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Mathematical Software

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1 MATLABÄ�ö�

2 MATLAB±ã���

3 LaTeX©���

4 MATLAB)û�ê¯K

5 MATLAB)�È©¯K

6 MATLABêâ?n

7 MATLABóä���è`z

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http://www.math.zju.edu.cn/xlhu/teaching/matlab/matlab2012.html

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1�ùµMATLABÄ�ö�

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úô�ÆêÆX

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2011c7�2F

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1 MATLABV�

2 MATLABêÆ$�

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Figure: MATLAB(MATrix LABoratory) logo

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MATLAB�õU

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�7©�¯K(P2)µ������/�E�±'~�Ý/÷v

1

φ=φ− 1

1⇔ φ2 − φ− 1 = 0.

1 ê�O���{

p = [1 -1 -1];

r = roots(p);

2 ÎÒO���{:

r = solve(’1/x = x-1’);

3 ÀúO�:

f = inline(’1/x - (x-1)’);

ezplot(f,[0,4*pi]);AAA::::õõõUUUrrr���¶¶¶���óóó{{{üüü¶¶¶***¿¿¿UUUååårrr¶¶¶´́́???§§§!!!���ÇÇÇ"""

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MATLABÌ�uÐ�ã

70"§Cleve MolerƬmuN^EISPACKÚLINPACK���

1983c§C�ómuû^�µê�O�Úêâã/z

1984c§¤áMath Worksúi§u1MATLAB11�

1993c§íÑ4.0(win)�§4.1�8¤MapleõU

1997c§5.0�¢yý��32 $�§5U�ÌJ,

2002c§uÙMATLAB 6.5 (R13)§õU��k4��U?

MATLAB R2009b(7.9)u2009c9�uÙ§��zcüguÙ

#��§�m©O3zc�3�Ú9�"8c��

´ 2012a "�c http://software.cc98.org/ e1Á^"

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MATLAB2009b.¡

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MATLAB·-

MATLAB�Ä�ó��ª´·-1�p§MATLABO�Ú�ò¢

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help �ÏXÚ exist Cþu�¼ê

what 8¹¥©��L which (½©� �

cd UCó�8¹ dir y¢8¹e�©�

path w«|¢´» disp w«Cþ½SN

who S�Cþ�L whos S�Cþ�[&E

clear �nS�Cþ clc �Ø·-I�

clf �Øã/I� hold ã/�±m'

save ��S�Cþ load \1�½Cþ

echo &Ew«m' quit òÑMATLAB

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��%�ë�]�

help !!!

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1 MATLABV�

2 MATLABêÆ$�

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'uMATLABCþ

MATLAB^Cþ�;êâÚé�"'uCþ��Ä�5Kk

MATLABCþÃL(²§UI©��;�m¶

i1�Þ§di1!êiÚey�|¤§Ø�k��ÚI

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Ù¦�¦Úº�Ä�U«c�ó¶

Øêêê���!ÝÝÝ!EEEêêêÚiiiÎÎÎGGG§�k�AÏCþµ

inf eps bitmax NaN½nan i½j realmin realmax

pi beep ans nargin varargin nargout varargout

12 / 26

MATLABÄ�êâa.�I–¢ê

3·-1¥¢yXeO�

1 �a = −24o , b = 75o ,O� sin(|a|+|b|)√tan(|a+b|)

��

2 �n�/n>�©O�a = 4, b = 3, c = 2,¦n�/¡È;

e s = a+b+c2 , °ÔúªA =

√s(s − a)(s − b)(s − c)

MATLAB¥%@�¢êþ�V°Ý£�,��î�(²��ê½

ü°Ý¤§�´¤k�¼ê$�þ�2:ê$�!�«OXe·

-��J

format short — �ÑÑ5 k�êi

format long — ÑÑ16 k�êi

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MATLABÄ�êâa.�II–Ý

1 �Ý��Ñ\[1 2 3;4 5 6;7 8 9];

2 �Ý�D��½�M-©�½lSÜ�ª��1\;

3 ,AÏÝ�)¤:

zeros "Ý ones ��Ý

eye ü  diag é�

rand �Å randn ��©Ù�Å

magic �� compan õ�ª��Ý

hilb HilbertÝ invhilb �HilbertÝ

hankel HankelÝ toeplitz ToeplitzÝ

gallery HighamÿÁ rosser A��ÿÁÝ

hadamard HadamardÝ wilkinson A��ÿÁÝ

pascal PascalÝ vander ���Ý

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�þ�MATLABL«

n��þ�@�´n × 1�Ý

�þ)¤�{:

1 ��Ñ\

2 �5�©¼êlinspace

3 éê�©¼êlogspace

�þ�Ä�$�:

1 �þ\~a + ~b�ê\a + ~b

2 ê¦!SÈdot(~a,~b)½~a. ∗ ~b3 Ècross(~a,~b)�·ÜÈ(5¿^S)

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«~IµÄ�$�

®��þa1 =

1

2

3

, a2 =

−1

4

0

, a3 =

2

0

2

,

�O�(J2a1 + 3a2 − 4a3.

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«~IIµ^�þL«õ�ª

õ�ªL«�{

1 Xê�þ��Ñ\:p = [1,−5, 6,−33];poly2sym(p)

2 A�õ�ª:A = [1, 2, 3; 4, 5, 6; 7, 8, 9];p=poly(A)

3 d�Mïõ�ª:v = [−5,−3 + 4i ,−3− 4i ];p=poly(v)

õ�ª$�

1 ¦�:polyval(p,[1, 2; 2, 1]);

2 ¦�roots(p)

3 ¦Ø{(=�þòÈ)p = conv(p1,p2); p1 = deconv(p,p2)

4 �©(polyder)

5 [Ü(polyfit)

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Ù¦~^Ýö�¼ê

ØÄ�oK$�µ\~!¦!�/mØ�:

reshape C� flipdim U�ê�=

flipud þe�= fliplr �m�=

rot90 _��^= diag �é��þ

tril J�en� triu J�þn�

det �1�ª inv ��_

cond �^�ê trace ��,

norm ¦�ê½� rank Ý��

d§�k4�~^�Ý�ÄÄÄ���!***ÐÐÐÚ©)"

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«~µ|^1�ªO�¡È/NÈ

n�üX/kn + 1�º:µ{xi , yi , zi}ni=0"Kn = 2��n�/µ

S = ±1

2

∣∣∣∣∣∣∣∣1 1 1

x0 x1 x2

y0 y1 y2

∣∣∣∣∣∣∣∣=x1y2 + x2y0 + x0y1 − x2y1 − x0y2 − x1y0. n = 3��o¡N:

V = ±1

6

∣∣∣∣∣∣∣∣∣∣∣

1 1 1 1

x0 x1 x2 x3

y0 y1 y2 y3

z0 z1 z2 z3

∣∣∣∣∣∣∣∣∣∣∣Á^¼êdet(A)O�?¿�½üX/�¡È/NÈ"

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Ý�ê|$�

�Ý$�ØÓ3uê|$�´Ó�ÝéA���m�$�"

1 ê|oK$�µ.∗�./

2 �(.ˆ )!�ê(exp)!éê(log)Úm�(sqrt)$�

3 Ü6'X¼ê$�µ

any!all!find!ianan!isnumeric!isempty!...

~: �|n�/º:�½(triangle.mat)§ÁO�§��¡È"

v = 0.5*abs(tri(:,2,1).*tri(:,3,2) - tri(:,3,1).*tri(:,2,2) + ...

tri(:,3,1).*tri(:,1,2) - tri(:,1,1).*tri(:,3,2) + ...

tri(:,1,1).*tri(:,2,2) - tri(:,2,1).*tri(:,1,2));

tri(i,j,k)L«1i�n�/�1j�º:�1k��I"

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Ý�Ù¦$�Î

�â$�Î + − ∗ .∗ ∧ .∧ \ .\ / ./

'X$�Î < <= > >= == ∼=

Ü6$�Î &(�) |(½) ∼(�)

Table: MATLAB�$�Î

: ���þ��½Ü© % 5º

; Ý©1!¶-w« = D�

! lMATLABN^XÚ·- , ©�Ý�

’ Ý=�!�Ý!iÎG ... Y1

() ¼êN^Ú�½$�^S [ ] Ýö�

Table: MATLABÙ¦ÎÒ

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MATLABÄ�êâa.�III–Eê

MatlabXÚ#N¦^Eê§�Lkïá��Eêħ�^

i =√−1 or j =

√−1.

ïáEêÄ�§Eê�^e¡�éÑ\

z = 3 + 4i ;

Xeü«Ñ\EêÝ��ª´�d�

A = [1 2; 3 4] + i ∗ [5 6; 7 8]

A = [1 + 5 ∗ i , 2 + 6 ∗ i ; 3 + 7 ∗ i , 4 + 8 ∗ i ]

3MATLAB¥Eê�oK$��{Ú¢ê��22 / 26

~^êƼê

sin(x) x��u asin(x) x���u

cos(x) x�{u acos(x) x��{u

tan(x) x��� atan(x) x����

log2(x)!log10(x) ±2!10�.éê log(x) xg,éê

round(x)!fix(x) xo�Ê\ sqrt(x)√x

floor(x)!ceil(x) x��!�m�� exp(x) ex

real(x)!imag(x) x�¢Ü!JÜ abs(x) |x |gcd(x,y) ��ú�ê lcm(x,y) ��ú�ê

conj(x) Eê��Ý angle(x) Eê���

mod(x,y) x/y�{ê vpa w«Cqê

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AÏêƼê

besselj 1�aBessel¼ê erf Ø�¼ê

bessely 1�aBessel¼ê legendre Legendre¼ê

besselh 1naBessel¼ê beta Beta¼ê

besseli U?1�aBessel¼ê gamma Gamma¼ê

besselk U?1�aBessel¼ê ellipj jacobiý�¼ê

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MATLABÄ�êâa.�IV–iÎG!��Ú(�

1 A = ’Hello there ! ’ ;

2 size (A)

3 B = double(A)

4 C = char(B)

5 b = 12; bb = ’13’;

6 C = [num2str(b) ’”s square root is ’ num2str(sqrt(b))]

7 D = str2num(bb) + 5

8 CELL = {’I am the first of cell . ’ , 1, [1 3; 4 5]};

9 CELL{1}10 CELL{3}11 S.f1 = ’I am structure! ’ ; S.f2 = [1 2; 3 4];

12 S.f1

13 S.f2

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F A Q I

1 �o´MATLABº§k=õUº

2 �o´MATLABó�«§�o´�có�8¹º

3 $1���o3¶4þÃ(Jw«º

4 ��o�ê:��w«o ºXÛ¥ä�c$�º

5 �þÚÝkÛ'Xº=�ª�Mï4× 4�ݺ

6 MATLABUmõ��ê|ºÝÚê|�Óí?

7 L�ª 0:100 ¥�”:”Ò��^¶qe A = rand(5,5)§

@o A(1:3,2:4) L«�oº

8 N�íØÝ��1½��ºlÑ�êâN�©�¤Ýº

9 *�.*�«Oº—Ý�ê|$�

10 éÜþ�flipdimÚéÝreshape�^{Ú�^º

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