Maple在工程与科学中的实战应用：节省成本的数学工具

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"《应用于工程师与科学家的Maple应用》是一本由Chris Tocci和Steve Adams合著的专业书籍，它深入探讨了Maple在工程和科学领域的强大应用价值。Maple作为一款计算机代数系统（Computer Algebra System, CAS），在当今经济环境中扮演着关键角色，它能够通过初始的定量问题计算机分析，显著节省人力和材料成本，提升组织的竞争力。本书的核心内容围绕“模板”应用案例研究展开，这些案例是根据读者特定的问题设计的，旨在激发他们思考如何利用Maple这一工具来解决实际工程和科研中的复杂数学问题。书中不仅讲解了Maple的基本原理和功能，还提供了丰富的实例，使读者能够熟练掌握如何在实践中运用Maple进行符号计算、数值计算、图形绘制、数据分析等任务，从而提高工作效率和精度。作者 Chris Tocci 和 Steve Adams，作为经验丰富的专家，他们对Maple的操作和其在工程数学和科学计算中的应用有着深厚的理解。书中的内容包括但不限于： 1. 工程数学与数据处理：阐述Maple如何在解决几何、微积分、线性代数等工程领域问题时发挥优势，提供高效的算法和求解策略。 2. 科学与数学数据处理：讲解Maple在物理、化学、生物学等科学学科中的应用，如方程求解、实验数据分析以及模型建立。 3. Maple编程基础：介绍Maple的编程环境，语法结构，以及如何编写和调试代码，帮助读者掌握Maple作为一种高级数学语言的特点。 4. 实战案例：书中详尽的案例分析展示了如何一步步通过Maple解决实际问题，这些案例既包括理论演示，也包含实际工程或科研场景。 5. 参考文献和索引：确保读者能够进一步扩展学习，查找相关研究和参考资料。《应用于工程师与科学家的Maple应用》是一本实用性很强的教材和参考书，不仅适合专业人员提升技能，也适合对Maple感兴趣的学生和研究人员作为学习工具。通过这本书，读者不仅能掌握Maple软件，还能学会如何有效地将其应用到自己的工作和研究中，从而推动科技进步和创新。"

gest that even the most advanced users should give this ﬁrst chapter a

cursory glance as a means of introducing the authors’ style. Chapters 2

through 8 concentrate on how to apply Maple to problems in the areas of

analog and discrete control theory, analog and digital ﬁltering, ordinary

diﬀerential equations, power supply design, and curve ﬁtting to data.

What is a CAS ?

A computer algebra system is just a calculator that does mathematics, but

unlike a conventional calculator it does more than just manipulate ﬂoating-

point numbers. A CAS can perform numerical computations using either

exact or ﬂoating-point arithmetic, and it can manipulate symbolic quanti-

ties and display both functions and data graphically. Some, but not all,

CASs are also sophisticated programming environments ideally suited for

the representation and manipulation of mathematical quantities and

objects.

Numbers

The majority of modern CASs are not limited to the number of signiﬁcant

digits set by the ﬂoating-point hardware so they are capable of providing

solutions that are exact or to a user-speciﬁed level of precision. Maple sup-

ports arbitrary precision arithmetic, which means that it is capable of stor-

ing and using numbers having in excess of 500,000 digits. This is in stark

contrast to a normal calculator or spreadsheet that can only support 10 dig-

its. Here we calculate the product of the cubes of the ﬁrst 40 odd numbers,

∏

I = 0

(2i + 1)

◗ product((2*x+1)^3, x=0..39);

507748306245828599556221571230208944802988775653262

350807652219192332706057011255827529763014747456

4870095938232290016243558763746110353766146334154

13352736271917819976806640625

This returns the ﬂoating-point approximation.

Applied Maple for Engineers and Scientists

◗ with(inttrans,[mellin]):

mellin(ln(y)*exp(-3*y^2), y, s);

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More about Maple

Maple Vr4 is a comprehensive CAS that can perform numerical, symbolic,

and graphical computations on PCs (DOS, Windows, Mac, Amiga, etc.)

and workstations (Apollo, HP, Sun, DEC, etc.). It is an interactive, easy-to-

use system comprising more than 2500 functions that can be used either

on its own or in conjunction with many commonly used numerical analysis

and oﬃce applications. It is also its own programming language: 95% of

Maple Vr4 is written in Maple, which means that its scope is essentially

limitless. If an application area is not initially supported, Maple is quickly

extended through the addition of new functions and procedures. It is there-

fore hardly surprising that Maple is the ﬁrst choice for many mathemati-

cians, engineers, scientists, educators, and others who need an easy-to-use

environment in which to perform mathematics.

Maple was ﬁrst conceived late in 1980 at the University of Waterloo as

a research project. Since then it has steadily grown to become the largest,

most robustly tested general mathematical software system currently avail-

able. It consists of three distinct parts: the kernel, the library, and the work-

sheet. The worksheet, with its typeset mathematics, text, and graphics

support is a natural medium for entering and manipulating mathematical

expressions, models, prototypes, and test data. The kernel, which is writ-

ten in C, contains the system core functions and accounts for approxi-

mately 5% of the Maple Vr4 system. The library, on the other hand, is

where the majority of the system resides. Functions held in the library are

written in Maple and are user accessible.

Maple: a tutorial

The goal of this tutorial is twofold: First, it introduces you to the Maple

syntax and, second, it gives you a quick tour of Maple itself. We should, at

this point, reiterate that this tutorial gives only the briefest of introductions

to the Maple syntax and may be skipped by the experienced user.

Introduction

Help

Maple’s Help database consists of more than 8 MB of data organized into

manual style pages containing examples and hypertext links. Every page

has the same basic format: Function, Calling Sequence, Parameters, De-

scription, Arguments, Examples, and See Also sections. Sections contain-

ing pointers to additional information, for example, the See Also section,

contain hyperlinks to other Help pages. This wealth of information is

searchable in a variety of ways via the Help menu or the Worksheet—con-

tents, topic/keyword, or full-text searches from the menu—and the manual

pages and hypertext links are directly accessible from the Worksheet. If we

access Maple’s Help system from the Help menu we do so via dialog

boxes, whereas when using the Worksheet we can use the either the ques-

tion mark notation (

?, ??, and ???) or the help function. Either method

of accessing the help system will result in a Help Worksheet being dis-

played for the topic or keyword used in the search if a match is found. Be-

cause the entries in the Help menu are self-explanatory, we will

concentrate on how to use the Help system from within the Worksheet.

The Help system is accessed from the Worksheet by using the question

mark as follows (note that the semicolon terminator is not required):

◗ ?help

The brackets on the left-hand side of the Worksheet shown in

Figure 1.1 are collapsible regions and the underlined text indicates hyper-

text. The requested help page is displayed as an inert Worksheet (the

Maple commands cannot be executed) in its own window, which means

that all or part of it can be copied into the currently active Worksheet using

the normal copy-and-paste procedure. The Examples section of a Help

page can be copied separately, without highlighting them beforehand, us-

ing the Edit:Copy Examples menu item. The selected items are then copied

into the active Worksheet using either

Edit:Paste or Edit:Paste Maple Text.

The ﬁrst method will result in inclusion of both the Maple input and out-

put regions, whereas the second only copies the Maple input regions into

the active Worksheet, as shown in Figure 1.2, in which the Examples sec-

tion for the Help topic

simplify[power] are used as an example.

The Help system will also look for partial matches, so, for example, en-

tering

?A will prompt us by providing pointers to the Maple functions

that begin with A.

◗ ?A

Applied Maple for Engineers and Scientists

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