MATLAB入门：编程与数值方法精要

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"《An Introduction to Programming and Numerical Methods in MATLAB》是一本深入浅出的教材，旨在引导读者掌握编程基础和在MATLAB这一强大的数值计算工具中应用数值方法。该书由S.R. Otto和J.P. Denier合著，针对初学者设计，包含111幅图解，使学习过程直观易懂。章节1主要介绍了MATLAB的基本操作，包括简单计算、变量命名规则、运算顺序、数学函数的使用、数字格式设置、向量操作（初始化、操作与点积）以及设置数学函数的方法。此外，还涵盖了MATLAB特有的命令，如查看变量信息、数组元素访问等，并通过一系列任务帮助读者巩固所学。第二部分着重于编写脚本和函数。章节21讲解了脚本和函数的创建，特别强调了函数的编写，包括用户自定义函数和一个简短的插曲来解释其重要性。接下来的章节演示如何绘制简单函数，如评估多项式和绘制曲线，以及更深入的绘图技巧。函数的嵌套应用也在这一部分有所涉及。错误处理是本书的重要组成部分，2.4节详细讨论了两种类型的错误：数值误差和用户错误，分别分析了它们的原因和应对策略。最后，每个章节都以实践性的任务来引导读者进行实际操作和应用。这本书对于希望学习MATLAB编程并理解其在数值分析中的应用的人来说，是一本不可或缺的入门指南，适合学术研究者、工程师和学生使用。在版权规定下，复制或传播此书需事先获得出版商的书面许可。"

1.2 Scalar Quantities and Variables 3

>>a=3;

>> b = a+1;

>> x = a+b;

Theﬁrstlinesetsthevariablea to be equal to 3, the semicolon instructing

MATLAB to execute the command but to suppress the output. The second

line sets b to be equal to a plus one, namely 4: again the semicolon suppresses

output. The third line sets x to be a+b which is 7 (again output is suppressed).

MATLAB can be used as a very powerful calculator and its operations fall

into two basic groups: unary and binary, the former operating on one quan-

tity and the latter on two. We shall begin by considering simple arithmetic

operations, which are binary. For instance typing 3*4 generates

>> 3*4

ans =

Notice here that we have multiplied the two integers 3 and 4, and the answer

has been returned correctly as 12. MATLAB uses the variable ans to store the

result of our calculation, in this case the value 12,sothatitcanbeusedin

the subsequent commands. For instance the command ans*3 will generate the

result 36 (and now the variable ans will have the value 36). We could also have

used the commands a=3;b=4;x=a*bwhichcanbetypedononeline

andreadas

set a equal to 3 (don’t output anything),

set b equal to 4 (don’t output anything)

and set x equal to a times b

Division works in exactly the same way as in the multiplication example above.

If we try the command 3/4, MATLAB returns the value 0.75.

It is a good idea to use meaningful variable names and we shall shortly

discuss valid forms for these.

Example 1.1 Try entering the following commands into MATLAB, but before

you do so try to work out what output you would expect.

>> 3*5*6

>> z1 = 34;

>> z2 = 17;

>> z3 = -8;

>> z1/z2

1.2 Scalar Quantities and Variables 5

with (whether it be a ﬁle containing MATLAB code, or data etc). We will

see more on this later in the section on script ﬁles.

2. Variable names in MATLAB are case sensitive, so that a and A are two

diﬀerent objects.

3. It is good programming practise to employ meaningful variable names.

In our initial examples we have only used very simple (but appropriate)

names: however as the examples become more complex our variable names

will be more informative.

4. Variables names should not coincide with a predeﬁned MATLAB command

or with any user-deﬁned subroutines. To see whether a variable name is al-

ready in use we can use the command type variable

name, but it may

be better to use the command which variable

name (this will tell you

whether the name variable

name corresponds to an existing code or in-

trinsic function.

1.2.2 Precedence: The Order in Which Calculations Are

Performed

This represents one of the most common sources of errors and it is often the

most diﬃcult to detect. Before proceeding we brieﬂy comment on the question

of precedence, or the order in which commands are executed. Consider the

mathematical expression a(b + c) which you might read as “a times b plus c”

which would appear to translate to the MATLAB command a*b+c. Hopefully

you can see that this actually is equal to ab+c. The correct MATLAB command

for a(b + c)isa*(b+c). The brackets have been used to force MATLAB to ﬁrst

evaluate the expression (b+c) and then to multiply the result by a. We should

avoid falling into the trap of assuming that commands are performed from left-

to-right, for instance c+a*b is equal to c + ab (not (c + a)b as if the addition

was performed ﬁrst).

At this point we should pause brieﬂy and make sure the ideas of brackets are

ﬁrmly in place. Brackets should always appear in pairs and the mathematics

contained within brackets (or equivalently MATLAB) will be evaluated ﬁrst.

Hopefully this concept is familiar to you: however it is worth reiterating, since

one of the most common problems in using MATLAB occurs due to either

unbalanced or incorrectly placed brackets. For example the commands (3+4/5)

and (3+4)/5 are obviously diﬀerent, the former being 3

and the latter being

3+4

The most critical use of brackets, which circumvents another popular source

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