Transcript Lu Guangqing`s Studio

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
UIC 吕广庆
吕广庆教育与教学工作室
数学教学辅助资料
课堂教学软件(1)
2016年4月6日
Lu Guangqing’s Studio
English Expressions on Basic
Mathematical Nomenclatures
(基本数学术语的英文表达)
§1.1： Words of Numbers
Lu Guangqing’s Studio
§1.1： Words of Numbers
Chinese
整数
实数
正数
English
integer
real number
positive
number
Chinese
分数
虚数
负数
English
fraction
（pure）
imaginary number
negative
number
hundreds
Chinese
小数
复数
English
decimal
complex
number
个位数
units or
ones
千
thousand
百万
million
万亿
trillion
十位数
tens
百位数
万
ten thousand
十万
亿
hundred
million
十亿
偶数
even number
奇数
odd number
（数的）
幂
power
approximate
number
significant
digit
hundred thousand
billion
基数
cardinal
number
序数
ordinal
number
近似数
百分数
percent
千分数
per-mille
有效
（位)数
Lu Guangqing’s Studio
§1.2： Reading Skill on Numbers
101: One (a) hundred (and/oh) one,
200: two hundred,
503: five hundred and one,
964:
nine hundred & sixty-four
2346: two thousand (,) three hundred and forty-three
23343: twenty-three thousand (,) three hundred and forty-three.
(read: the) third
第3:
第5: (the) fifth,
(the) ninth
第9:
第12: (the) twelfth
:
第16: (the) sixteenth
第20: (the) twentieth,
第22: (the) twenty-second
第56: (the) fifty-sixth
第100 : one hundredth
第123: one hundred and twenty-third
第365: three hundred and sixty-fifth
第2000: two thousandth
四舍五入: round(-ing)-off
three point five six seven
3.567:
zero point four five
0.45:
2050.0438: two thousand and fifty point zero four three eight
one hundredth (point zero zero one)
0.01:
0.001:
one thousandth (point zero zero one, point two zeroes one)
Lu Guangqing’s Studio
§1.2： Reading Skill on Numbers (Cont.)
1
: a (one) half
2
1
7
1
: one-hundred oh fourth
104
: one-seventh,
2
: two-thirds
3
6
3
10
: 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 sixtysevenths (one hundred and twenty-three over five hundred and
sixty-seven)
5.7%: five point seven percent (or per cent)
6%o: six permille (or per mille)
Lu Guangqing’s Studio
§1.3： Identifying & Reading Skill on Numbers
1. What’re the following groups of numbers?
0, 3,
2
-4 3
1
7
0.3, -4.5
0.3i, -4.5i
3-4.5i
1,3, 5,7,9,11,… 2, 4, 6, 8, 10, 12,…
2. Read the digits’ name and tell how much of them?
806543212.564823
tenth, hundredth, thousandth, ten thousandth, hundred thousandth, millionth
3. Read:
4. Read:
3
7
= 0.428571428571…= 0.428571
百分位：percentile
35.6078: after ? To the ? Its ? =35.61
Lu Guangqing’s Studio
§2.1： Words of Operations (I)
中文
(数)运算
乘
比率
英文
中文
operation
加
plus, add
times, multiplied by
ratio of (A to B),
除
divided by, over
round brackets,
Parenthesi(e)s
A is to B
花括号
{ }
braces
be not equal to
大于
be greater than
(相除)商
乘方(xn)
圆括号
（）
等于＝
be equal to,
equals
正比于∝
不等于
≠
阶乘(n!)
英文
n factorial
quotient
小于
(累加)
和
最大值
power (the nth power 开方
of x, x to the nth power) ( n
x
中文
减
比例
英文
minus
proportion
方括号
square brackets
[ ]
恒等于 be identical
with/to,
≡
be equivalent
to
be in direct
proportion to
近似等
于≈
be
approximately
equal to
be less than
绝对值
｜ x｜
absolute value
of x
(乘积)
the sum of,
product
the summation of 积
最小值 minimum value
maximum value
root-extract(-ing), 指数
) the nth root of x
exponent
Lu Guangqing’s Studio
§2.1： Words of Operations (I-cont.)
中文
英文
中文
英文
中文
π
Ratio of the
circumference of a
circle to its diameter
趋近于
approaches to, 区间，
开区间,
tends to
闭区间,
半开区间
e=2.7183 base of natural
logarithm(自然对数)
∆x
i=√-1
多元函
数
multivariate 对数，
常用对数
function
lnx
Ell en x
以20为
底的对
数
symbol of imaginary
number(复数符号)
Logarithm with base
20
反三角
函数
集(合）
交集∩
Inverse
Trigonometric
function
Set
intersections
双曲函
数
子集 
并集∪
delta x,
increment x
y’,
y”
三角函数
英文
interval，
open interval，
closed interval
half-open interval
y prime,
y double prime
Logarithm，
Common
logarithm
Trigonometric
function
双曲正切
Hyperbolic
tangent
subsets
unions
空集
Empty set
Hyperbolic
function
补集  complements
定律
law
因式
factor
因式分解
定理
theorem
法则
rule
理论
factorize
theory
Lu Guangqing’s Studio
§2.1： Words of Operations (I) (Cont.)
中文
英文
中文
Mixed
operation
函数
function
极限
limit
无穷大
infinity
微分
differential
导数
derivative
偏导数
partial
derivative
全微分
积分
integral
不定积分
indefinite
integral
定积分
三重积分
triple
integral
正弦
（sin）
tangent
余切
(cot)
混合运算
正切
（tan）
余割 (csc)
闭环积分
cosecant
英文
中文
complete
differential
definite integral
sine
cotangent
英文
二重积
分
double
integral
余弦
（cos）
cosine
正割
(sec)
inverse sine
反正弦
(数)集
function
－1
（合）
closed linear （sin ）
(arcsine function)
integral
secant
set
Lu Guangqing’s Studio
§2.1： Words of Operations (I) (Cont.)
中文
英文
中文
交换律
Commutative 函数
property
结合律
Associative
property
Distributive
property
微分
分式
fraction
根式
多项式
polynomial
figure
分配律
通分
化简
约分
Reduction of 公分母
fractions to a
common
denominator
提取公
因式
simplify
英文
中文
英文
function
极限
limit
differential
导数
derivative
积分
integral
cancellation
radical
(expression)
数字、图
Common
Denominator
Abstracting
common
factors
单项式
次数,
阶数
monomial
degree，
order
平方差
Difference
of squares
分组
grouping
Lu Guangqing’s Studio
§2.1： Words of Operations (I) (Cont.)
中文
英文
中文
英文
中文
英文
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
同底幂
Similar terms
Powers
With same base
2阶行
列式
Determinant
of order 2
余子式
graph
示意
图
diagram
cofactor
图形
Lu Guangqing’s Studio
§2.2： Reading Skill on Signs
x3+2ay4+2 :
x to the third power plus two times a times y to the fourth power plus two
6 x
:
x 2 ( x 5  4) 3
six plus x over (divided by) the quantity x squared times the quantity
x to the fifth power minus four to the third power.
6
{
10
a [b + (c - d) ] } :
six-tenths open brace, a open square bracket b plus left round bracket
c minus d right round bracket close square bracket, close brace.
dy
(一阶导数) y’(x)=
dx
: the first derivative of y with respect to x equals dy over dx.
2 y
(二阶偏导数) y”(x，z)=
x 2
:
the second partial derivative of y with respect to x is
equal to delta squared y over delta x squared.
Lu Guangqing’s Studio
b

a
f ( x)dx  [ g ( x)]ba 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
The difference
of g of x evaluated (a,b) 积分区间－integral interval
at b and a
definite integral of f, a to b, equals g, a to b
二阶混合偏导数: the second mixed partial derivative
of f with respect to x and y

f ( x, y)dxdy
d
b
c
a
R

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
f ( x, y)dxdy of f of x, y w.r.t. x and from c to d w.r.t. y
Lu Guangqing’s Studio
m
b a
b根底数－radicand（base），
m根指数－index（root），
a是b的m次根－principal mth root of b
n
a
k
k 1
连(乘)积：Product of all ak from k equals 1 to n
n
S
k 1
k
累加(求和)：Capital Sigma ak from k equals 1 to n
Lu Guangqing’s Studio
§2.2：Practice on Reading Skill of Signs
1. A ≠ B,
2. ｜ x｜=4,
3.
6
4!=4×3×2×1,
4. sin－1(0.5)=30o,
5.
F ∝ a,
A+ B≡ C,
1 2
xdx

x C

2
x =8,
x ≈ 4.5
lim(y )= 
x-->3
e2x=2x+1,
tan( 45o) =1,
log10(10)=1
2
2
xy
dxdy

4
(
m
)

S
n
2
3
(
x

y

2
z
)
dV

3
(
m
)


6.
 ( xdy  ydx )
c
the closed linear integral of (xdy-ydx) in
the integral region with boundary curve c
Lu Guangqing’s Studio
§3.1： Words of Operations (II)
Chinese
English
Chinese
English
subtraction 乘法
(subtractive)
multiplier 被乘数
加法
(的)
addition
(additive)
减法
(的)
除法
division
乘数
分子
被除数
定理
代数
numerator 分母
dividend
theorem
algebra
Chinese
denominator 除数
English
multiplication
multiplicand
divisor
余数
remainder
因子
factor
法则
rule
定律
/规则
law
单项式
monomial
多项式
polynomial
Lu Guangqing’s Studio
§3.1： Words of Operations (II) (Cont.)
Chinese
方程
equation
未知数
Chinese
(方程的) 解
English
solution
Chinese
English
已知数
known
方程组
a system of
equations
变量
variable
linear
不等式
equation
inequality
常数
constant
(方程等的)
根
root
unknown
线性方程
标量
English
scalar
coefficient
矢（向）量
vector
Lu Guangqing’s Studio
§3.2： Reading Skill on the Expressions
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

a
is a?
b=5 is
1
7
Lu Guangqing’s Studio
§3.2： A practice on solving an equation
Explain the steps to solve: x2-2x-15=0
Solution:
x2-2x=15
x2-2x+1=1+15
(x+1)2=16
x-1=±4
x=1±4
x1=1+4, x2=1-4
x1=5, x2= -3
Place the constant term on the right side.
Complete the square of (x+1) by adding the square of half
the coefficient of x (12) to both sides.
Complete the square.
Use the square root property.
Solve for x
x sub 1 equals 1 plus 4, and x sub 2 is equal to 1 minus 4.
At last, x sub one equals 5 , and x sub 2 equals minus 3.
Lu Guangqing’s Studio
§4.1： Vocabulary of Geometry
Chinese
线
线段
直线
垂直的
相交
直角
平角
Chinese
English
Chinese
角
angle
点
point
端点
endpoint
折线
broken line
horizontal
perpendicular
intersect(-ing) 垂直于
(to)
acute angle
锐角
right angle
supplementary
补角
straight angle
angle
倾斜的
slant (declined)
平行于
parallel (to)
钝角
obtuse angle
complementary
angle
English
line
line segment 射线
straight line
曲线
ray
curve (line)
vertical (to) 水平的
余角
English
对顶角
vertex angle
对角线
diagonal
三角形
triangle
四边形
quadrilateral
多边形
polygon
平行
四边形
parallelogram
矩形
rectangle
菱形
lozenge,
rhombuses
正方形
square
Lu Guangqing’s Studio
§4.1： Vocabulary of Geometry (Cont.)
Chinese
梯形
圆(形)
同心的
切线
扇形
English
trapezoid
circle
concentric
Chinese
周长
弦
圆周
(向)的
tangent line 割线
sector
半径
segment
长度
宽度
width
高度
棱柱
prism
(圆)弓形
侧面
正方体
圆锥
表面积
多面体
lateral face 长方体
tetragonal
solid /cube
cone
棱锥
圆台
| surface area| 球冠
English
perimeter
chord
circumferential
secant line
Chinese
面积
弧
内接的
内切
radii（radius） 直径
length
体积
altitude、height 厚度
polyhedron
rectangular solid
pyramid
truncated cone
底面
六面体
圆柱
球(体)
English
area
arc
inscribed
inner tangency
diameter
volume
thickness
base
hexahedron
cylinder
sphere
| spherical crown | 旋转体 | rotational solid
Lu Guangqing’s Studio
§4.2： Practice on Plane/Space Graphs
Lu Guangqing’s Studio
§5.1： Practice on Geometrical Computation
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.,
B
50o
A
AC  5  cotan( 30o )  5  cotan( 50o )
5m
30o
D
C


 5  cotan（30o）＋cotan（50o）(m)
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=
1
(AC*5)=xxx (m2).
2
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.
Lu Guangqing’s Studio
§5.2： Practice on Solving a Physics Problem
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.
m
F1
V
30o
A
W
F2
B
h=20 m
C
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
kinetic energy at the endpoint of the slope, A).
Vt =
2 gh =
2 * 9.8 * 20 ≈ 20(m/s)
Lu Guangqing’s Studio
§5.2: Practice on Solving a Physics Problem (cont.)
(2) Secondly, Resolute the gravity force W into two components, F1
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, and
The Definition of acceleration, a =( Vt - V0)/t, etc.
We can also get the same result.
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！！！
Lu Guangqing’s Studio
Measurement of Mounting
Compliance and Transmissibility
Hs,c(a)c(a)
Hs,c(b)c(a)
Hs,c(b)c(b)
Body (A)
Bottom view:
Connector (KS)
Suspension (B)
Hs,c(a)c(b)
Body
(Component A)
A
Side view:
B
A
Rear(rr)
xca_rt
Fca_ctr
xcbr
Subframe
(Component B)
Fcbr
Front(fr)
Lu Guangqing’s Studio
A Table of Measurement Parameters
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: ½inch 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
N/A
I-DEAS
Test
NT-based Signal Processing
Software