上海财经大学英语高数课件02
d 3 y d d 2 f ( x) d 3 f ( x) 3 3 f ' ' ' ( x) y ' ' ' 3 ( ) D f ( x ) D x f ( x) 2 3 dx dx dx dx
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And we can define f' ' ' ' (x)=[f ' ' ' (x)] '. From now on instead of using f' ' ' ' (x) we use f(4)(x) to represent f ' ' ' ' (x). In general, we define f(n)(x)=[f(n-1)(x)] ', which is called the nth derivative of f(x). We also like to use the following notations, if y=f(x),
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Corollary: If the differential of f(x) is df(x)= A(x) x,
then f(x) is differentiable and A(x)=f '(x).
Proof: From the definition,
f (t ) f ( x) A( x)t B(t , x) f ' ( x) lim lim A( x). tx t 0 tx t
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Example Use differentials to find an approximate (65)1/3 .
From definition of the differential, we can easily get
If f(x) is differentiable at x=a, and x is very closed to a, then f(x) f(a)+f '(a)(x-a). The approximation is called Linear approximation or tangent line approximation of f(x) at a. And function L(x)= f(a)+f '(a)(x-a) is called the linearization of f(x) at a.
(b) Find the equation of the tangent to the curve x3+y3 =28 at point (1,3).
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Example (a) If x3+y3 =6xy, find y'. (b) Find the equation of the tangent to the folium of Descartes x3+y3 =6xy at point (3,3).
d 2 y d df ( x) d 2 f ( x) 2 2 f ' ' ( x) y ' ' 2 ( ) D f ( x ) D x f ( x) 2 dx dx dx dx
Similarly f ' ' ' (x)=[f '' (x)] '
of f(x), and
is called the third derivative
2.9 Differentials, Linear and Quadratic Approximations
Definition: Let x=x-x0, f(x) =f(x)-f(x0). If there
exists a constant A(x0) which is independent of x and x such that f(x)=A(x0) x+B(x, x0) where
f(x)cos[ xf ( x)]-2 x y cos(xy) 2 x f ' ( x) 2 2 3[ f ( x)] xcos[xf ( x)] 3 y x cos(xy)
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Example (a) If
x3+y3
=27, find
dy . dx
Corollary: (a) If f(x)=x, then dx=df(x)=x.
(b) If f(x) is differentiable, then differential
of f(x) exists and df(x)=f '(x)dx.
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end
Example (a) Find dy, if y=x3+5x4.
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3) Derivatives of implicit function Suppose y=f(x) is an implicit function defined by sin(xy)= x2+y3. Then sin[xf(x)]=x2+ [f(x)]3. From the equation, we
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2.7 Higher derivatives
Derivative f' (x) of differentiable function f(x) is also a
function. If f' (x) is differentiable, then we have [f ' (x)] '. We will denote it by f ' ' (x), i.e., f' ' (x)=[f ' (x)] '. The new function f ' ' (x) is called the second derivative of f(x). If y=f(x), we also can use other notations:
Chapter 2
Derivatives
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2.6 Implicit differentiation
1) Explicit function: The function which can be
described by expressing one variable explicitly in terms of another variable (other variables) are generally called explicit function---for example, y=xtanx, or y=[1+x2+x3]1/2 , or in general y=f(x).
B(x, x 0 ) lim 0 . Then A x is called B(x, x0) satisfies x 0 x
differential of f(x) at x0. Generally A x is denoted by df(x)|x=x = A(x0) x. Replacing x0 by x, the differential 0 is denoted by df(x) and df(x)= A(x) x.
Example The equations xy=c (c0) represents a family
of hyperbolas. And the The equations x2-y2=k (k0) represents another family of hyperbolas with asymptotes y=x. Then the two families of curves are trajectores of each other.
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Example Find the linearization of the function
f(x)=(x+3)1/2 and approximations the numbers (3.98) 1/2 and (4.05)1/2.
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Quadratic approximation to f(x) near x=a: Suppose f(x) is a function which the second derivative
(b) Find the value of dy when x=2 and dx=0.1.
Solution:
Geometric meaning of differential of f(x), df(x)=QS
y
y=f(x) R P d=RS
o
x
x
As x=dx is very small, y=dy ,i.e., f(t)-f(x) f '(x) t.
2) Implicit function: The functions which are defined
implicitly by a relation between variables--x and y--are generally called implicit functions--- such as x2+y2 =4, or 7sin(xy)=x2+y3 or, in general F(x,y)=0.If y=f(x) satisfies F(x, f(x))=0 on an interval I, we say f(x) is a function defined on I implicitly by F(x,y)=0, or implicit function defined by F(x,y)=0 .
上财金融学院高宏课件(谭继军) (2)
— Again, we are interested in the properties of s. This time we use implicit function theorem to find
∂st ∂st ∂w1 , ∂w2
rief review of implicit function theorem (see Appendix ) — Define H (st , w1 , w2 , rt ) ≡ −U1 (w1 − st ) + rt U2 (wt + rt st ) = 0, where st is endogenous variable, and w1 , w2 and rt are parameters. If U is additive separable, which ensures c1 and c2 are normal goods, then 1> U11 ∂st 1 = − ∂w = > 0, 2U ∂H ∂w1 U11 + rt 22 ∂s
∂H rU2 ∂s ∂τ = − ∂H = < 0. 2 ∂τ U11 + r (1 − τ )U22 ∂s
From
∂s ∂τ ,
only substitute effect exists, no income effect.
— Because τ only changes gross real interest rate, real income doesn’t change at all (rsi (1 − τ ) + w2 + a and τ rsi = a ⇒ rsi + w2 ). Income is compensated. — Another word: Though people’s real income doesn’t change, they still response to the tax by decreasing saving. Another word: No neutral tax on price (interest rate), even if real income doesn’t change.
高数双语课件section9.2
Example
Show that
f
(
x,
y
)
x
2
xy
y2
,
x2 y2 0
0,
x2 y2 0
is not continuous at the origin.
Proof If we take y kx, then
lim
x0
xy x2 y2
lim
x0
x2
kx 2 k2x2
y0
y kx
is a product of
u x2 y2
1 and v x2 y2 .
Since u x2 y2
1
is a continuous function,
v x2 y2
is a continuous function on the plane R2 expect at the point (0, 0).
in the domain of f,
| f ( x, y) A | , holds for all 0 ( x x0)2 ( y y0)2 .
We write
lim f ( x, y) A,
( x, y)( x0 , y0 )
and assume ( x0, y0 ) is an accumulation point of the domain of f.
lim f ( x, y) A,
( x, y)( x0 , y0 )
and we say, “The limit of f as ( x, y) approaches ( x0 , y0 ) equals A.”
This is like the limit of a function of one variable, except that two independent variables are involved instead of one, complicating the issue of “closeness.”
高等数学课件详细
多元微积分的应用实例
物理学：描述物理现象，如流体力学、电磁学等 工程学：解决工程问题，如结构分析、控制系统设计等 经济学：分析经济模型，如市场均衡、最优化问题等 计算机科学：用于图像处理、机器学习等领域
无穷级数与常微分
07
方程
无穷级数的概念和性质
性质：收敛性、发散 性、绝对收敛性、条
件收敛性等
数
常微分方程的概念和分类
常微分方程：描述函数在某点或某区 间上的变化规律的方程
一阶常微分方程：只含有一个未知函 数和一个自变量的方程
二阶常微分方程：含有两个未知函数 和两个自变量的方程
高阶常微分方程：含有多个未知函数 和多个自变量的方程
线性常微分方程：未知函数和自变量 之间的关系是线性的方程
非线性常微分方程：未知函数和自变 量之间的关系是非线性的方程
常微分方程的基本解法与实例
基本解法：分离变量法、积分因子法、常数变易法等 实例：求解一阶线性常微分方程、求解二阶线性常微分方程等 应用：在物理、化学、生物等领域有广泛应用 难点：求解高阶常微分方程、求解非线性常微分方程等
微分方程的应用实例
生物：描述生物种群增长、 生态平衡等现象
化学：描述化学反应速率、 物质扩散等现象
06
多元函数微积分
多元函数的极限与连续性
多元函数的极限：定义、性质、计算方法 多元函数的连续性：定义、性质、判断方法 多元函数的可微性：定义、性质、判断方法 多元函数的可导性：定义、性质、判断方法 多元函数的可积性：定义、性质、判断方法 多元函数的积分：定义、性质、计算方法
偏导数与全微分
性质。
函数连续性的 性质：连续函 数具有局部有 界性、局部保 号性、局部保 序性等性质。
高数双语课件section1_5.pptx
kind [第一类间断点] of the function; all other discontinuous points are called discontinuity of the second kind[第二类间断点].
y
y
O
x
First kind
x O
Second Kind
11
The Classification of Discontinuous Points
Finish.
7
The Continuity of Function
2x 1, 1 x 0
Example
Prove
f
(
x
)
x
2
3,
0 x1
does not continuous at
x0 .
Proof Since f (0) 3 and
xlim0 f ( x) xlim0( x2 3) 3 f (0)
x) sin( x0)
2cos
x0
x 2
sin
x 2
then
lim
x0
y
2
lim cos
x0
x0
x 2
sin
x 2
0.
Hence sin x is continuous at x x0. Since, x0 is arbitrary point
in the interval (,), we have sin x C(,) .
(
x0
)
x x0
lim
x x0
f (x) f (x)
f ( x0)
.
f ( x0)
4
The Continuity of Function
高数双语课件section3_2.pptx
F ( x) F ( x) F ( x0 ) F ( ) f ( ) , G( x) G( x) G( x0 ) G( ) g( ) where lies between x0 and x .
x
.
SolutionIt is easy to check that the conditions of L’Hospital’s rules are satisfied for the function x sin x and x3. By L’Hospital’s rules, we have
cos x
we have
lim x lnsin
x0
x2 lim
x
lim x0
0.
ln sin 1 x
x
lim
x0
sin x
1 x2
x0 sin x
Thus,
lim (sin x)x e xlim0 xlnsin x e0 1.
x0
Finish.
13
Indeterminate Forms
means So, Finish.
f ( x)
lim
A
xx0 g( x)
f ( )
lim
x x0
g( )
A
.
f (x)
F(x)
f ( )
lim
x x0
g( x)
lim
x x0
G( x)
lim
上海财经大学英语高数课件03
f (a)(x a) f which is what we wanted to prove. . (c)(x a) For the case where x < a,we have f'(c) < f'(a), but multiplication by the negative number x - a reverses the inequality, so we get (3) and (4) as before.
Since f '(3) = 0 and f "(3) >0,f (3) = -27 is a local minimum. The point (0,0) is an inflection point since the curve changes from concave upward to concave downward there. Also (2, -16) since the curve changes from concave downward to concave upward there.
f ( x2 ) f ( x1 ) f (c)(x2 x1 )
This shows that f is increasing on [a,b]. It is similar to prove (b).
f ( x2 ) f ( x1 ) 0
or f ( x1 ) f ( x2 ).
(2) DEFINITION A point P on a curve is called a point of inflection if the curve changes from concave upward to concave downward or from concave downward to concave upward at P.
(高等数学英文课件)Some exercises of CHAPTER 2
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P159 40.
Analysis
f0limf0hf0...
h 0
h
f 0 02 f 0 0
f0 lim f0 h f0 lim fh
h 0
h
h 0 h
h2 f h h 2
h
h
h
目录 上页 下页 返回 结束
P159 40.
Analysis
f0limf0hf0
3. Horizontal Asymptotes
alxi m fxx,blxi m fxax
yaxb
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P123
60. Asymptotes
f
x
x3 x2 1 x2 1
1. Horizontal Asymptotes
limf x ...
x
2. Vertical Asymptotes
rx2000011x
1. 销量为100台的边际收益.
rx20000x2 r100 2
2. 用收益函数的导数来估计当销量从每周100台增加 到每周101台时所产生的额外的收益.
r r100
3. 计算极限并解释经济意义.
lim rxlim 2 0 0 0 0x20
x
x
目录 上页 下页 返回 结束
x
2. Vertical Asymptotes
limf x x0
x?
3. Horizontal Asymptotes
a
lim x
f
x
x
lxim
2sinx x
1 x2
0
目录 上页 下页 返回 结束
P132 6.
2.1Output, the stock market and interest rate
American Economic AssociationOutput, the Stock Market, and Interest RatesAuthor(s): Olivier J. BlanchardSource: The American Economic Review, Vol. 71, No. 1 (Mar., 1981), pp. 132-143Published by: American Economic AssociationStable URL: /stable/1805045Accessed: 28/01/2010 09:24Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at/action/showPublisher?publisherCode=aea.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@.American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to TheAmerican Economic Review.。
上海财经大学英语二 英语翻译
I. 中译英:Unit 1: P.16-17 Unit 2: P. 42-43 Unit 3: P. 66 Unit 4: P. 92 Unit 5: P. 115-116 Unit 6: P. 152-153 Unit 7: P. 177-178Unit 11 When she slammed the door and left without a word, their argument ended.2 The guest who attend dinner party feel like slightly surprise at commanding tone of this American.3 Johnny is no longer fear stay at home alone because he has been grown up and mature.4 While all the passengers walk to exit, he stays at seat alone seems like doesn’t want leave airphone.5 This letter must handle to Dr. Wilson himself.6 Even she felt like joining in the argument, Nancy was too shy to dare to open her mouth.7 Do you think when is the most likelihood to find him at home.8 Excitement flash the hunter’s face while he saw a fox emerge from the bushes and run in the direction of the trap he had laid.Unit 21 It was suggested at the meeting that a committee of eleven people be appointed to make new article of association.2 These young scientists obtained primal information what they needed in their researchwork through investigation on-site.3 It is very possible that he will be rejected by the army due to his poor eyesight.4 the members of committee have different opinions as to the best location of the airport.5 Henry’s artworks are superior in many aspects than his brother’s.6 The steady rise in the quality of our products is because improvement of equipment.7 Jim would like to prefer to act on his own point of view, but he didn’t because as a soldier he had to obey the command.8 I will choose latter resolutely if let me to decide whether we should have a city without bicycle or vehicle.Unit 31 She got a job as a cashier at a local bank, but she was soon be fired because of incompetent.2 It is obviously his young assistant who is running the business of book store.3 As the proposal has been announced at the meeting, she stood up and to protest.4 Bill has applied the position of teaching assistantship from Harvard University, but the possibility he got it is very little.5 Due to lack of funds, they are trying to attract foreign capital.6 The has smell of musty, it must have been vacant for a long time.7 In terms of hobbies are concerned, she and her sister have little in common.8 It is self-evident that the education of teenager is great importance to the future of a country.Unit 41 That litter girl running too fast that get out of control her balance and fell over.2 I was impressed by his devotion to research, but I did not have the slightest interest in his profound theories.3 Be sure not to say anything capable of being misunderstand.4 I was confused by their conflicting advice that I didn’t know how to act.5 At first the complicated problem frustrated them, but after considering carefully they finally worked out a solution.6 The commander of sports delegation beamed with delight with a young pioneer presented him with a bunch of flowers.7 I really don’t see why our English teacher single praise our monitor since we all done quite well this semester.8 I believe the theory that higher form of animals evolves from lower ones.Unit 51 If the wealthy company spend more money on green energy industry instead of on build up military machines and unclear weapons, many of current pollution problems would gradually disappear.2 When burning the coal not only consume the oxygen in the house but also throw off poisonous gases.3 Apparently, find out alternative energy is crucial for stable development of economy.4 Solar cells can absorb sunlight and convert into electricity.5 If the temperature on the earth to go rise from year to year, the polar ice caps will begin to melt then half of the buildings in coastal cities will disappear beneath splashing sea waves.6 Because these creatures are microscopic and tend to hide beneath leafy plants, are not always visible to the naked eyes.7 As a result of invasion to atomic radiation, he finally collapsed at work.8 There is distinct evidence of connection between high pressure of work and some disease of the body.Unit 61 As long as you keep trying, you will be able to solve this complicate problem latter.2 We anticipate that we will encounter resistance to our plan.3 Jim’s friends said that the noise pollution is very serious in their city, but they ha d to endure it.4 At first Tom thought that with his knowledge, skill and experience he was bound to find a satisfactory job.5 It would be advisable to handle this delicate problem with calmness and patience.6 Dick thought if he couldn’t take machine apart, no workers in other factory could, either.7 Do you think bus driver should take full responsibility for the passenger’s safety?8 You don’t need to dwell on your mistakes in judgment any more, what’s important is to try your best to avoid repeating them.Unit 71 Under the leadership of the local government, the villager rose to the serious food crisis caused by the floods.2 This exhibition is very popular and is attracting the steady stream of visitors3 When Mom came upstairs to check us kids, I turned over and pretended to be asleep.4 To fight with drug traffickers is a challenge to Armstead, she felt rather nervous, but she decided to confront them.5 The old lady told me to be cautious and not talk with the guy who hanging out on the street corner.6 A health organization prompted the local government to raise three-billion-dollar fund for construct new hospital.7 When open the door, the man who had set fire to the church found himself confronted bya dozen policemen with guns.8 It is reported that fire which raged for more than two hours started in an abandoned warehouse.。
《上海财经大学》PPT课件
2021/4/26
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商标抢注
➢美国：青岛啤酒 ➢日本：同仁堂，女儿红，杜康（27） ➢菲律宾：阿诗玛 ➢印度：凤凰，蝴蝶 ➢澳大利亚（150） ➢印尼（48）
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产权界定问题
➢谁是有资格的谈判者？
➢红帽子企业
➢科斯定理
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政府参与问题
中国当前企业并购重组中 的若干重大问题
——理念与战略
干春晖
教授 博士 博士生导师
上海财经大学
干春晖 博士 教授 博
导
上海财经大学
1
常用的概念
➢兼并 merger ➢收购 acquisition ➢并购 M&A ➢合并 consolidation ➢接管 take over ➢ 要约收购 tender offer
➢ 这个企业是否积累了足够的人才和资金 ➢ 新进入的行业是否能带动原来的主业或
受原来主业的带动
– CASE：多角化（巨人） ， 不多角化（长虹）
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跨国并购
➢ 第五次全球并购浪潮 ➢ 中国企业并购海外企业 ➢ 外资并购中国企业
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第五次并购浪潮的成因
➢放松规制 ➢技术变革
26
中国企业海外并购的动因
➢ 资源寻求 ➢ 市场寻求 ➢ 技术寻求
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中国企业海外并购中存在的问题－微观
➢ 企业能力薄弱 ➢ 信息不完全风险 ➢ 融资困难 ➢ 中国式整合难通行 ➢ 国际化人才匮乏 ➢ 文化冲突： ➢ 战略冲突
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中国企业海外并购中存在的问题－宏观