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Lu Guangqing’s Studio Lu’s Studio 吕 广 庆 教 育 教 学 工 作 室 LU Guang-qing’s Education & Teaching Studio For : 1st Term of Year 2010-2011 Students.

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Presentation on theme: "Lu Guangqing’s Studio Lu’s Studio 吕 广 庆 教 育 教 学 工 作 室 LU Guang-qing’s Education & Teaching Studio For : 1st Term of Year 2010-2011 Students."— Presentation transcript:

1 Lu Guangqing’s Studio Lu’s Studio 吕 广 庆 教 育 教 学 工 作 室 LU Guang-qing’s Education & Teaching Studio For : 1st Term of Year 2010-2011 Students

2 吕广庆教育与教学工作室 2015年5月2日 2015年5月2日 2015年5月2日 2015年5月2日 2015年5月2日 2015年5月2日 课堂教学软件 (1) 2015年5月2日 2015年5月2日 2015年5月2日 2015年5月2日 2015年5月2日 2015年5月2日 UIC 吕广庆 数学教学辅助资料

3 Lu Guangqing’s Studio §1.1 : Words of Numbers English Expressions on Basic Mathematical Nomenclatures ( 基本数学术语的英文表达 )

4 Lu Guangqing’s Studio §1.1 : Words of Numbers ChineseEnglishChineseEnglishChineseEnglish 整数分数小数 实数虚数复数 正数负数个位数 十位数百位数千 万十万百万 亿十亿万亿 偶数奇数(数的) 幂 基数序数近似数 百分数千分数有效 (位 ) 数 integerfractiondecimal real number ( pure ) imaginary number complex number positive number negative number units or ones tens hundreds thousand ten thousandhundred thousand million even numberodd numberpower cardinal number ordinal number approximate number percentper-mille significant digit hundred million billiontrillion

5 Lu Guangqing’s Studio §1.2 : §1.2 : Reading Skill on Numbers : 101: 200: 503: 964: 2346: 23343: 第 3: 第 5: 第 9: 第 12: 第 16: 第 20: 第 22: 第 56: 第 100 : 第 123: 第 365: 第 2000: 四舍五入 : 3.567: 0.45: 2050.0438: 0.01: 0.001: One (a) hundred (and/oh) one, two hundred, five hundred and one, nine hundred & sixty-four two thousand (,) three hundred and forty-three twenty-three thousand (,) three hundred and forty-three. (read: the) third (the) fifth, (the) ninth (the) twelfth (the) sixteenth (the) twentieth, (the) twenty-second(the) fifty-sixth one hundredthone hundred and twenty-third three hundred and sixty-fifth two thousandth round(-ing)-off three point five six seven zero point four five two thousand and fifty point zero four three eight one hundredth (point zero zero one) one thousandth (point zero zero one, point two zeroes one)

6 Lu Guangqing’s Studio : a (one) half : one-seventh, : two-thirds : three and six-tenths : thirty-three over eighty-seven (thirty-three divided by eighty-seven) : one hundred and twenty-three (,) five hundred and sixty- sevenths (one hundred and twenty-three over five hundred and sixty-seven) 5.7%: 6%o: : one-hundred oh fourth 3 §1.2 : §1.2 : Reading Skill on Numbers (Cont.) five point seven percent (or per cent) six permille (or per mille)

7 Lu Guangqing’s Studio 806543212.564823 0, 3, -4 0.3, -4.5 0.3i, -4.5i 3-4.5i 1,3, 5,7,9,11,…2, 4, 6, 8, 10, 12,… 35.6078: after ? To the ? Its ? =35.61 4. Read: 1. What’re the following groups of numbers? 2. Read the digits’ name and tell how much of them? = 0.428571428571…= 0.428571 3. Read: § §1.3 : Identifying & Reading Skill on Numbers 百分位: percentile tenth, hundredth, thousandth, ten thousandth, hundred thousandth, millionth

8 Lu Guangqing’s Studio 中文英文中文英文中文英文 ( 数 ) 运算加减 乘除比例 比率圆括号 () 方括号 [ ] 花括号 { } 等于=恒等于 ≡ 不等于 ≠ 正比于∝近似等 于 ≈ 大于小于绝对值 | x | 阶乘 (n!)( 累加 ) 和 ( 乘积 ) 积 ( 相除 ) 商最大值最小值 乘方 (x n ) 开方 ( ) 指数 § §2.1 : Words of Operations (I) operationplus, addminus times, multiplied bydivided by, overproportion ratio of (A to B), A is to B round brackets, Parenthesi(e)s square brackets braces be equal to, equals be identical with/to, be equivalent to be not equal to be in direct proportion to be approximately equal to be greater thanbe less thanabsolute value of x n factorialthe sum of, the summation of product quotientmaximum value minimum value power (the nth power of x, x to the nth power) root-extract(-ing), the nth root of x exponent

9 Lu Guangqing’s Studio 中文英文中文英文中文英文 πRatio of the circumference of a circle to its diameter 趋近于区间, 开区间, 闭区间, 半开区间 e=2.7183base of natural logarithm( 自然对数 ) ∆x∆xy’, y” i=√-1 多元函 数 对数, 常用对数 Logarithm , Common logarithm 以 20 为 底的对 数 lnx 三角函数 反三角 函数 双曲函 数 双曲正切 集 ( 合) Set 子集空集 交集 ∩ 并集∪补集 complements 定律 law 因式 factor 因式分解 定理 theorem 法则 rule 理论 theory § §2.1 : Words of Operations (I-cont.) approaches to, interval , symbol of imaginary number( 复数符号 ) tends to open interval , closed interval delta x, increment x half-open interval multivariate function y prime, y double prime Logarithm with base 20 Ell en x Trigonometric function Inverse Trigonometric function Hyperbolic function Hyperbolic tangent subsets Empty set intersectionsunions factorize

10 Lu Guangqing’s Studio 混合运算 Mixed operation 函数极限 无穷大微分导数 偏导数全微分积分 不定积分定积分二重积 分 三重积分正弦 ( sin ) 余弦 ( cos ) 正切 ( tan ) 余切 (cot) 正割 (sec) 余割 (csc) 反正弦 ( sin - 1 ) ( 数 ) 集 (合) § §2.1 : Words of Operations (I) (Cont.) 闭环积分 中文英文中文英文中文英文 functionlimit infinitydifferential derivative partial derivative complete differential integral indefinite integral definite integral double integral triple integral sinecosine tangent cotangent secant cosecantinverse sine function (arcsine function) set closed linear integral

11 Lu Guangqing’s Studio 交换律 Commutative property 函数极限 结合律微分导数 分配律约分积分 分式根式单项式 多项式 figure 次数, 阶数 通分公分母平方差 化简提取公 因式 分组 grouping § §2.1 : Words of Operations (I) (Cont.) 中文英文中文英文中文英文 functionlimit Associative property differential derivative Distributive property cancellation integral fraction radical (expression) monomial polynomial 数字、图 degree , order Reduction of fractions to a common denominator Common Denominator Difference of squares Abstracting common factors simplify

12 Lu Guangqing’s Studio 分数指数幂 Power of factional exponent 代数方 程 Algebraic equation 未知 数 unknown 已知数 known 线性方 程 Linear equation 二次 方程 Quadratic equation 方程组 System of equations 二元方 程 Equation with 2 variables 一次 方程 First-degree eq. 配方法 Completing The square 判别式 discriminant 代入 法 Substitution method 不等式 inequality 矩阵 matrix 逆矩 阵 Inverse Matrix 合并同类项 Combining Similar terms 同底幂 Powers With same base 2 阶行 列式 Determinant of order 2 余子式 cofactor 图形 graph 示意 图 diagram § §2.1 : Words of Operations (I) (Cont.) 中文英文中文英文中文英文

13 Lu Guangqing’s Studio § §2.2 : Reading Skill on Signs x to the third power plus two times a times y to the fourth power plus two six plus x over (divided by) the quantity x squared times the quantity x to the fifth power minus four to the third power. six-tenths open brace, a open square bracket b plus left round bracket c minus d right round bracket close square bracket, close brace. : the first derivative of y with respect to x equals dy over dx. the second partial derivative of y with respect to x is equal to delta squared y over delta x squared. ( 一阶导数 ) y’(x)= : { a [b + (c - d) ] } : ( 二阶偏导数 ) y”(x , z)= : x 3 +2ay 4 +2 :

14 Lu Guangqing’s Studio 二阶混合偏导数 : the second mixed partial derivative of f with respect to x and y 函数份 f(x) 从 a 到 b 的定积分 : the definite integral of f of x with limits a and b (from a to b) g(x) 积分函数- function of integral (a,b) 积分区间- integral interval The difference of g of x evaluated at b and a definite integral of f, a to b, equals g, a to b f(x,y) 的二重积分 : the double integral of f Over (region) R w.r.t. x and y f(x,y) 的二重积分 : Integrating from a to b of f of x, y w.r.t. x and from c to d w.r.t. y

15 Lu Guangqing’s Studio b 根底数- radicand ( base ), m 根指数- index ( root ), a 是 b 的 m 次根- principal mth root of b 连 ( 乘 ) 积: Product of all a k from k equals 1 to n 累加 ( 求和 ) : Capital Sigma a k from k equals 1 to n

16 Lu Guangqing’s Studio 1. A ≠ B, A+ B≡ C, F ∝ a, x ≈ 4.5 3. 4!=4×3×2×1, e 2x =2x+1, 4. sin - 1 (0.5)=30 o, tan( 45 o ) =1, log 10 (10)=1 5. 2. | x | =4, =8, x-->3 lim(y )= § §2.2 : Practice on Reading Skill of Signs the closed linear integral of (xdy-ydx) in the integral region with boundary curve c 6.

17 Lu Guangqing’s Studio ChineseEnglishChineseEnglishChineseEnglish 加法 ( 的 ) 减法 ( 的 ) 乘法 除法乘数被乘数 分子分母除数 被除数余数因子 定理法则定律 / 规则 代数单项式多项式 § §3.1 : Words of Operations (II) addition (additive) subtraction (subtractive) multiplication divisionmultipliermultiplicand numeratordenominatordivisor dividendremainderfactor theorem rulelaw algebramonomialpolynomial

18 Lu Guangqing’s Studio ChineseEnglishChineseEnglishChineseEnglish 方程 ( 方程的 ) 解已知数 未知数方程组变量 线性方程不等式常数 标量矢(向)量 ( 方程等的 ) 根 § §3.1 : Words of Operations (II) (Cont.) equationsolutionknown unknown a system of equations variable linear equation inequalityconstant scalarvector root coefficient

19 Lu Guangqing’s Studio Give the names of the following Operations: 2 + 3 = 5, 5 - 4 = 1, 5 × 3 = 15, 20 ÷ 8 = 2.5 Tell the names of the numbers in the above operations is a? b=5 is § §3.2 : Reading Skill on the Expressions

20 Lu Guangqing’s Studio Solution: x 2 -2x=15 Place the constant term on the right side. x 2 -2x+1=1+15 Complete the square of (x+1) by adding the square of half the coefficient of x (1 2 ) to both sides. (x+1) 2 =16 Complete the square. x-1=±4 Use the square root property. x=1±4 Solve for x x 1 =1+4, x 2 =1-4 x sub 1 equals 1 plus 4, and x sub 2 is equal to 1 minus 4. x 1 =5, x 2 = -3 At last, x sub one equals 5, and x sub 2 equals minus 3. § §3.2 : A practice on solving an equation Explain the steps to solve: x 2 -2x-15=0

21 Lu Guangqing’s Studio Chinese English Chinese English Chinese English 线角点 线段射线端点 直线曲线折线 垂直的水平的倾斜的 相交垂直于平行于 直角锐角钝角 平角补角余角 对顶角对角线三角形 四边形多边形平行 四边形 矩形菱形正方形 § §4.1 : Vocabulary of Geometry lineanglepoint line segmentrayendpoint straight linecurve (line)broken line vertical (to)horizontalslant (declined) intersect(-ing) perpendicular (to) parallel (to) right angle acute angleobtuse angle straight angle supplementary angle complementary angle vertex anglediagonaltriangle quadrilateralpolygonparallelogram rectangle lozenge, rhombuses square

22 Lu Guangqing’s Studio 梯形周长面积 圆(形)圆(形) 弦弧 同心的圆周 ( 向 ) 的 内接的 切线割线内切 扇形半径直径 ( 圆 ) 弓形长度体积 宽度高度厚度 棱柱多面体底面 侧面长方体六面体 正方体棱锥圆柱 圆锥圆台球(体)球(体) § §4.1 : Vocabulary of Geometry (Cont.) Chinese English Chinese English Chinese English 表面积 | | 球冠 | | 旋转体 | trapezoidperimeterarea circlechordarc concentriccircumferential inscribed tangent linesecant lineinner tangency sector radii ( radius ) diameter segment lengthvolume width altitude 、 height thickness prismpolyhedronbase lateral facerectangular solid hexahedron tetragonal solid /cube pyramidcylinder cone truncated conesphere surface area spherical crownrotational solid

23 Lu Guangqing’s Studio § §4.2 : Practice on Plane/Space Graphs

24 Lu Guangqing’s Studio The length of line segment AD is computed by: AD=5 times cotangent(50 degrees) meters The length of DC is: DC=5 times cotangent(30 degrees) meters The base line of the triangle AC is then the sum of AD and DC, i.e., AC=AD+DC=5 times left square bracket cotangent(50 degrees) plus cotangent(30 degrees) right square bracket. Unit is meters Thus, according to the formula of triangle area, we can get the area to be found as follow: S= (AC*5)=xxx (m 2 ). 50 o 30 o A D C B 5 m The area of the triangle, denoted by S, is equal to one half times Left round bracket AC times the height 5 right round bracket. The unit is meter squared. § §5.1 : Practice on Geometrical Computation

25 Lu Guangqing’s Studio Condition: mass of the car: no friction on the way, start at the top B with V o =0 m/s 。 To Find: the speed of the car at the point A (the end) of the slope. Solution: We can have two different ways to find out the results. (1)Firstly, According to law of energy conservation, potential energy of the car at the top of the slope is equal to the kinetic energy of the car at the endpoint of the slope. i.e., The potential energy at the top of the slope: mgh=(equals) m V t 2 /2 (the kinetic energy at the endpoint of the slope, A). V t = = ≈ 20(m/s) § §5.2 : Practice on Solving a Physics Problem 30 o m h=20 m V W F2F2 A F1F1 B C

26 Lu Guangqing’s Studio (2) Secondly, Resolute the gravity force W into two components, F 1 and F 2 parallel to the motion of the car and perpendicular to the surface of the slope, respectively. According to: The second Newton’s law: F=ma, and Displacement S = at 2 /2 if initial velocity V 0 =0, & Considering S=h/sin(30 o ), and F 1 = W sin ( 30 o ),W=mg, and The Definition of acceleration, a =( V t - V 0 )/t, etc. We can also get the same result. § §5.2: Practice on Solving a Physics Problem (cont.)

27 Lu Guangqing’s Studio § §6 : About Understanding on Long Expressions 准确!!!!! 主谓宾等主成份与从句成份清楚!!! 修饰关系明确!!! 介词理解、用法准确!!! 遵从数学的习惯、专用表达词及习惯!!! Do more and more exercises !!!

28 Lu Guangqing’s Studio Measurement of Mounting Compliance and Transmissibility B F cbr Subframe (Component B) Body (Component A) Front(fr) Rear(rr) F ca_ctr A A x ca_rt x cbr Bottom view: Side view:

29 Lu Guangqing’s Studio equipmentmodelsensitivitymake Uni-axial Accelerometer (weight=5.2g) 333A32102.7 mV/gPCB Tri-axial Accelerometer (weight=4.5g) 356A1110.43 mV/gPCB Modal Hammer086C032.06 mV/NPCB Sound Level Meter (mic type: ½- inch prepolarized condenser) NA-2739.81 mV/Pa RION 16-channel Signal Conditioner481N/APCB Multi-channel VXI FrontendE1432AN/AHP NT-based Signal Processing Software N/AI-DEAS Test A Table of Measurement Parameters

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