数学与应用数学专业英语期末考试试题
-
一、英文表示：
1.13.25
thirteen-point-two-five 2.
log
b
5
n
a
the logarithm of n to the base b
equals a
3.5/8 five eighths 4.
< br>5.
x
6.
a
< br>
2
3
a
x
2
1
3
the fifth root of a
squared plus x to the minus one third
5
a
2
<
/p>
0
x to the minus two thirds
plus the fifth root of a squared equals zero
3
b
3
(
a
< br>b
)(
a
2
ab
b
2
)
a cubed plus b cubed
equals a plus b into a squared minus ab plus b
squared
二、英语名词定义
on
An equation is a
statement of the equality between two equal number
symbols.
on
The modern
definition of a
function y
of
x is simply a
mapping
from
a
space
X to another
space Y.A
mapping defined
when every
point x of X has a definite image y, a point of
Y.
limit of a sequence
f
(
n
)
L
) :
f(n)<
/p>
(for example
lim<
/p>
n
A
sequence
f(n)
is said to have a limit L if ,for every positive
number
,there is another
positive number
f
(
n
)
L
for
all
n>=N
In
this
case,
we
say
the
sequence
f(n)
converges
N
(which
may
depend
on
)such
that
to
L
and we
write
divergent.
derivative of function f(x)
The
derivative
lim
f
(
n
)
L
n
,or
f
(
n
)
L
as
n
.A
sequence which does not converge
is
called
f
‘
< br>(
x
)
is
defined
by
the
equation
f
‘
(
x
)
< br>lim
h
0
< br>f
(
x
h
)
f
(
x
)
provided
the
limit
exists.
The
h
number
f
‘
(
x
)
is also called the rate of change
of f at x.
tical population
A statistical population is the set of
measurements (or record of some qualitative
trait)corresponding to the
entire
collection of units about which information is
sought.
三
几何图形的名称
1.
圆
Circle
2.
椭圆
ellipse
3.
长方形
rectangle
4.
正方形
square
5.
平行四边形
parallelogram
6.
三角形
triangle
7.
立方体
cube
8.
圆锥
cone
9.
曲线
curve
10.
双曲线
hyperbola
四．英译汉
device for
representing real numbers geometrically is a very
worthwhile aid that helps us to discover and
understand better certain properties of
real numbers. However, the readers should realize
that all properties
of real numbers
that are to be accepted as theorems must be
deducible from the axioms without any reference to
geometry. This does not mean that one
should not make use of geometry in studying
properties of real numbers.
On
the
contrary ,the geometry
often suggests
the method
of
proof
of 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).In
this book, geometric arguments are used to large
to help motivate or clarify a particular discuss.
译文：几何化地表示实数的方法是一种非常有益的辅助手段，它可以帮助我们发现和更好
的了解实数的某些性质。然而，读
者应该意识到，那些将要被采用作为定理的所有有关实
数的性质时不应该使用几何学。相反地，几何学经常启发特殊定理的
证明方法，而且，有
时候，几何学方面的论点比纯分析（它完全依赖与实数的公理）的证明更直观。在本书中，几何学的论
点会大范围地使用，以帮助人们推动或阐明一些特殊的讨论。
1
ons are of
very great use. We can use equations in many
mathematical problems. We may notice that almost
every problem gives us one or more
statement that something is equal to something;
this gives us equations, with
which we
may work if we need to. To solve an equation means
to find the value of the unknown term. To do this,
we must change the terms about until
the unknown term stand alone on one side of the
unknown and the answer to
the
question.
To
solve
the
equation,
therefore,
means
to
move
and
change
the
terms
about
without
making
the
equation
untrue, until only the unknown quantity
is left on one side, on matter which side.
译文：方程的用处很大。我们能将方程用于许多数学问题。我们或许注意到几乎每一个问题都给了我们以
一种或多种表示某
物和某物相等的说明；这就是给出了方程，如果我们需要的话，我们就
可以进行运算、解方程就是找出未知数的值。要做到
这点我们必须一项直到使未知项单独
处于方程的一边为止，这样一来，就是使得它等于方程另一边的那些项。然后，我们就
得
到未知数的值也就是问题的答案。因此解方程意味着进行移项，而不是方程失真，直到方程的一边（无论那一边）
只留下
一个未知数时为止。
study
of
differential
equation
is
one
part
of
mathematics
that,
perhaps
more
than
any
other,
has
been
directly
inspired by
mechanics, astronomy, and mathematical physics.
Its history began in the 17
century
when Newton,
Leibniz, and the
Bernoullis solved some simple differential
equations arising from problems in geometry and
mechanics. These early discoveries,
beginning about 1690,gradually led to the
development of a lot of
“s
pecial
tricks”
for
solving
certain
special
kings
of
differential
equations,
Although
these
special
tricks
are
applicable
in
relatively
few
cases,
they
do
enable
us
to
solve
many
differential
equations
that
arise
in
mechanics
and
geometry.
译文：微分方程的研究是数学的一个部分
，它可能比其他部分，更多地直接受到了理学，天文学和数学物理的推动。它的历
史开始
于
17
世纪，当时，牛顿，莱布尼茨和伯努利家族解决了一些来
源于几何学和力学的简单的微分方程。这些早期发现，
大约开始于
1690
年，逐渐导致了解决一些特定类型的微分方程的大量的“特殊窍门”的发展。
尽管这些特殊窍门只适用于相
当少的情形，它们确实能使我们解决许多起源与力学和几何
学的微分方程。
4. A
large
variety
of
scientific
problems
arise
in
which
one
tries
to
determine
something
from
its
rate
of
change.
For
example, we could try to compute the position of a
moving particle from a knowledge of its velocity
or
acceleration.
Or
a
radioactive
substance
may
be
disintegrating
at
a
known
rate
and
we
may
be
required
to
determine
the amount of
material preset after a give time. In example like
these, we are trying to determine an unknown
function
from
prescribed
information
expressed
in
the
form
of
an
equation
involving
are
least
one
of
the
derivatives
of
the
unknown
function. These
equations
are
called
differential
equations, and
their study forms one
of the most
challenging branches of mathematics.
译文：大量的科学问题人们根据事物的变化率去确定改事物（的量）
。例如，我们可能试图根据速度或加速度的知识计算一个
移动微粒的位置；又如，某种放
射性物质可能正在以已知的速度进行衰变，需要我们确定在给定的时间后遗留物质的总量。
在类似的例子中，我们力求通过以方程的形式表述的指定来确定未知函数，而这种方程至少包含了未知函数的一
个导数。这
些方程被称为微分方程，而且它们的研究形成了数学上最具有挑战性的分支之
一。
5.
In
discussing
any
branch
of
mathematics,
be
it
analysis,
algebra,
or
geometry,
it
is
helpful
to
use
the
notation
and
terminology of set theory. This subject, which was
developed by Boole and Cantor in the latter part
of the
19
century, has had a
profound influence on the development of
mathematics in the in the 20
century.
It has
unified many seemingly
disconnected ideas and has helped to reduce many
mathematical concepts to their logical
foundations in an elegant and
systematic way. In mathematics, the word “set” is
used to represent a collection
of
objects viewed as a single entity. The individual
objects in the collection are called elements or
members
of the set,
and
they are said
to belong
to or
to be
contained
in the set.
The
set
is said
to contain or
be composed
of its elements. In many applications
it is convenient to deal with abstract sets.
Abstract set theory has been
developed
to deal with such collections of arbitrary
objects, and from this generality the theory
derives its
power.
译文：
在讨论数学的任何一个分支时
，也许是分析学，代数学，几何学，使用集合论的记号和术语是非常有益的。这个学科是由布
尔和康尔在
19
世纪后期发展起来的，它对于
20
世纪数学的发展具有深远的影响。它统一了许多看起来似乎不相关的概念
，
而且以简练的、系统化的方式帮助人们把许多数学概念归并到它们的逻辑基础。在数学
中，这个词“集合”被用来表示看成
一个单个整体的一些物体的集合。集合中单个的物体
称为集合的元素和成员，集合被称为包含或由元素组成。在许多应用中，
2
th
th
th