数学专业英语(第二版)部分句子翻译2
-
数学英语（下）
3.1.1
1.
调和函数，即拉普拉
斯方程的调解，在数学、物理学、工程学的许多领域中扮演着一个至
关重要的角色。
Harmonic
functions
—
the
solutions
of
Laplace
‟
s
equation
—
play
a
crucial
role
in
many
areas
of
mathematics, physics, and
engineering.
2.
本书的主要目的是让学习调和
函数更容易些。
The main purpose of
our text, then, is to make learning about harmonic
functions easier.
3.
唯一的准备条件是在实分析、复分析以及泛函分析的基本理论上有坚实的基础。
The only prerequisite for the book is a
solid foundation in real and complex analysis,
together with
some basic results from
functional analysis.
4.
为完整起见
，我们包含了一些低年级研究生课程中经常忽略的分析学的专题。
For completeness, we include some
topics in analysis that frequently slip through
the cracks in a
beginning graduate
student
‟s curriculum
.
5.
本书的作者除了写这本书，还开发了一个软件包去处理调和数论中出现的
许多表达式。
In addition to
writing the text, the authors have developed a
software package to manipulate many
of
the expressions that arise in harmonic function
theory.
6.
附录
B
告诉读者如何免费得到我们的软件包。
Appendix B explains how readers can
obtain our software package free of charge.
3.1.2
1.
< br>在过去三十年间拓扑向量空间领域取得了许多进展。
During
the
last
three
decades
much
progress
has
been
made
in
the
field
of
topological
vector
spaces.
2.
在本书中作者打
算写出这些出现在拓扑向量空间、序拓扑向量空间、拓扑基和拓扑代数中
的反例。
In this book the author has
attempted to present such counterexample in
topological vector spaces,
ordered
topological vector spaces, topological bases and
topological algebras.
3.
对于本书中的大部分反例，作者不打算给出其原作者的规属认定。
He makes no attempt to give due
recognition to the authorship of most of the
counterexamples
presented in this book.
4.
本书假定读者已掌握一份拓扑学的知识，读者可参见
B[18]
了解一份拓扑学相关的知识。
It is assumed that the reader is
familiar with general topology. The reader may
refer to B[18] for
information about
general topology.
5.
在本书末的参考文
献中，参考书与论文分别开来，参考文献中的书籍记为
B[]
，
论文记为
P[]
。
The
books
and
papers
are
listed
separately
in
the
bibliography
at
the
end
of
the
book.
Any
reference to a book is indicated by
writing B[] and to a paper by P[].
3.2.4
1.
一个集合
S
上的关系指的是
S
到它
自身的一种对应，例如“亲戚”就是所有的人组成的集
合上的一种关系（如果能提供一份
完整的家族谱的话）
。
By
a
relation
on
a
set
S
we
mean
a
correspondence
of
S
with
itself.
E.g.,
„
being
related
‟
is
a