数学专业英语课后答案(1)
数学专业英语
数学专业英语课后答案2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
数学专业英语课后答案（1）
数学专业英语课后答案（1）2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place 汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
数学专业英语课后答案
数学专业英语课后答案1、He kept walking up and down, which was a sure（）that he was very worried. [单选题] *A. sign(正确答案)B. characterC. natureD. end2、20．Jerry is hard-working. It’s not ______ that he can pass the exam easily. [单选题] * A．surpriseB．surprising (正确答案)C．surprisedD．surprises3、--What’s the weather like today?--It’s _______. [单选题] *A. rainB. windy(正确答案)C. sunD. wind4、Many of my classmates are working _______volunteers. [单选题] *A. as(正确答案)B. toC. atD. like5、Mary is interested ______ hiking. [单选题] *A. onB. byC. in(正确答案)D. at6、We need a _______ when we travel around a new place. [单选题] *A. guide(正确答案)B. touristC. painterD. teacher7、While they were in discussion, their manager came in by chance. [单选题] *A. 抓住时机C. 碰巧(正确答案)D. 及时8、Our campus is _____ big that we need a bike to make it. [单选题] *A. veryB. so(正确答案)C. suchD. much9、57．Next week will be Lisa's birthday. I will send her a birthday present ________ post. [单选题] *A．withB．forC．by(正确答案)D．in10、The manager demanded that all employees _____ on time. [单选题] *A. be(正确答案)B. areC. to be11、He has two sisters but I have not _____. [单选题] *A. noneB. someC. onesD. any(正确答案)12、______! It’s not the end of the world. Let’s try it again.（）[单选题] *A. Put upB. Set upC. Cheer up(正确答案)D. Pick up13、My brother usually _______ his room after school. But now he _______ soccer. [单选题] *A. cleans; playsB. cleaning; playingC. cleans; is playing(正确答案)D. cleans; is playing the14、The museum is _______ in the northeast of Changsha. [单选题] *A. sitB. located(正确答案)C. liesD. stand15、______ my great joy, I met an old friend I haven' t seen for years ______ my way ______ town. [单选题] *A. To, in, forB. To, on, to(正确答案)C. With, in, toD. For, in, for16、In the closet（）a pair of trousers his parents bought for his birthday. [单选题] *A. lyingB. lies(正确答案)c. lieD. is lain17、44．—Hi, Lucy. You ________ very beautiful in the new dress today.—Thank you very much. [单选题] *A．look(正确答案)B．watchC．look atD．see18、They all choose me ______ our class monitor.（）[单选题] *A. as(正确答案)B. inC. withD. on19、My mother’s birthday is coming. I want to buy a new shirt ______ her.（）[单选题] *A. atB. for(正确答案)C. toD. with20、--Could you please tell me _______ to get to the nearest supermarket?--Sorry, I am a stranger here. [单选题] *A. whatB. how(正确答案)C. whenD. why21、?I am good at schoolwork. I often help my classmates _______ English. [单选题] *A. atB. toC. inD. with(正确答案)22、He was very excited to read the news _____ Mo Yan had won the Nobel Prize for literature [单选题] *A. whichB. whatC. howD. that(正确答案)23、Becky is having a great time ______ her aunt in Shanghai. （）[单选题] *A. to visitB. visitedC. visitsD. visiting(正确答案)24、In the future, people ______ a new kind of clothes that will be warm when they are cold, and cool when they’re hot.（）[单选题] *A. wearB. woreC. are wearingD. will wear(正确答案)25、This message is _______. We are all _______ at it. [单选题] *A. surprising; surprisingB. surprised; surprisedC. surprising; surprised(正确答案)D. surprised; surprising26、Your homework must_______ tomorrow. [单选题] *A. hand inB. is handed inC. hands inD. be handed in(正确答案)27、Since the war their country has taken many important steps to improve its economic situation. [单选题] *A. 制定B. 提出C. 讨论D. 采取(正确答案)28、How _______ Grace grows! She’s almost as tall as her mother now. [单选题] *A. cuteB. strongC. fast(正确答案)D. clever29、_____ is not known yet. [单选题] *A. Although he is serious about itB. No matter how we will do the taskC. Whether we will go outing or not(正确答案)D. Unless they come to see us30、You cannot see the doctor _____ you have made an appointment with him. [单选题] *A. exceptB.evenC. howeverD.unless(正确答案)。
高等数学双语教材答案
高等数学双语教材答案Chapter 1: Limits and ContinuitySection 1: Introduction to Limits and ContinuityThe concept of limits and continuity is fundamental in higher mathematics. In this section, we will introduce the basic definitions and properties associated with limits and continuity.1.1 Definitions of LimitsIn order to understand limits, we need to define what it means for a function to approach a particular value. Let f(x) be a function defined on an open interval containing c, except possibly at c. We say that the limit of f(x) as x approaches c is L, denoted bylim (x→c) f(x) = L, if for every ε > 0, there exists a δ > 0 such that |f(x) - L| < ε whenever 0 < |x - c| < δ.1.2 Basic Limit LawsOnce we have a clear understanding of limits, we can explore some basic laws that govern their behavior. These laws include the sum law, constant multiple law, product law, quotient law, and the power law.1.3 ContinuityA function f(x) is said to be continuous at a point c if three conditions are met: (1) f(c) is defined, (2) the limit of f(x) as x approaches c exists, and (3) the limit of f(x) as x approaches c is equal to f(c). We can also discuss continuity on an interval or at infinity.Chapter 2: DifferentiationSection 1: Introduction to DifferentiationDifferentiation is an important concept in calculus that allows us to find the rate at which a function is changing at any given point. In this section, we will introduce the concept of differentiation and its applications.2.1 Derivative DefinitionThe derivative of a function f(x) at a point c is defined as the limit of the difference quotient as h approaches 0. Mathematically, this can be written as f'(c) = lim (h→0) [(f(c + h) - f(c))/h].2.2 Differentiation RulesThere are several rules that allow us to find the derivative of a function quickly. These rules include the constant rule, power rule, sum rule, difference rule, product rule, quotient rule, and chain rule.2.3 Applications of DifferentiationDifferentiation has many applications in various fields, such as physics, economics, and engineering. It can be used to find maximum and minimum values, determine rates of change, and solve optimization problems.Chapter 3: IntegrationSection 1: Introduction to IntegrationIntegration is the reverse process of differentiation. It enables us to find the area under a curve and solve various mathematical problems. In this section, we will introduce the concept of integration and its applications.3.1 Indefinite IntegralsThe indefinite integral of a function f(x) is the collection of all antiderivatives of f(x). It is denoted by ∫ f(x) dx and represents a family of functions rather than a single value.3.2 Integration TechniquesThere are various techniques for finding antiderivatives and evaluating definite integrals. These techniques include basic integration rules, substitution, integration by parts, and trigonometric substitution.3.3 Applications of IntegrationIntegration has numerous applications, such as finding the area between two curves, calculating the length of curves, determining volumes of solids, and solving differential equations.ConclusionIn conclusion, the study of high-level mathematics, particularly limits, continuity, differentiation, and integration, is crucial for a comprehensive understanding of advanced mathematical concepts. This article has provided a brief overview of these topics, highlighting their definitions, properties, and applications. By mastering these concepts, students can develop strong problem-solving skills and apply them in various academic and real-world scenarios.。
数学建模英文版习题与答案
数学建模第一章 Modeling Change1.Difference equation （差分方程） Example 1. A Savings CertificateSuppose that you deposited $1,000 into your saving account initially. The interest is paid each month at a rate of 1% per month, then the value of your account will be as follows ：Letn=number of months,n a =the value of the account after n monthsThen we have ,01.01n n n n a a a a =-=∆+ So the difference equation is n n n a a a 01.01+=+ We have the dynamical system(动态系统) model{1000,.......2,1,001.10,1===+a n a a n n*Suppose you withdraw(提取) $50 each month,then the change is5001.01-=-=∆+n n n n a a a aTherefore the model becomes{1000....2,1,0,5001.101==-=+a n a a n n1.2动态方程,1b ra a n n +=+r and b are constants.(1≠r )An equilibrium value(均衡值)（or fixed point(不动点)）of a dynamical system )(1n n a f a =+is a solution a to equation a=f(a),which means that,if a a =0,then all a a n = Thus in this case the equilibrium value is rb a -=1 1st month $1,000 0a 3a 2a 1a 4th month $1,030.30 3rd month $1,020.10 2nd month $1,010Nowbra a b ra a n n +=+=+1Therefore )(1a a r a a n n -=-+Set a a b n n -=, then n n rb b =+1,thus 0b r b n n =,i.e, )(0a a r a a n n -=- hence rbr b a r a n n -+--=1)1(0 In practice, we may write rbc r a n n -+*=1 write C to be determined by 0a 1.3差分方程组【求均衡点 实际意义 说明参数】 Example 1. A Car Rental CompanyA car rental company operates in Orlando and Tampa. A traveler will rent a car in one city and return the car in either of the cities. The company wants to know if there are sufficiently many cars in each city.Let On=number of.cars in Orlando after n days Tn=number of cars in Tampa after n days Then the model is{nn n n n n T O T T O O 7.04.03.06.011+=+=++ To find the equilibrium value:{TO T T O O 7.04.03.06.0+=+=So 4O=3T ，i.e.,if 730=O Total cars and 740=T Total cars,then n O and n T will be unchanged.第二章 The Modeling Process, Proportionality, and Geometric Similarity(几何相似)【写一定的假设（Assumption ）要明确合理】 We already know kx y x y =⇔∝,k is constant.We may also consider .,,ln ,2etc e y x y x y x ∝∝∝Also y=mx+b is a usual assumption,i.e.,x b y ∝-.Geometrically, it is a straight line,which is easy to spot. Example 2. Modeling a Bass （欧洲鲈鱼） Fishing DerbyA fishing club will hold a fishing contest. In order to be environment friendly, the fish will be released immediately after caught. How to determine the weight of a fish?Problem Identification: Determine the weight of a fish in terms of some easily measurable dimensions(度量)Assumption: All fishes are geometrically similar, and the density of a bass is constant.Thus weight W ∝volume V ∝length 3L .that is,3kL W =Model Refinement: We only assume that the cross sectional areas are similar and use another dimension – girth g.Assume effective V ≈ length ⨯average cross sectional areaNow effective length ∝L average cross sectional area ∝2gThus ∝W L 2g ,i.e.,2kLg W =第三章 Least-Squares Criterion:Minimize the sum of the squares of deviations.(最小二乘法)【怎样画散点图 画趋势线 怎样运用最小二乘法公式】 Fitting a Straight LineGiven a collection of data(i i y x ,),i=1,.....m,and a linear model y=ax+b Recall the deviation of the model y=f(x) at (i i y x ,) is )(i i x f y - Thus the least-squares criterion is to minimize 2121)())((∑∑==--=-=mi iimi iib ax y x f y S79LCrossTherefore we need to solve for a and b from0)1()(20)()(211=---=∂∂=---=∂∂∑∑==mi i i i mi i i b ax y b S x b ax y a S That is∑∑∑∑∑=+=+ii i i i i y mb a x y x b x a x )()()(2We get 最小二乘法公式（其中m 为数据个数）)(,)()(,)(22222截距斜率Intercept x x m x y x y x b Slope x x m y x y x m a i iii i i i i i i i i i ∑∑∑∑∑∑∑∑∑∑∑--=--=第四章 Experimental Modeling 【给出一个散点图再给出数据然后怎样变化可让散点图直一点】Thus if the original curve is （1）concave up:（凸）Then usey or lny to squeeze the tail downward,OR use 2x or 3x to stretch the tail to theright(2) concave down:(凹)：Then use 2y or 3y to stretch the tail up-ward,OR usex or lnx to squeeze the tail to the left第五章 Simulation Modeling 【给一个随机现象描述模拟过程（random number 随机数） 按概率来分 用公式语言描述结果】Monte Carlo Fair Dice Algorithm Flip of a Fair Coin （抛硬币）： Head Tail0 0.51Let x be a random number in [0,1],define掷骰子第九章. Graphs of Functions as Models （量纲分析） Mass(质量) M Momentum （动量） 1-MTLLength(长度) LWork （功） 22-T ML Velocity （速度）1-LTDensity （密度） 3-ML Acceleration （加速度） 2-LT Viscosity （摩擦系数） 11--T ML Specific weight(重量) 22--T ML Pressure （压力） 21--T ML Force （力） 2-MTL Surface tension(张力) 2-MT Frequency （频率） 1-T Power （功率） 32-T ML Angular velocity （角速度） 1-T Rotational inertia （惯性） 2MLAngular acceleration （角加速度） 2-TTorque （转力距） 22-T ML Angular momentum （角动量） 12-T MLEntropy （能量） 22-T ML Energy （能量）22-T MLHeat22-L MLExample 1. Drag Force on a SubmarineWe are interested in the drag force experienced by a submarine. The main factors are Fluid velocity v,Characteristic dimension r (the length),Fluid density ρ,Fluid viscosity μ.Thus the model is f(D,v,r,ρ,μ)=0We haveD v rρμ2-MTL1-LT L 3-ML11--TMLTo find dimensionless(量纲) products 1)()()()()(11312=-----edcba TMLMLLLTMLTWe haveChoose a and e as free variables,then(1)a=1,e=0:b= -2,d=-1,c= -2,thusρρ221221rvDrDv==∏---(2)a=0,e=1:b= -1,d= -1,c= -1,thusρμμρvrrv==∏---1112Note that21∏is the Reynolds numberHence we have the model )(21∏=∏h,this is )(22ρμρvrhrvD=Suppose we use the model to test the drag force with rrm101=第十章Graphs of Functions as Models【军备竞赛能源危机】军备竞赛 Observations:(1) y is increasing, that is, y'>0. (2) y is concave up, that is, y''≤ 0. (3) If x=my, then y=y0 /sm.We propose the continuous model10,/0<<=s S y y y x ，Similary 10,/0<<=t t x x xy （S,t 为各自的生存率） (1) Change in 0y :If X increases its civil defense, then 0y and y' both increase. Therefore the curve y=f(x) shifts upward and has a larger slope than before.On the other hand, if missiles of Y are more effective, then 0y and y' decrease. Therefore the curve shifts downward and has a smaller slope than before.(2) Change in s:If missiles of Y are well protected, then s increases and y' decreases. Therefore the curve y=f(x) rotates downward and has a smaller slope than before.On the other hand, if the technology and weapon effectiveness of X ’s missiles is improved, then s decreases and y' increases. Therefore the curve rotates upward and has a larger slope than before.(3) Change in exchange ratio e=x/y:If X uses multiple warheads, then e increases. Therefore the curve y=f(x) rotates upward and has a larger slope than before.能源危机（供求曲线）SupposeS(q) = p* + α(q – q*), D(q) = p* – β(q – q*).After a tax of t, the new supply curve is S'(q).The new supply curve isS'(q) = p* + t + α(q – q*).To find the new equilibrium: S'(q) = D(q), that is, p* + t +α(q – q*) = p* – β(q – q*). Thusq1 = q* – t /(α+β) p1 = p* + βt /(α+β). Hence the price increase is p1 – p* = βt /(α+β). Thus,When D(q) is very steep, consumers will pay a larger portion of the tax; When S(q) is very steep, the industry will pay a larger portion of the tax.第十一章 Modeling with a Differential Equation 【画解的曲线（积分曲线）】 Example: Sketch solution curves (integral curves)：)2)(1('-+=y y y Equilibrium: y = – 1, y = 2Equilibrium point y* is stable ify(t) →y* when y0 is close to y*Therefore the equilibrium y* = –1 is stable but y* = 2 is unstable.Example: Sketch solution curves (integral curves)第十二章Modification: If there is no competition, the model is{y k ym dt dy x k xa dt dx )1()1(21-=-=Logistic modelThen the model with competition is{ymnxkymdtdyxabykxadtdx)1()1(21--=--=。
数学专业英语课后习题2.6
1.1）function，domain，range，the identity function，the absolute-value function，the real-valued function，real variable2）cube，volume，edge-length，prime，totality3）Hooke's law，stretch，displacement，spring，constant，proportional4）schematic representation，plot，image，output，input5）it is not difficult to imagine，the idea was much too limited2.（1）常用英语字母和希腊字母来表示函数。
Letters of the English and Greek alphabets are often used to denote functions.（2）若 f 是一个给定的函数，x 是定义域里的一个元素，那么记号f(x)用来表示由 f 确定的对应于x 的值。
If f is a given function and if x is an object of its domain, the notation f(x) is used to designate that object in the range which is associated to x by the function f.（3）该射线将两个坐标轴的夹角分成两个相等的角。
The ray makes equal angles with the coordinates axes.（4）可以用许多方式给出函数思想的图解说明。
The function idea may be illustrated schematically in many ways.（5）容易证明，绝对值函数满足三角不等式。
数学专业英语课后习题2.4
1.1）integer，rational number，irrational number，real number，negative number，the negative，real line，real axis，scale，to the left/right of 2）sum，difference，product，quotient，power，inequality3）axiom，the field axiom，the order axiom4）ordered，entirely complete，Euclidean，appropriate，distinguished，illuminating5）can be deduced formula，formula interchangeably，using a set of formulas，corresponding to an object，proof by induction，the two set to be distinguished2.1）Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”.2）The sum, difference, or product of two integers is an integer, but the quotient of two integers need not be an integer.3）This device for representing real numbers geometrically is a very worthwhile aid that helps us to discover and understand better certain properties of real numbers.4）The geometry often suggests the method of proof of a particular theorem, and sometimes a geometric argument is more illuminating than a purely analytic proof (one depending entirely on the axioms for the real numbers).5）If a set consisting of real numbers satisfies the following conditions we call it an open interval.6）The real number a is the negative number of –a and their absolute values are equal. When a ≠ 0, their notations are different.7）Each real number corresponds to exactly one point on this line and, conversely, each point on the line corresponds to one and only one real number.8）In geometry, the ordering relation among the real numbers can be expressed clearly in real axis.3.1）一个常见的错误是认为x 是一个负数。
高等数学英文教材答案
高等数学英文教材答案Title: Answer Key for Advanced Mathematics English TextbookI. IntroductionAdvanced Mathematics is a fundamental subject for students pursuing a higher education in STEM fields. To aid in their learning, an English textbook for Advanced Mathematics has been developed. This article serves as an answer key for the textbook, providing students with accurate solutions to exercises and guiding them towards a better understanding of the subject.II. Chapter 1: Functions and Their Graphs1.1 Linear FunctionsExercise 1:Solution: The equation of the line is y = 2x - 3.Exercise 2:Solution: The slope of the line passing through the points (-1, 4) and (3, -2) is -1. The equation of the line is y = -x + 3.1.2 Quadratic FunctionsExercise 1:Solution: The vertex of the parabola y = x^2 - 2x + 1 is (1, 0).Exercise 2:Solution: The equation of the parabola passing through the points (-1, 3), (0, 1), and (2, -1) is y = -x^2 + x + 1.III. Chapter 2: Differentiation2.1 Derivative of FunctionsExercise 1:Solution: The derivative of f(x) = 3x^2 - 2x + 1 is f'(x) = 6x - 2.Exercise 2:Solution: The derivative of g(x) = 5x^3 + 2x^2 - 4x is g'(x) = 15x^2 + 4x - 4.2.2 Rules of DifferentiationExercise 1:Solution: The derivative of h(x) = sin(x) + cos(x) is h'(x) = cos(x) -sin(x).Exercise 2:Solution: The derivative of i(x) = ln(x^2) is i'(x) = 2/x.IV. Chapter 3: Integration3.1 Indefinite IntegralsExercise 1:Solution: The integral of f(x) = 3x^2 - 2x + 1 is F(x) = x^3 - x^2 + x + C, where C is the constant of integration.Exercise 2:Solution: The integral of g(x) = 5x^3 + 2x^2 - 4x is G(x) = x^4/4 +2x^3/3 - 2x^2/2 + C.3.2 Definite IntegralsExercise 1:Solution: The definite integral of h(x) = sin(x) + cos(x) from 0 to π/2 is ∫[0, π/2] (sin(x) + cos(x)) dx = 2.Exercise 2:Solution: The definite integral of i(x) = ln(x) from 1 to e is ∫[1, e] ln(x) dx = 1.V. ConclusionThis answer key provides students using the Advanced Mathematics English textbook with accurate solutions to exercises, enabling them to verify their work and further enhance their understanding of the subject. By following the provided solutions, students can gain confidence in their problem-solving abilities and excel in the field of mathematics.。
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2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches.（2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。
No modern scientific and technological branches could be regularly developed without the application of mathematics.（3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。
Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often.（4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。
Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered.（5）方程与算数的等式不同在于它含有可以参加运算的未知量。
Equation is different from arithmetic identity in that it contains unknown quantity which can join operations.（6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。
Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it.（7）方程很有用，可以用它来解决许多实际应用问题。
Equations are of very great use. We can use equations in many mathematical problems.（8）解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。
To solve the equation means to move and change the terms about without making the equation untrue, until the root of the equation is obtained, which is the value of unknown term.英译汉1.Algebra has evolved from the operations and rules of arithmetic.The study of arithmetic begins with addition,multiplication,subtraction,and division ofnumbers:4+7,37×682,49-22,40÷8.In algebra we introduce symbols or letters—such as a,b,c,d,x,y,z—to denote arbitrary numbers and，instead of special cases，we often consider general statements：a+b,cd,x-y,x÷a.代数是从算术的运算和规则当中逐渐发展起来的，算术的研究是从数的加减乘除开始的。
例如4+7，37×682，49-22，40÷8。
在代数学里,我们采用符号或字母。
例如a,b,c,d,x,y,z来表示任意的数字，而不考虑那些特殊情况。
我们经常考虑的是一般的表达式，例如a+b,cd,x-y,x÷a。
2.The language of algebra serves a twofold purpose.First,we may use it as a shorthand to abbreviate and simplify long or complicated statements.Second,it proves a convenient means of generalizing many specific statements.代数的语言有两个作用。
第一个是使用它作为一种速记法去缩减和减化那些又长又复杂的表达。
第二，它被证明是一种概括许多具体的表达方式的便捷途径。
3.Many expressions involve two or more operations.Grouping symbols tell us which operation is to be done first.The common grouping symbols areparentheses,(),brackets.[],and the fraction bar,—.For example,in the expression2(3+4),we do the addition first and then we do the multiplication:2(3+4)=2(7)=14.许多数学表达式包含两个或更多的运算。
分组符号告诉我们哪一个运算先做。
常见的分组符号是圆括号，方括号和分数线。
例如，在数学表达公式2（3+4）里。
我们先做加法再做乘法2（3+4）=2（7）=142.2 几何与三角词组翻译1.学会institution，建筑师architect, 机械师machinist, 制图员draftsman, 测量者surveyor, 木匠carpenter2.点point, 端点endpoint, 线line, 直线straight line, 线段line segment, 曲线curved line, 折线broken line, 射线ray , 平面plane,曲面curved surface3.立体solid, 柱体cylinder, 立方体cube,球sphere, 棱锥pyramid,圆锥cone ,4.圆circle,圆心center, 直径diameter, 半径radius, 半圆semicircle, 弦chord, 弧arc, 优弧major arc, 劣弧minor arc5.角angle, 边side, 三角形triangle, 直角三角形right triangle,斜边hypotenuse, 直角边right-angle side6.长度length,宽度breadth/width,厚度thickness, 位置position7.几何的geometrical,立体的three-dimensional , 弯曲的curved,等距离的equidistant ,无限的infinite8.培养创造力train originality,必须的毅力necessary perseverance ,提高鉴赏力raise/improve the appreciation ability9.消失了的边界vanishing boundaries/landmarks,有序性和优美感orderliness and sense of beauty, 几何图形大量存在geometric forms abound in , 定理成立的先决条件a prerequisite to a theorem汉译英（1）许多专家都认为数学是学习其他科学技术的必备基础和先决条件。
Many experts recognize that mathematics is the necessary foundation and prerequisite of studying other science technology.（2）西方国家的专家认为几何起源于巴比伦和埃及人的土地测量技术，其实中国古代的数学家对几何做了许多出色的研究。