包邮实用数学建模.分析.逼近(影印版)

nbsp;   言
    为了更好地借鉴国外数学教育与研究的成功经验，促进我国数学教育与研究
事业的发展，提高高等学校数学教育教学质量，本着“为我国热爱数学的青年创
造一个较好的学习数学的环境”这一宗旨，天元基金赞助出版“天元基金影印数
学丛书”。
    该丛书主要包含国外反映近代数学发展的纯数学与应用数学方面的优秀书籍，
天元基金邀请国内各个方向的知名数学家参与选题的工作，经专家遴选、推荐，
由高等教育出版社影印出版。为了提高我国数学研究生教学的水平，暂把选书的
目标确定在研究生教材上。当然，有的书也可作为高年级本科生教材或参考书，
有的书则介于研究生教材与专著之间。
    欢迎各方专家、读者对本丛书的选题、印刷、销售等工作提出批评和建议。
    天元基金领导小组
    2007年1月

This book was bom out of my fascination with applied mathematics
as a place where the physical world meets the mathematical structures
and techniques that are the cornerstones of most applied mathematics
courses. I am interested largely in human-sized theatres of interaction,
leaving cosmology and particle physics to others. Much of my research
has been motivated by interactions with industry or by contact with
scientists in other disciplines. One immediate lesson from these contacts
is that it is a great asset to an interactive applied mathematician to be
open to ideas from any direction at all. Almost any physical situation has
some mathematical interest, but the kind of mathematics may vary from
case to case. We need a strong generalist streak to go with our areas of
technical expertise.
    Another thing we need is some expertise in numerical methods. To
be honest, this is not my strong point. That is one reason why the book
does not contain much about these methods. (Another is that if it had
then it would have been half as long again and would have taken five
more years to write.) In the modem world, with its fast computers and
plethora of easy-to-use packages, any applied mathematician has to be
able to switch into numerical mode as required. At the very least, you
should learn to use packages such as Maple and Matlab for their data
display and plotting capabilities and for the built-in software routines for
solving standard problems such as ordinary differential equations. With
more confidence, you can write your own programs. In many cases, a
quick and dirty first try can provide valuable information, even if this
is not the finished product. Explicit finite differences (remember to use
upwind differencing for first derivatives) and tiny time steps will get you
a long way.
Who should read this book? Many people, I hope, but there are some
prerequisites. I assume that readers have a good background in calculus
up to vector calculus (grad, div, curl) and the elementary mechanics of
particles. ! also assume that they have done an introductory (inviscid)
fluid mechanics course and a first course in partial differential equations,
enough to know the basics of the heat, wave and Laplace equations
where they come from, and how to solve them in simple geometries).
Linear algebra, complex analysis and probability put in an occasional
appearance. High-school physics is an advantage. But the most important
prerequisite is an attitude: to go out and apply your mathematics, to see
it in action in the world around you, and not to worry too much about
the technical aspects, focusing instead on the big picture.
    Another way to assess the technical level of the book is to position
it relative to the competition. From that point of view it can be thought
of as a precursor to the books by .Tayler [58] and Fowler [19], while
being more difficult than, say, Fowkes & Mahoney [18] or Fulford &
Broadbridge [22]. The edited collections [9, 38] are at the same general
level, but they are organised along different lines. The books [40, 56]
cover simil