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Lu’sStudio

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

吕广庆教育与教学工作室吕广庆教育与教学工作室

2023年4月18日 星期二2023年4月18日 星期二

课堂教学软件课堂教学软件 (1)(1)

2023年4月18日 星期二2023年4月18日 星期二

UIC UIC 吕广庆吕广庆

数学教学辅助资料数学教学辅助资料

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§1.1§1.1 ： ： Words of NumbWords of Numbers ers

English Expressions on Basic Mathematical Nomenclatures ( 基本数学术语的英文表达 )

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§1.1§1.1 ： ： Words of NumbWords of Numbers ers

Chinese English Chinese English Chinese English

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

integer fraction decimal

real number （ pure ）imaginary number

complex number

positive number

negative number

units or ones

tens hundreds thousand

ten thousand hundred thousand million

even number odd number power

cardinal number

ordinal number

approximate number

percent per-mille significant digit

hundred million billion trillion

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:

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-fourtwo thousand (,) three hundred and forty-threetwenty-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-sixthone hundredth one hundred and twenty-third

three hundred and sixty-fifthtwo thousandth

round(-ing)-offthree point five six sevenzero point four five

two thousand and fifty point zero four three eightone hundredth (point zero zero one)

one thousandth (point zero zero one, point two zeroes one)

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1

2: a (one) half

1

7: one-seventh,

2

3: two-thirds : three and six-tenths

33

87 : thirty-three over eighty-seven (thirty-three divided by eighty-seven)

123

567

: 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:

104

1: one-hundred oh fourth

36

10

§1.2§1.2 ：： Reading Skill on Numbers (Cont.)

five point seven percent (or per cent)

six permille (or per mille)

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806543212.564823

0, 3, -4 0.3, -4.5 2

31

7 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?

7

3= 0.428571428571…= 0.4285713. Read:

§§1.3 ： Identifying & Reading Skill on Numbers

百分位： percentile

tenth, hundredth, thousandth, ten thousandth, hundred thousandth, millionth

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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 (xn) 开方 ( )

指数n x

§§2.1 ： Words of Operations (I)

operation plus, add minus

times, multiplied by divided by, over proportion

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 tobe in direct proportion to

be approximately equal to

be greater than be less than absolute value of x

n factorial the sum of, the summation of

product

quotient maximum value minimum value

power (the nth power of x, x to the nth power)

root-extract(-ing),the nth root of x exponent

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中文 英文 中文 英文 中文 英文π Ratio 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=2.7183 base of natural logarithm(自然对数 )

∆x y’,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 toopen interval ，closed interval

delta x,increment x

half-open interval

multivariatefunction

y prime,y double prime

Logarithm with base20

Ell en x Trigonometricfunction

Inverse Trigonometricfunction

Hyperbolicfunction

Hyperbolictangent

subsets Empty set

intersections unions

factorize

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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function limit

infinity differential derivative

partial derivative

complete differential

integral

indefinite integral

definite integraldouble integral

triple integral

sine cosine

tangent cotangentsecant

cosecant inverse sine function (arcsine function)

set

closed linearintegral

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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function limit

Associativeproperty

differential derivative

Distributiveproperty

cancellation integral

fraction radical(expression)

monomial

polynomial 数字、图 degree ，order

Reduction of fractions to a common denominator

CommonDenominator

Differenceof squares

Abstractingcommonfactorssimplify

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分数指数幂 Power offactional exponent

代数方程

Algebraicequation

未知数

unknown

已知数 known 线性方程

Linearequation

二次方程

Quadraticequation

方程组 System ofequations

二元方程

Equation with2 variables

一次方程

First-degree eq.

配方法 CompletingThe square

判别式 discriminant 代入法

Substitution method

不等式 inequality 矩阵 matrix 逆矩阵

InverseMatrix

合并同类项 CombiningSimilar terms

同底幂 PowersWith 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

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§§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.

dx

dy( 一阶导数 ) y’(x)=

352 )4(

6

xx

x:

{ a [b + (c - d) ] } :10

6

2

2

x

y

( 二阶偏导数 ) y”(x ， z)= :

x3+2ay4+2 :

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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

( , )R

f x y dxdy

( , )d b

c af x y dxdy

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

( ) [ ( )]b

ba

a

f x dx g x

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m b ab 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 ak from k equals 1 to n1

n

kk

a

累加 ( 求和 ) ： Capital Sigma ak from k equals 1 to n1

n

kk

S

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1. A ≠ B, A+ B≡ C, F ∝ a, x ≈ 4.5

3. 4!=4×3×2×1, e2x=2x+1,

4. sin － 1(0.5)=30o, tan( 45o) =1, log10(10)=1

)(4 22 mdxdyxyS

Cxxdx 2

2

1

)(3)2( 32 mdVzyx n

5.

2. ｜ x ｜ =4, =8, 6 x x-->3

lim(y )=

§§2.2 ： Practice on Reading Skill of Signs

c

)ydxxdy( the closed linear integral of (xdy-ydx) in the integral region with boundary curve c

6.

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Chinese English Chinese English Chinese English

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

division multiplier multiplicand

numerator denominator divisor

dividend remainder factor

theorem rule law

algebra monomial polynomial

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Chinese English Chinese English Chinese English

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.)

equation solution known

unknowna system of equations

variable

linear equation

inequality constant

scalar vector root

coefficient

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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

7

1

a is a? b=5 is

§§3.2 ： Reading Skill on the Expressions

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Solution:x2-2x=15 Place the constant term on the right side.x2-2x+1=1+15 Complete the square of (x+1) by adding the square of half the coefficient of x (12) to both sides.(x+1)2=16 Complete the square.x-1=±4 Use the square root property.x=1±4 Solve for xx1=1+4, x2=1-4 x sub 1 equals 1 plus 4, and x sub 2 is equal to 1 minus 4.x1=5, x2= -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: x2-2x-15=0

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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

line angle point

line segment ray endpoint

straight line curve (line) broken line

vertical (to) horizontal slant (declined)

intersect(-ing)perpendicular(to)

parallel (to)

right angle acute angle obtuse angle

straight anglesupplementary angle

complementary angle

vertex angle diagonal triangle

quadrilateral polygon parallelogram

rectanglelozenge, rhombuses

square

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梯形 周长 面积圆 (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

)

§§4.1 ： Vocabulary of Geometry (Cont.)

Chinese English Chinese English Chinese English

表面积 | | 球冠 | | 旋转体 |

trapezoid perimeter area

circle chord arc

concentric circumferential inscribed

tangent line secant line inner tangency

sector radii （ radius ） diameter

segment length volume

width altitude 、 height thickness

prism polyhedron base

lateral face rectangular solid hexahedron

tetragonal solid /cube

pyramid cylinder

cone truncated cone sphere

surface area spherical crown rotational solid

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§§4.2 ： Practice on Plane/Space Graphs

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The length of line segment AD is computed by: AD=5 times cotangent(50 degrees) metersThe length of DC is: DC=5 times cotangent(30 degrees) metersThe 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 metersThus, according to the formula of triangle area, we can get the area to be found as follow:

S= (AC*5)=xxx (m2).

)(50cotan30cotan5

)50cotan(5)30cotan(5oo

oo

m

AC

）（）＋（

50o

30o

A D C

B

5 m

2

1

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

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Condition: mass of the car: no friction on the way, start at the top B with Vo

=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 Vt 2/2 (the kin

etic energy at the endpoint of the slope, A).

gh2Vt = 20*8.9*2= ≈ 20(m/s)

§§5.2 ： Practice on Solving a Physics Problem

30o

m

h=20 mVW

F2

A

F1

B

C

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(2) Secondly, Resolute the gravity force W into two components, F

1

and F2 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 ＝ at2/2 if initial velocity V0=0,

& Considering S=h/sin(30 o), and F1 ＝ W sin （ 30 o ） ,W=mg, a

nd The Definition of acceleration, a =( Vt - V0)/t, etc.

We can also get the same result.

§§5.2: Practice on Solving a Physics Problem (cont.)

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§§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 ！！！

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Measurement of Mounting Compliance and Transmissibility

Connector (KS)

Hs,c(a)c(a) Hs,c(b)c(a)

Hs,c(b)c(b)

Hs,c(a)c(b) Suspension (B)

Body (A)

B

Fcbr

Subframe(Component B)

Body(Component A)

Front(fr)Rear(rr)Fca_ctr

A

A

xca_rt

xcbr

Bottom view:

Side view:

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equipment model sensitivity make

Uni-axial Accelerometer (weight=5.2g)

333A32 102.7 mV/g PCB

Tri-axial Accelerometer (weight=4.5g)

356A11 10.43 mV/g PCB

Modal Hammer 086C03 2.06 mV/N PCB

Sound Level Meter (mic type: ½-inch prepolarized condenser)

NA-27 39.81 mV/Pa

RION

16-channel Signal Conditioner 481 N/A PCB

Multi-channel VXI Frontend E1432A N/A HP

NT-based Signal Processing Software

N/A I-DEAS Test

A Table of Measurement Parameters