上号,你从10号洞出发,先到1号洞找我；第二次隔一个洞找我，第三次隔2个洞找我，以后依此类推,次数不限.若能找到我,你就可以饱餐一顿.不过在没有找到我以前不能停下来."狐狸满口答应就开始找了，它从早到晚找了1000次洞，累得昏了过去也没有找到兔子。

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Unfortunately nature is i EncyclopediaMathematics-Topology an Algebraic geometry is one of the m EnglishMathematics Ever wonder why cats land on their EnglishMathematics Numerical Methods provides a clear EnglishMathematics A website''s ranking on Google can EnglishThis comprehensive textbook is intended for a two-semester sequence in analysis. The f Static & DynaOptical networks epitomize complex communication systems, and they comprise tThis work is a concise introduction to spectral theory of Hilbert space operators. Its Math This volume contains research and EnglishMath This book is the first to be devot EnglishMath This book studies generalized Dona EnglishMATHEMATICS / General EnglishMath This volume is a collection of pap EnglishMath The volume contains the proceeding EnglishMath In the last 200 years, harmonic an EnglishMath The book is an innovative modern e EnglishMath This book considers evolution equa EnglishMath This book is a comprehensive treat EnglishThe self-taught mathematician Hua Loo-Keng (1910–1985) spent most of his wor The CambridgeThe aim of this graduate-level text is to equip the reader with the basic too Cambridge StuThis book deals with equations that have played a central role in the interpl Cambridge StuMathematics-Topology an This book was first published in 2EnglishThis is a rigorous introduction to real analysis for undergraduate students, Australian MaOriginally published in 1957, this book was written to provide physicists and engineerOriginally published in 1931, this volume was created to mark the centenary of James CThe new edition of Calculus continues to bring together the best of both new and tradiAfter a brief review of first-order differential equations, this book focuses on seconThis textbook by respected authors helps students foster computational skills and intuThis text explores the beauty of topology and homotopy theory in a direct, engaging, aPapers based on selected lectures given at the Current Development Mathematics Confere Mathematics At the crossroads of mathematics, EnglishElectrical & Computer E Sponsor: System Dynamics SocietyEnglishMathematics This book introduces and exchanges EnglishMathematics STATISTICAL ALGORITHMS integrates EnglishMathematics ALGEBRAIC TOPOLOGY: An Introductio EnglishMath The goal of geometric numerical in EnglishMathematics Eigenvalues and eigenvectors of ma EnglishMathematics This is the first of two volumes o EnglishMathematics The text is intended for students EnglishMathematics This textbook is addressed to the EnglishMathematics In recent years, technological pro EnglishMathematics This monograph aims to give a self EnglishMathematics This is the second of two volumes EnglishPartial Differential Eq This book contains lecture notes o EnglishThe subject theory is important in finance, economics, investment strategies, Atlantis StudThis volume consists of research papers and expository survey articles presented by thThis book provides a broad introduction to the generalized inverses, Moore–Penrose inThe Mathematical Structure of Language Patterns provides a comprehensive comp World ScientiMathematics-Geometry & This invaluable book features bibl EnglishMathematics-Geometry & This invaluable book features bibl EnglishWhen not immersed in science, he relaxes by searching for Wagner's leitmotifs World ScientiSince the first edition of this book, the literature on fitted mesh methods fundergraduate and beginning graduate students taking a course on mathematical physics taught out of mion of real analysis concepts and principles, presenting a broad range of topics in a clear and concisuids, this text for graduates and researchers in applied mathematics develops the most recent ideas and concepts in the ly nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, orience in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts hey comprise the Internet’s infrastructural backbone. The first of its kind, this book develops the mathematical frame rt space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering ost of his working life in China and suffered at first hand the turbulence of twentieth-century Chinese politics. His i the basic tools and techniques needed for research in various areas of geometric analysis. Throughout, the main theme in the interplay between partial differential equations and probability theory. Most of this material has been treated ate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any precon physicists and engineers with a means of solving partial differential equations subject to boundary conditions. The tex he centenary of James Clerk Maxwell's birth. Comprised of ten essays dealing with various aspects of Maxwell's life and t of both new and traditional curricula in an effort to meet the needs of even more instructors teaching calculus. The s book focuses on second-order equations with constant coefficients that derive their general solution using only resul ational skills and intuitive understanding with a careful balance of theory, applications, historical development and o n a direct, engaging, and accessible manner while illustrating the power of the theory through many, often surprising, ent Mathematics Conference, held in November 2010 at Harvard University.nt strategies, health sciences, environment, industrial engineering, etc.rticles presented by the invited speakers of the conference on “Harmony of Gröbner Bases and the Modern Industrial Soc rses, Moore–Penrose inverses, Drazin inverses and T–S outer generalized inverses and their perturbation analyses in t rehensive compilation, description, and discussion of recent advancements on quantitative linguistics carried out from r's leitmotifs, musing over Kandinsky's chaos, and contemplating Wittgenstein's inner thoughts.This penultimate volumemesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes haof math departments. The text presents some of the most important topics and methods of mathematicaloncise manner. The book is excellent at balancing theory and applications with a wealth of examples aas and concepts in the theory of compressible fluids, in particular, the question of existence for optimal values of th psoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computationalhe tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear the mathematical framework needed from a control perspective to tackle various game-theoretical problems in optical net mary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics hinese politics. His influence has been credited with inspiring generations of mathematicians, while his papers on numb ghout, the main theme is to present the interaction of partial differential equations and differential geometry. More s rial has been treated elsewhere, but it is rarely presented in a manner that makes it easy to understand for people who book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete order ry conditions. The text gives a systematic and unified approach to a wide class of problems, based on the fact that the of Maxwell's life and achievements, the text includes contributions from the following figures: J. J. Thomson; Max Pla eaching calculus. The author team's extensive experience teaching from both traditional and innovative books and their ution using only results described previously. Higher-order equations are provided since the patterns are more readily ical development and optional materials.ny, often surprising, applications. It offers a comprehensive presentation that uses a combination of rigorous argument Modern Industrial Society”. Topics include computational commutative algebra, algebraic statistics, algorithms of D-m urbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operatotics carried out from the perspective of complex systems. It provides an overview of the emergence and construction of is penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Pears, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential etical physics. The premise is to study in detail the three most important partial differential equatioles and exercises. The authors take a progressive approach of skill building to help students learn toor optimal values of the adiabatic exponent, which up to now has been unsolved.e kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harm e presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding a problems in optical networks. In doing so, it aims to help design control algorithms that optimally allocate the resour The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreahile his papers on number theory are regarded as 'virtually an index to the major activities in that subject during the ential geometry. More specifically, emphasis is placed on how the behavior of the solutions of a PDE is affected by the derstand for people whose background is probability theory. Many results are given proofs designed for readers with lim nts of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonom ed on the fact that the solution may be viewed as a point in function-space, this point being the intersection of two l J. J. Thomson; Max Planck; Albert Einstein; Joseph Larmor; James Jeans; William Garnett; Ambrose Fleming; Oliver Lodge vative books and their expertise in developing innovative problems put them in an unique position to make this new curr tterns are more readily grasped by students. Stability and fourth order equations are also discussed since these topicon of rigorous arguments and extensive illustrations to facilitate an understanding of the material. The author covers tics, algorithms of D-modules and combinatorics. This volume also provides current trends on Gröbner bases and will sti perator theory, operator algebras, global analysis and approximation theory and so on.S table Perturbations of Operatorsce and construction of linguistic structures, addressing those concepts that have become the key ideas of complexity: o al cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules,partial differential equations. In the revised version of this book, the reader will find an introduction to the basicuations in the field - the heat equation, the wave equation, and Laplace’s equation. The most commonrn to absorb the abstract. Real world applications, probability theory, harmonic analysis, and dynamied to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains cla ial in understanding analysis. From Calculus to Analysis prepares readers for their first analysis course—important be ly allocate the resources of these networks. With its fresh problem-solving approach, 'Game Theory for Control of O ures often left untreated. Spectral Theory of Operators on Hilbert Space is addressed to an interdisciplinary ahat subject during the first half of the twentieth century.' Introduction to Higher Mathematics is based on the lecture PDE is affected by the geometry of the underlying manifold and vice versa. For efficiency the author mainly restricts h d for readers with limited expertise in analysis. The author covers the theory of linear, second order partial differen atment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a ge intersection of two linear subspaces orthogonal to one another. Using this method the solution is located on a hyperci Fleming; Oliver Lodge; Richard Glazebrook; Horace Lamb. This book will be of value to anyone with an interest in Maxwe to make this new curriculum meaningful for those going into mathematics and those going into the sciences and engineer ssed since these topics typically appear in further study for engineering and science majors. In addition to applicatial. The author covers basic topology, ranging from the axioms of topology to proofs of important theorems. He also discK ey Features: • Compre ner bases and will stimulate further development of many research areas surrounding Gröbner bases.urbations of Operators and Related Topics is self-contained and unified in presentation. It may be used as an advanced ideas of complexity: order and entropy, information, correlation, self-organization, network patterns, evolution, and st only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from aroduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations.ommon techniques of solving such equations are developed in this book, including Green’s functions, tynamical systems theory are included, offering considerable flexibility in the choice of material to c oblems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory is course—important because many undergraduate programs traditionally require such a course. Undergraduates and some a Theory for Control of Optical Networks' is a unique resource for researchers, practitioners, and graduate students in a an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. Itis based on the lectures given by Hua at the University of Science and Technology of China from 1958. The course reflec thor mainly restricts himself to the linear theory and only a rudimentary background in Riemannian geometry and partial order partial differential equations of parabolic and elliptic type. Many of the techniques have antecedents in proba f the book provide a gentle, example-based introduction to metric spaces with an application to differential equations is located on a hypercircle in function-space, and the approximation is improved by reducing the radius of the hypercir th an interest in Maxwell and his key role in the development of physics and mathematics.e sciences and engineering. This new text exhibits the same strengths from earlier editions including an emphasis on n addition to applications to engineering systems, applications from the biological and life sciences are emphasized. theorems. He also discusses the classification of compact, connected manifolds, ambient isotopy, and knots, which leadK ey Features:• A guid • Comprehensive treatment of Gröbner bases • Articles by leading figures in the mathematics worlds.be used as an advanced textbook by graduate students. It is also suitable for researchers as a reference. The proofs ofT he focus of quantitative linguistics is to detect, characterize, and explain the patter terns, evolution, and strategy.174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 2differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perns, the Fourier transform, and the Laplace transform, which all have applications in mathematics andto cover in the classroom. The accessible exposition not only helps students master real analysis, b functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an inte ergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom graduate students in applied mathematics and systems/control engineering, as well as those in electrical and computer e ering, and physics. It will also be useful to working mathematicians using spectral theory of Hilbert space operators,958. The course reflects Hua's instinctive technique, using the simplest tools to tackle even the most difficult proble n geometry and partial differential equations is assumed. Originating from the author's own lectures, this book is an i e antecedents in probability theory, although the book also covers a few purely analytic techniques. In particular, a c ifferential equations on the real line. The author's exposition is concise and to the point, helping students focus on radius of the hypercircle. The complexities of calculation are illuminated throughout by simple, intuitive geometricalcluding an emphasis on modeling and a flexible approach to technology.nces are emphasized. Ecology and population dynamics are featured since they involve both linear and nonlinear equatio and knots, which leads to coverage of homotopy theory.• A guidebook for graduate students • The reader can see a panoramic view of Gröbner baseshematics worldference. The proofs of statements and explanations in the book are detailed enough that interested readers can study it and explain the patterns of language by means of mathematical tools. The last two decades have witnessed a sharp increa-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence.Another surpnts for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwiseand physics far beyond solving the above equations. The book’s focus is on both the equations and tis, but also makes the book useful as a reference., which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally rience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.ectrical and computer engineering.lbert space operators, as well as for scientists wishing to apply spectral theory to their field. e most difficult problems, and contains both pure and applied mathematics, emphasising the interdependent relationships ures, this book is an ideal introduction for graduate students, as well as a useful reference for experts in the field. ues. In particular, a chapter is devoted to the DeGiorgi-Moser-Nash estimates and the concluding chapter gives an intro ping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to th intuitive geometrical pictures. This book will be of value to anyone with an interest in solutions to boundary value pr and nonlinear equations, and these topics form one application thread that weaves through the chapters. Diffusion ofK ey Features: • The stable perturbation theory of generalized inverses, Drazin inv ed readers can study it by themselves.itnessed a sharp increase in the interest of physicists and applied mathematicians on language, and it is not surprisinquivalence.Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the supesured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but thend their methods of solution. Ordinary differential equations and PDEs are solved including Bessel Fuolve formally boundary value problems. End-of-chapter problems complement the theory and test the rea ependent relationships between different branches of the discipline.experts in the field.chapter gives an introduction to the theory of pseudodifferential operators and their application to hypoellipticity, i y of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced st ns to boundary value problems in mathematical physics.hapters. Diffusion of material, heat, and mechanical and electrical oscillators are also important in biological and e d inverses, Drazin inverses and index of a Fredholm element relative to a homomorphismare are of unique interest in thind it is not surprising that this explosion was parallel to the expansion of the interest in complex systems. This book string called the super string S, which contains all random bit strings of finite length as sub-strings. As an illustra。

(完整版)matlab上机题目一

上机一1、（1（2）查询所有人的成绩。

2、已知：A=[27,24,0,-1;23,35,1,14;e 4,-8,13,20;10,12,19,21;11,18,ln2,0]，求：（1）求A 中第4、5、2行与第2、4、1列组成的C 阵，并将C 中第2行元素全改成8，得到D 阵；（2）创建与A 同维的G 阵，使C 阵左右翻转后位于G 中第2行至第4行、第2列至第4列位置，且G 中第1行第1列元素为1，其余元素为0。

（3）求A 阵除以3的余数阵H 。

3、已知：A=[5,17,-2,3;-1,0,21,11;14,9,-10,8]，B=[2,5,8,-1;12,-2,7,8;11,13,16,4] 求：（1）将A 除以B 阵的对应元素，并将结果朝负无穷大方向取整。

（2）求A./B ， B.\A ，A.*B 和A*B ’的值。

（3）求2*ones(3,4)-eye(3,4)|A-B>B&B-8的值.4、要求在闭区间[0，2π ]上产生50个等距采样的一维数组。

试用两种不同的指令实现。

5、对矩阵，⎥⎦⎤⎢⎣⎡=4321A 问如下MATLAB 指令：)(),(),5.0(^),5.0(.^A sqrtm A sqrt A A 所得的结果相同吗？他们中的哪个结果为复数矩阵？ 6、说出MATLAB 指令A （3，1，2，：）=1：4所产生数组的维数、大小和长度；然后对A 进行降维处理；最后指出所有非零元素的“全下标”位置。

7、现有五个数组： (2×3)的实数数组A ； (2×3)的复数数组B ； (2×3)的字符串数组C ； (2×3)的异质（元胞）数组D ； (2×3)的结构（构架）数组E 。

问，它们各占多少字节？8、写出使以下这段文字成为字符串的MATLAB 程序。

注意保持这段文字的格式。

在英式用法中，引号通常是单引号，如‘Fire!’。

数学专业英语第五讲精读课文2.9-2.12

5 Mathematical English
Or a radioactive substance may be disintegrating at a known rate and we may be required to determine the amount of material present after a given time.
2.9 微分方程简介 Introduction to Differential Equations
New Words & Expressions:
approximate evaluation 近似估计 initial 初始的
disintegrate 解体，衰变
differentiable 可微的 exponential 指数的数
initial value problem 初值问题
initial condition 初始条件
mathematical physics 数学物理
boundary condition 边界条件
2 Mathematical English
Key points:
Introduction to Differential Equations
integrate 求积分
polynomial 多项式 rational function 有理函
1
Mathematical English
2.9 Introduction to Differential Equations
New Words & Expressions:
differential equation 微分方程 partial differential equation 偏微分方程 inverse trigonometric function 反三角函数 approximate evaluation 近似估计

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பைடு நூலகம்
end of the fundraiser, they had exceeded their goal by $2,100. How much did they raise? a. $7,400 b. $13,600 c. $10,600 d. $11,600
14. Mount Everest is 29,028 ft high. Mount Kilimanjaro is 19,340 ft high.
30. Jennifer ﬂipped a coin three times and got heads each time. What is the
probability that she gets heads on the next ﬂip? a. 1 b. 116 c. 1 2 d. 0
6
Team-LRN
4
Team-LRN
501 Math Word Problems 20. Shane rolls a die numbered 1 through 6. What is the probability Shane
rolls a 5? a. 5 6 b. c. d.
1 6 1 5 1 2
21. Susan traveled 114 miles in 2 hours. If she keeps going at the same rate,
miles. What was the plane’s average speed? a. 545 mph b. 615 mph c. 515 mph d. 612 mph
23. Larry purchased 3 pairs of pants for $24 each and 5 shirts for $18 each.
square? a. 8 cm b. 16 cm c. 32 cm d. 24 cm
16. Mrs. Farrell’s class has 26 students. Only 21 were present on Monday.
How many were absent? a. 15 b. 5 c. 4 d. 16
cans each. How many boxes did they need? a. 280 b. 10 c. 8 d. 5
5. Joey participated in a dance-a-thon. His team started dancing at 10 A.M. on
Friday and stopped at 6 P.M. on Saturday. How many hours did Joey’s team dance? a. 52 b. 56 c. 30 d. 32
29. Sherman took his pulse for 10 seconds and counted 11 beats. What is
Sherman’s pulse rate in beats per minute? a. 210 beats per minute b. 110 beats per minute c. 66 beats per minute d. 84 beats per minute
28. The total ticket sales for a soccer game were $1,260; 210 tickets were
purchased. If all the tickets are the same price, what was the cost of a ticket? a. $6.00 b. $3.50 c. $10.00 d. $7.50
19. Jeff left Hartford at 2:15 P.M. and arrived in Boston at 4:45 P.M. How long
did the drive take him? a. 2.5 hours b. 2.3 hours c. 3.25 hours d. 2.75 hours
a. b. c. d.
8 4 12 36
33. Twelve coworkers go out for lunch together and order three pizzas. Each
25. Raul’s bedroom is 4 yards long. How many inches long is the bedroom?
5
Team-LRN
501 Math Word Problems 26. Jeff burns 500 calories per hour bicycling. How long will he have to ride to
6. Which expression has an answer of 18?
a. b. c. d.
2×5+4 2 × (4 + 5) 5 × (2 + 4) 4×2+5
7. Callie’s grandmother pledged $0.50 for every mile Callie walked in her
walk-a-thon. Callie walked 9 miles. How much does her grandmother owe? a. $4.50 b. $18.00 c. $5.00 d. $9.00
8. What is the square root of 36?
a. b. c. d.
501 Math Word Problems 31. Jody’s English quiz scores are 56, 93, 72, 89, and 87. What is the median of
her scores? a. 72 b. 87 c. 56 d. 85.6
32. What is the greatest common factor of 24 and 64?
2. Oscar sold 2 glasses of milk for every 5 sodas he sold. If he sold 10
glasses of milk, how many sodas did he sell? a. 45 b. 20 c. 25 d. 10
Team-LRN
501 Math Word Problems 3. Justin earned scores of 85, 92, and 95 on his science tests. What does he need
17. Lucy’s youth group raised $1,569 for charity. They decided to split the
money evenly among 3 charities. How much will each charity receive? a. $784.50 b. $423.00 c. $523.00 d. $341.00
to earn on his next science test to have an average (arithmetic mean) of 93%? a. 93 b. 100 c. 85 d. 96
4. Brad’s class collected 320 cans of food. They boxed them in boxes of 40
12 72 18 6
2
Team-LRN
501 Math Word Problems 9. Mr. Brown plowed 6 acres in 1 hour. At this rate, how long will it take him
to plow 21 acres? a. 3 hours b. 4 hours c. 3.5 hours d. 4.75 hours
How much did Larry spend? a. $42 b. $72 c. $162 d. $186
24. How many square centimeters are in one square meter?
a. b. c. d. a. b. c. d.
100 sq cm 10,000 sq cm 144 sq cm 100,000 sq cm 144 inches 48 inches 400 inches 4,000 inches
1. Bonnie has twice as many cousins as Robert. George has 5 cousins,
which is 11 less than Bonnie has. How many cousins does Robert have? a. 17 b. 21 c. 4 d. 8
How much taller is Mount Everest? a. 9,688 feet b. 10,328 feet c. 11,347 feet d. 6,288 feet
3
Team-LRN
501 Math Word Problems 15. The area of a square is 64 cm2. What is the length of one side of the
18. Jason made 10 two-point baskets and 2 three-point baskets in Friday’s
basketball game. He did not score any other points. How many points did he score? a. 22 b. 12 c. 24 d. 26
temperature in Los Angeles, California was 63°F. What is the difference in the two low temperatures? a. 59° b. 67° c. 57° d. 14°