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MATLAB Primer Third Edition

Apr 21, 2023

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Khang Minh
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Page 1: MATLAB Primer Third Edition

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Page 2: MATLAB Primer Third Edition

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Page 3: MATLAB Primer Third Edition

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Page 4: MATLAB Primer Third Edition

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Page 5: MATLAB Primer Third Edition

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Page 6: MATLAB Primer Third Edition

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Page 7: MATLAB Primer Third Edition

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Page 13: MATLAB Primer Third Edition

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Page 14: MATLAB Primer Third Edition

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Page 21: MATLAB Primer Third Edition

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" ��.W� - % 0 1 4 , , > B 0�C ! , - ! : � > %" ��.�AX� - % 0 1 4 , , > B 0�C ! , - ! : � > % 7 � ) B .K� ) , @A # @ �Y% ! C >�2�) , , % *�! 1 >KC ! , - ! : � > %�0 )3* - % ,� .�#�7 , > 0 , - > C >KC ! , - ! : � > %?� , ) @Z* - % ,6 � � # 1 1 � > ! ,�C ! , - ! : � > %'! B * � 4 B 1 0 - ) B %�� , ) @ @=> @=) , +��#�6 / 1 ) B % ) � - *�! 0 >�2�) , , % *�! 1 >;@=> @=) , +A 5 [ � % - \ >;) �@+! 0 , - E� � B�]�$ �^� > B . 0 / ) ��C > 1 0 ) ,75 A �_* - % * � ! + @+! 0 , - E ) ,#0 > E 0

� A ) 4 , 1 > `?&+:�;�<�:�=JF#> � > , > B 1 >�a�4 - * > 7 C > , % - ) B+b�c 3� ;#/ >?0 ) ) � : ) E > % 7 2#/ - 1 /I! , >?) * 0 - ) B�! � 7 @+! + B ) 0 : >;- B % 0 ! � � > *=) B=+ ) 4 ,'% + % 0 > @�c

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Page 27: MATLAB Primer Third Edition

T� �O�U �� � ��S �� Q R�������� ��S�R��KV R O�� �� ���� ��� ��R �6 7 1 /�! B . > 1 4 , , > B 0�2�) , , - B .�* - , > 1 0 ) , +� " 7 % / ) 2 1 4 , , > B 0�2�) , , - B .�* - , > 1 0 ) , +75 1 �� A * - , > 1 0 ) , ++� - % 0 - B .7� � � $ � * > � > 0 >�)�� >]�� $ � B @ . > 0�> B C - , ) B @=> B 0�C ! , - ! : � >� > E > 1 4 0 > ) * > , ! 0 - B .3% + % 0 > @ 1 ) @=@+! B *� B�5 > E > 1 4 0 > ) * > , ! 0 - B .3% + % 0 > @ 1 ) @=@+! B *� , > 0 4 , B , > % 4 � 075 # 1 - % ! C >?0 > E 0�) ��&+:�;�<�:�=D% > % % - ) B

�� �����O� �Q Q �� ��S�R �� ����������JT� ���� �6 � 6 1 � > ! , 1 ) @=@+! B *�2#- B * ) 2��.�89� % > B * 1 4 , % ) ,�/ ) @=> ��0 );0 ) * ) ��% 1 , > > B0 .�1 89# $ % > 0#) 4 0 * 4 0?� ) , @+! 0� 6 ��. > 1 / ) 1 ) @=@+! B * %- B % - * >�% 1 , - * 0 1 ) @=@+! B * %89.�1 � 1 ) B 0 , ) ��*�! . > * ) 4 0 * 4 0#- B 1 ) @=@+! B *�2#- B * ) 2

� � ��O �� �� ������ K�� ���� ���� O� �� �������������� 5 $ 0 > , @=- B�! 0 >�&+:�;�<�:�=A $ # 1 $ � � & ( )�� >�> E > 1 4 0 > *�2#/ > B�&+:�;�<�:�=�- %?% 0 ! , 0 > *89# $ � # ��1 6 @+! % 0 > ,?% 0 ! , 0 4 *�& ( )�� >

��� ��O� ���KV R O�� � �O� �KO�O�� ���KV R O�� � �O�� ! * * - 0 - ) B � ! * * - 0 - ) B� % 4 : 0 , ! 1 0 - ) B � % 4 : 0 , ! 1 0 - ) B @34 � 0 - * � - 1 ! 0 - ) B � @34 � 0 - * � - 1 ! 0 - ) B! * ) 2�> , � ! * ) 2�> , , - . / 0?* - C - % - ) B � , - . / 0?* - C - % - ) B# � > � 0?* - C - % - ) B � # � > � 0?* - C - % - ) B! 1 ) B " 4 . ! 0 >?0 , ! B % * ) % >� ! 0 , ! B % * ) % >/�1 .�B <?, ) B > 1 , > ,�0 > B % ) ,�* , ) * 4 1 0

#�R Q � �� �����QI�������� � ����Q$�KV R O�� � �O�� � > % %�0 /�! B % ! B *�'& � > % %�0 /�! B ) ,#> ( 4�! � � ) ,� . , > ! 0 > ,�0 /�! B � B ) 0� & . , > ! 0 > ,�0 /�! B ) ,#> ( 4�! � �.�1 > E 1 � 4 % - C >?) ,&)& > ( 4�! �� & B ) 0#> ( 4�! �

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Page 28: MATLAB Primer Third Edition

� V R��� ��Q���S���O�������R O�& ! % % - . B @=> B 0�% 0 ! 0 > @=> B 0��� 4 % > * 0 )�� ) , @ZC > 1 0 ) , %�! B * @+! 0 , - 1 > % > B 1 � ) % >;@34 � 0 - * � >�� 4 B 1 0 - ) B ) 4 0 * 4 0'C ! , - ! : � > %��� ! , - 0 / @=> 0 - 1 > E * , > % % - ) B * , > 1 > * > B 1 > �> B 1 � ) % >�� 4 B 1 0 - ) B=- B * 4 0'C ! , - ! : � > %� * > 1 - @+! � * ) - B 0� � *�! , > B 0'* - , > 1 0 ) , +� � � 1 ) B 0 - B 4 >�% 0 ! 0 > @=> B 0�0 ) B > E 0�� - B >� % > *�! , ! 0 >K% 4 : % 1 , - * 0 % 7 � 4 B 1 0 - ) B+! , . 4 @=> B 0 % 7 % 0 ! 0 > @=> B 0 %� > B * , ) 2'% 7 % 4 * * , > % %�* , - B 0 - B .� 1 ) @=@=> B 0 %� % 4 : % 1 , - * 0 - B . 7 C > 1 0 ) ,#. > B > , ! 0 - ) B� > E > 1 4 0 >;) * > , ! 0 - B .3% + % 0 > @ 1 ) @=@+! B *

� V R��� ��QIN���O� ��P�Q R��3�����J�� ��� ��O��� ����# B�A ! B % 2�> ,'2#/ > B > E * , > % % - ) B B ) 0'! % % - . B > *� ��A M ) ! 0 - B .;* ) - B 0#* , > 1 - % - ) B1 � # � 89# � ! , . > % 0?M ) ! 0 - B . * ) - B 0�B 4 @ : > ,1 � # 89895 B % @+! � � > % 0�* ) % - 0 - C >�M ) ! 0 - B . * ) - B 0�B 4 @ : > ,��5 5 � - @+! . - B�! , +K4 B - 05 B0 - B ) B - 0 + # � ) 0 ( ! ( � 4 @ : > ,��.���A M ) ! 0 - B .;* ) - B 0#) * > , ! 0 - ) B 1 ) 4 B 0B�# 1 ]�5 B B 4 @ : > ,�) �� 4 B 1 0 - ) B - B * 4 0'! , . 4 @=> B 0 %B�# 1 ]�. � $ B 4 @ : > ,�) �� 4 B 1 0 - ) B ) 4 0 * 4 0�! , . 4 @=> B 0 %6 .�89� � $ � 1 1 ) @=* 4 0 > ,�0 + * >

�� ��RI������ �� ��R7# $ � 1 4 , , > B 0�*�! 0 >6 � .6 / 2'! � � 1 � ) 1 ,� $ 5 89� > � ! * % > * 0 - @=>?� 4 B 1 0 - ) B$ 5 6 �$ .6 % 0 ) * 2'! 0 1 / 0 - @=> ,�� 4 B 1 0 - ) B %6 � � $ 5 89� > � ! * % > * (���� 0 - @=>

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Page 29: MATLAB Primer Third Edition

� V R��� ��Q9��� ��O� ��R��[ � 1 .�A @+! 0 , - E ) ��\ > , ) %.�B�� A @+! 0 , - E ) ��) B > %� -�� - * > B 0 - 0 +75 # ] * - ! . ) B�! �$ .�� ��� 5 $ [ ;) > * � - 0 \89# ]�5 6 @+! . - 1 % ( 4�! , >6 .�89��# B 1 ) @=*�! B - ) B� 5 B�A ��#�6 � � - B > ! , � +3% *�! 1 > *IC > 1 0 ) , %� .�]�A ��#�6 � � ) . ! , - 0 / @=- 1 ! � � +�% *�! 1 > *IC > 1 0 ) , %89� A ��]�1 5 7 ! , , ! +3� ) , 9 ( H2* � ) 0 %1 # B�7 4 B - � ) , @ � +�* - % 0 , - : 4 0 > * , ! B * ) @ B 4 @ : > , %1 # B�7B B ) , @+! � � +�* - % 0 , - : 4 0 > * , ! B * ) B B 4 @ : > , %��5 � � � - � : > , 05 B @ ��5 � � - B C > , % > � - � : > , 0�� > E ! 1 0 �@ # B�7� 1 �?! B * > , @=) B * >��#�A 6 # � ��! % 1 ! ���#�7# 89# 1 7 � ! *�! @+! , *��# B�/�� � � ! B , > �1 .�A A � 1 % + @=@=> 0 , - 1 > - . > B C ! � 4 >�0 > % 0�@+! 0 , - E" 5 � /�5 B�A .�B L�- � , - B % ) B> %�> - . > B C ! � 4 >�0 > % 0�@+! 0 , - E]�# � � � 1 - 0 2�)3% @+! � � 0 > % 0�@+! 0 , - 1 > %

��� ��O� �D������ V ��Q � �� ��75 # ] 1 , > ! 0 >;) ,#> E 0 , ! 1 0�* - ! . ) B�! � %1 .�$ ��� , ) 0 ! 0 >?@+! 0 , - E 5 � * > . , > > %��5 ��� 1 M - *=@+! 0 , - E�� > � 0 ( 0 ) ( , - . / 0��5 � � 7 M - *=@+! 0 , - E�4 * ( 0 ) ( * ) 2#B1 � A ��# ��� 1 /�! B . >�% - \ >$ 1 5 � � ) 2�> ,�0 , - ! B . 4 � ! ,�*�! , 0$ 1 5 � 4 * * > ,�0 , - ! B . 4 � ! ,�*�! , 0� ! 0 , ! B % * ) % >� 1 ) B C > , 0#@+! 0 , - E 0 )3% - B . � > 1 ) � 4 @=B� � 8 � 9

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Page 30: MATLAB Primer Third Edition

�� � ����Q���������� ���� �5 A $ 1 / > 1 , - ��C ! , - ! : � > %�) ,?� 4 B 1 0 - ) B %#> E - % 0# B- 0 , 4 >;- ��! B + > � > @=> B 0#) ��C > 1 0 ) ,�- %�0 , 4 ># � � 0 , 4 >;- ��! � ��> � > @=> B 0 %�) ��C > 1 0 ) ,�! , >;0 , 4 >��B�7 ) B * - B * - 1 > %�) �B ) B ( \ > , ) > � > @=> B 0 %5 A B�# B 0 , 4 >�� ) , � ! � %5 A 5 B0 0 , 4 >�� ) ,#- B ) B - 0 >�> � > @=> B 0 %��B�5 $ � 0 , 4 >�� ) ,?) B - 0 >?> � > @=> B 0 %5 A 5 � � � 0 , 4 >�� ) ,�� G�G�G9M ) ! 0 - B . * ) - B 0'! , - 0 / @=> 0 - 15 A � 89��$ - 0 , 4 >�� ) ,#> @=* 0 + @+! 0 , - E5 A A ��# 1 A � 0 , 4 >�� ) ,'% *�! , % >;@+! 0 , - E5 A A $ 1 0 , 4 >�� ) ,#0 > E 0'% 0 , - B .A $ 1 6 89� 1 ) @=*�! , >�% 0 , - B .3C ! , - ! : � > %

�� �����O� �Q9��Q �5 0 1 ) B * - 0 - ) B�! � � + > E > 1 4 0 >K% 0 ! 0 > @=> B 0 %� � A � 4 % > *+2#- 0 /+5 0� � A � 5 0 4 % > *+2#- 0 /+5 0� B�7 0 > , @=- B�! 0 >�5 0 ��0 .�1 � " ��5 � �0 .�1 , > * > ! 0�% 0 ! 0 > @=> B 0 %?� ) ,'!�% * > 1 - ) 1 B 4 @ : > ,#) �0 - @=> %" ��5 � � , > * > ! 0�% 0 ! 0 @=> B 0 %?2#/ - � > 1 ) B * - 0 - ) B=- %#0 , 4 >��1 � # / 0 > , @=- B�! 0 >�> E > 1 4 0 - ) B ) �0 .�1;) , " ��5 � ��� ) ) * %1 � $ � 1 B , > 0 4 , B 0 ) - B C ) , - B .K� 4 B 1 0 - ) B� 1 1 .�1 * - % * � ! + @=> % % ! . >�! B *I! : ) , 0?� 4 B 1 0 - ) B

�?O� �O������� ��5 B�� � $ * , ) @=* 0�� ) ,?4 % > ,�- B * 4 0/�� - ��.�# 1 7 - B C ) , >�, > + : ) ! , *I! %#- �- 0'2�> , >�!K% 1 , - * 0')�� >89� B � . > B > , ! 0 >;@=> B 4=) � 1 / ) - 1 > %?� ) ,'4 % > ,�- B * 4 0��# � A � 2'! - 0�� ) ,'4 % > ,�, > % * ) B % >0 � B�6 $ 5 .�B * > ) B >�� 4 B 1 0 - ) B� @ # � > E > 1 4 0 >�% 0 , - B .32#- 0 /I&+:�;�<�:�=�> E * , > % % - ) B0 � @ # � > C ! � 4�! 0 >�� 4 B 1 0 - ) B % * > 1 - ) > * : + % 0 , - B .]�� .���# � * > ) B >;. � ) : ! ��C ! , - ! : � > %B�# 1 ]�6 ��/ C ! � - *�! 0 >�B 4 @ : > ,�) �- B * 4 0�! , . 4 @=> B 0 %

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Page 31: MATLAB Primer Third Edition

��R ���9������� ��O� ����A $ 1 5 B�] ! : ) 4 0 1 /�! , ! 1 0 > ,�% 0 , - B . %�- B+&+:�;�<�:�=# ��A 1 ) B C > , 0�% 0 , - B . 0 ) B 4 @=> , - 1 C ! � 4 > %��� # B�/A !�% 0 , - B . ) � : � ! B , %� @ # � > C ! � 4�! 0 >�% 0 , - B .32#- 0 /+&+:�;�<�:�=2> E * , > % % - ) BB � 8 � A $ 1 1 ) B C > , 0�B 4 @ : > ,�0 )3% 0 , - B .5 B$ � A $ 1 1 ) B C > , 0�- B 0 > . > ,#0 )3% 0 , - B .A $ 1 � B � 8 1 ) B C > , 0�% 0 , - B . 0 ) B 4 @ : > ,5 A A $ 1 0 , 4 >�� ) ,'% 0 , - B .3C ! , - ! : � > %A $ 1 6 89� 1 ) @=*�! , >�% 0 , - B .3C ! , - ! : � > %� ����� 1 1 ) B C > , 0�% 0 , - B . 0 )34 * * > , 1 ! % >� . " � 1 1 ) B C > , 0�% 0 , - B . 0 )3� ) 2�> , 1 ! % >��� � B � 8 1 ) B C > , 0�/ > E % 0 , - B . 0 )�M ) ! 0 - B . * ) - B 0�B 4 @ : > ,��� � 7� 6 1 ) B C > , 0�/ > E % 0 , - B . 0 )3* > 1 - @+! � - B 0 > . > ,7� 6 � ��� 1 ) B C > , 0�* > 1 - @+! � - B 0 > . > ,#0 ) / > E % 0 , - B .

�R P����� ��7���A $ .�� % > 0 : , > ! , * ) - B 07��?6 � � # 1 , > @=) C > : , > ! , * ) - B 07��?6 .�B$ , > @=) C >�> E > 1 4 0 - ) B7��?7. " B 1 /�! B . >K� ) 1 ! ��2�) , , % *�! 1 > 1 ) B 0 > E 07���A $ #�6 / � - % 0'2#/ ) 1 ! � � > *+2#/ ) @7���A $ # $ � A � - % 0�! � � : , > ! , * ) - B 0 %7���A $ � � > E > 1 4 0 > ) B >?) ,#@=) , >�� - B > %7���$ -���� � - % 0�& ( )�� >�2#- 0 / � - B >�B 4 @ : > , %7�� � � 1 /�! B . >K� ) 1 ! ��2�) , , % *�! 1 > 1 ) B 0 > E 07��?7. " B ) * * ) % - 0 >?) �?7�� � �7�� ��� 5 $ ( 4 - 0'* > : 4 . @=) * >

�� ������ �?O� ��R�� � ��D��������� ���A # �5 A % ) 4 B *I! E - %'% 1 ! � - B .A . � B�7 1 ) B C > , 0�C > 1 0 ) ,#0 )3% ) 4 B *# � 1 � #�7 F#> ! * A 4 BI! 4 * - )K)�� ># �" 1 5 $ � L , - 0 >;A 4 BI! 4 * - )K)�� >� 5 B � 8 � � - B > ! ,#0 ) @34 ( � ! 2 1 ) B C > , % - ) B8 � � � 5 B @34 ( � ! 2 0 )3� - B > ! , 1 ) B C > , % - ) B

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Page 32: MATLAB Primer Third Edition

�?Q R ��R ��� ��O � ��� ��SD��������� ���# ��A ! : % ) � 4 0 >�C ! � 4 >?) , 1 ) @=* � > E @+! . B - 0 4 * ># B�]�� � * /�! % >�! B . � >A � 1 $ % ( 4�! , >;, ) ) 01 � # � , > ! �&*�! , 05 89# ] - @+! . - B�! , +;*�! , 06 .�B 1 ) @=* � > E 1 ) B " 4 . ! 0 >]�6 7 . , > ! 0 > % 0 1 ) @=@=) B�* - C - % ) ,� 6 8 � > ! % 0 1 ) @=@=) B @34 � 0 - * � >1 . � B�7 , ) 4 B * 0 ) B > ! , > % 0�- B 0 > . > ,� , ) 4 B * 0 ) 2'! , *+\ > , )��.�.�1 , ) 4 B * 0 ) 2'! , * � 6 � 5 � , ) 4 B * 0 ) 2'! , * A 5 ]�BY% - . B 4 @ � 4 B 1 0 - ) B1 � 8 , > @+! - B * > ,� �� > E * ) B > B 0 - ! � : ! % >?>� .�] B�! 0 4 , ! �� ) . ! , - 0 / @� .�]�� � � ) . : ! % > 3 �

��O� �� �� ���R ��O� �9��������� ���A 5 B �#�A 5 B ��A 5 B�� ��#�A 5 B�� % - B > 7 ! , 1 % - B > 7 / + * > , : ) � - 1 % - B > 7 / + * > , : ) � - 1 ! , 1 % - B >6 .�A ��#�6 .�A �?6 .�A � �#�6 .�A � 1 ) % - B > 7 ! , 1 1 ) % - B > 7 / + * > , : ) � - 1?1 ) % - B > 7 / + * > , : ) � - 1 ! , 1 1 ) % - B >$ # B ��# $ # B �$ # B�� �# $ # B�� 0 ! B . > B 0 7 ! , 1 0 ! B . > B 0 7 / + * > , : ) � - 1 0 ! B . > B 0 7 / + * > , : ) � - 1 ! , 1 0 ! B . > B 06 .�$ ��#�6 .�$ ��6 .�$ � �#�6 .�$ � 1 ) 0 ! B . > B 0 7 ! , 1 1 ) 0 ! B . > B 0 7 / + * > , : ) � - 1?1 ) 0 ! Bc 7 / + * > , : ) � - 1 ! , 1 1 ) 0 ! BcA � 6 ��#�A � 6 �?A � 6 � �#�A � 6 � % > 1 ! B 0 7 ! , 1 % > 1 ! B 0 7 / + * > , : ) � - 1 % > 1 ! B 0 7 / + * > , : ) � - 1 ! , 1 % > 1 ! B 06 A 6 ��#�6 A 6 ��6 A 6 � ��#�6 A 6 � 1 ) % > 1 ! B 0 7 ! , 1 1 ) % > 1 ! B 0 7 / + * > , : ) � - 1?1 ) % > 1 ! B 0 7 / + * > , : ) � - 1 ! , 1 1 ) % > 1 ! B 0

� V R��� ��Q���������� ������ A A � � : > % % > �� 4 B 1 0 - ) B��� $ # : > 0 !K� 4 B 1 0 - ) B]�# 8989# . ! @=@ !'� 4 B 1 0 - ) B1 # $ , ! 0 - ) B�! ��! * * , ) E - @+! 0 - ) B1 # $ A , ! 0 - ) B�! � ) 4 0 * 4 0� 1 0 > , , ) ,'� 4 B 1 0 - ) B� 1 0 5 B @ - B C > , % >?> , , ) ,'� 4 B 1 0 - ) B� � � 5 ��/�� 1 ) @=* � > 0 >�> � � - * 0 - 1 - B 0 > . , ! �� � � 5 ���� ! 1 ) : - ! B=> � � - * 0 - 1 - B 0 > . , ! �� ���5 B$ > E * ) B > B 0 - ! ��- B 0 > . , ! �� .�] � * - % % > 1 0'M ) ! 0 - B . * ) - B 0�B 4 @ : > , %��. " � % 1 ! � >�M ) ! 0 - B . * ) - B 0�B 4 @ : > , %

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Page 33: MATLAB Primer Third Edition

��� ��O� � �R��� ���V� � �� ���3�����J� ����� �O� � � �� ���5 B @ - B C > , % >� � � ! 1 0 ) , %?� , ) @ aK! 4 % % - ! B=> � - @=- B�! 0 - ) B1 1 � 0 , > * 4 1 > * , ) 22> 1 / > � ) B � ) , @6 ��.�� (�/ ) � > % , +3� ! 1 0 ) , - \ ! 0 - ) B� 1 ) , 0 / ) . ) B�! � ( 0 , - ! B . 4 � ! ,�* > 1 ) @=* ) % - 0 - ) BB�B�� A B ) B B > . ! 0 - C >�� > ! % 0'% ( 4�! , > %� A 6 . @ � > ! % 0'% ( 4�! , > %�- B=* , > % > B 1 > ) ��, B ) 2 1 ) C ! , - ! B 1 >B � � � B 4 � ��% *�! 1 >.�1 $ � ) , 0 / ) . ) B�! � - \ ! 0 - ) B� 5 ] > - . > B C ! � 4 > %'! B * > - . > B C > 1 0 ) , %��� A A � > % % > B : > , . � ) , @A 6 � � 1 A 1 / 4 ,'* > 1 ) @=* ) % - 0 - ) B6 7�0 � 1 7�0 1 ) @=* � > E�* - ! . ) B�! � � ) , @ 0 ) , > ! � : � ) 1 , * - ! . ) B�! � � ) , @1 A 0 � 6 A 0 , > ! � : � ) 1 ,3* - ! . ) B�! � � ) , @ 0 ) 1 ) @=* � > E3* - ! . ) B�! � � ) , @��# � # B�6 � * - ! . ) B�! ��% 1 ! � - B .K� ) ,#> - . > B C ! � 4 >�! 1 1 4 , ! 1 +� [ . > B > , ! � - \ > * > - . > B C ! � 4 > %��.�� -�� 5 ] * ) � + B ) @=- ! � > - . > B C ! � 4 >�% ) � C > ,A @ 7 % - B . 4 � ! ,?C ! � 4 >�* > 1 ) @=* ) % - 0 - ) B��5 B @ * % > 4 * ) - B C > , % >

��� ��O� �D�� ���� �� ��� ��6 .�B�7 1 ) B * - 0 - ) B=B 4 @ : > ,�- B 8 ( B ) , @1 6 .�B�7 < � � ��:�(�< , > 1 - * , ) 1 ! � 1 ) B * - 0 - ) B=B 4 @ : > ,�> % 0 - @+! 0 ) ,6 .�B�7� A $ � ! . > , � � - . /�! @ 1 ) B * - 0 - ) B B 4 @ : > ,�> % 0 - @+! 0 ) ,B�.�1 8 3 ( B ) , @ 7 8 ( B ) , @ 7 � ( B ) , @ 7 ( B ) , @B�.�1 89� A $ 8 ( B ) , @ > % 0 - @+! 0 ) ,1 # B�/ , ! B ,

�?Q R ��R ��� ��O � ��� ��O� �D��������� ���� ���8 @+! 0 , - E > E * ) B > B 0 - ! �� ���8 � & ( )�� >?- @=* � > @ > B 0 ! 0 - ) B ) ��� ���8� ���8 � @+! 0 , - E > E * ) B > B 0 - ! �C - !K;�! + � ) ,�% > , - > %� ���8�� @+! 0 , - E > E * ) B > B 0 - ! �C - !;> - . > B C ! � 4 > %'! B * > - . > B C > 1 0 ) , %� .�]�8 @+! 0 , - E�� ) . ! , - 0 / @A � 1 $ 8 @+! 0 , - E�% ( 4�! , >;, ) ) 00 � B�8 > C ! � 4�! 0 >?. > B > , ! �&@+! 0 , - EK� 4 B 1 0 - ) B��.�� - 1 /�! , ! 1 0 > , - % 0 - 1 * ) � + B ) @=- ! �7� $ * > 0 > , @=- B�! B 0$ 1 #�6 � 0 , ! 1 >

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Page 34: MATLAB Primer Third Edition

�' �Q �� ��� ��Q ���.�� - 1 ) B % 0 , 4 1 0�* ) � + B ) @=- ! � 2#- 0 / % * > 1 - ) > * , ) ) 0 %1 .�.�$ A * ) � + B ) @=- ! � , ) ) 0 % � 1 ) @=*�! B - ) B @+! 0 , - E @=> 0 / ) *1 .�.�$ A � * ) � + B ) @=- ! � , ) ) 0 % �J<! . 4 > , , > > %�@=> 0 / ) *��.�� - @ # � > C ! � 4�! 0 >�* ) � + B ) @=- ! ���.�� - @ # � 8 > C ! � 4�! 0 >�* ) � + B ) @=- ! � 2#- 0 /=@+! 0 , - E3! , . 4 @=> B 06 .�B @ @34 � 0 - * � +;* ) � + B ) @=- ! � %7� 6 .�B @ * - C - * >�* ) � + B ) @=- ! � %1 � A 5 7 � � *�! , 0 - ! � ( � , ! 1 0 - ) B > E *�! B % - ) B � , > % - * 4 > % ���.�� - ��$ ) 0#* ) � + B ) @=- ! � 0 )3*�! 0 !��.�� -7� 1 * - ��> , > B 0 - ! 0 >?* ) � + B ) @=- ! �

�� �Q ������� � � R �� � � �K����Q ��� �89# � ! , . > % 0 1 ) @=* ) B > B 0895 B % @+! � � > % 0 1 ) @=* ) B > B 089� # B ! C > , ! . >�) ,#@=> ! B C ! � 4 >89� 75 # B @=> * - ! B3C ! � 4 >A $ 7 % 0 ! B *�! , *+* > C - ! 0 - ) BA .�1 $ % ) , 0#- B+! % 1 > B * - B .=) , * > ,A � 8 % 4 @ ) ��> � > @=> B 0 %��1 .7 * , ) * 4 1 0#) ��> � > @=> B 0 %6 � 8 A � 8 1 4 @34 � ! 0 - C >'% 4 @ ) �> � > @=> B 0 %6 � 89��1 .7 1 4 @34 � ! 0 - C >#* , ) * 4 1 0#) ��> � > @=> B 0 %��5 A $ / - % 0 ) . , ! @

� �����Q �?O� ��R�� � ��# ��A 1 ) @=* � > E @+! . B - 0 4 * ># B�]�� � * /�! % >�! B . � >6 .�B @ 1 ) B C ) � 4 0 - ) B+! B *=* ) � + B ) @=- ! � @34 � 0 - * � - 1 ! 0 - ) B7� 6 .�B @ * > 1 ) B C ) � 4 0 - ) B+! B * * ) � + B ) @=- ! � * - C - % - ) B6 .�1 1 6 .�� 0 1 ) , , > � ! 0 - ) B 1 ) > � 1 - > B 0 %6 . @ 1 ) C ! , - ! B 1 >?@+! 0 , - E��� $ � 1 ) B > ( * - @=> B % - ) B�! ��* - . - 0 ! � )�� 0 > ,��� $ � 1 � 0 2�) ( * - @=> B % - ) B�! � * - . - 0 ! � )�� 0 > ,6 ��� ���# 5 1 % ) , 0#B 4 @ : > , %#- B 0 ) 1 ) @=* � > E *�! - , %� B " 1 # � , > @=) C >�* /�! % >�! B . � >�" 4 @=* %'! 1 , ) % % 9 � � � : ) 4 B *�! , - > %B�� �$ ��. " � B > E 0#/ - . / > ,#* ) 2�> ,�) � 8�?$ , ! * - E ( 8 � ! % 0 � ) 4 , - > ,#0 , ! B % � ) , @�?$ � 0 2�) ( * - @=> B % - ) B�! � � � ;5 �?$ - B C > , % >�� ! % 0 � ) 4 , - > ,#0 , ! B % � ) , @5 �?$ � - B C > , % > 8 ( H � � ;�?$ A ��5 0 $ \ > , ) ( 0 /I� ! . 0 ) 1 > B 0 > ,?) ��% * > 1 0 , 4 @

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Page 35: MATLAB Primer Third Edition

�� �� ��R � � � R O�R ���R��3������ �� � ��� ����R O�V� �Q � �� ��75 � ! * * , ) E - @+! 0 >'* > , - C ! 0 - C > %]�1 #�75 � B$ ! * * , ) E - @+! 0 >#. , ! * - > B 07� � � )�C >?* ) - B 0'* - % 1 , > 0 >�<! * � ! 1 - ! BA � ��A ��#�6 � ! B . � > : > 0 2�> > B 0 2�)�% 4 : % *�! 1 > %A ��� 5 B�� 1 4 : - 1 % * � - B >?- B 0 > , * ) � ! 0 - ) B5 B$ � 1 � � 3 ( HJ*�! 0 ! - B 0 > , * ) � ! 0 - ) B5 B$ � 1 � � 8 ( HJ*�! 0 ! - B 0 > , * ) � ! 0 - ) B5 B$ � 1 �0 $ 3 ( HJ*�! 0 ! - B 0 > , * ) � ! 0 - ) B C - ! � � ;2@=> 0 / ) *]�1 5 7�7# $ # *�! 0 ! . , - * * - B .

������R O� ����Q�� ����R��O�� �� ��

��� #�7 ! *�! * 0 - C > 8 ( *�! B > �&A - @=* % ) B> %?F'4 � >��� #�7�� ! *�! * 0 - C > 6 ( *�! B > � � > 2#0 ) B ( (�) 0 > %�F'4 � >$ 1 # ��[ 0 , ! * > \ ) - *�! ��@=> 0 / ) *

� � � R O�R ���� ��Q ������� �� ����� �Q ���� ��.7� � � 8 B * � 9 , *=) , * > ,�F'4 B . > ( <�4 0 0 ! @=> 0 / ) *.7� � � � % ) � C >�C - !K.7� � � 7 * - % * � ! + - B .;* � ) 0.7� � b 0 / � � 0 /=) , * > ,�F'4 B . > ( <�4 0 0 ! ( � > / � : > , . @=> 0 / ) *

�K ���Q ��R ��O ������� �� ���3�������KV �� �� � � �� ��0 895 B @=- B - @ - \ >?� 4 B 1 0 - ) B=) �) B >KC ! , - ! : � >0 895 B�A @=- B - @ - \ >?� 4 B 1 0 - ) B=) ��% > C > , ! ��C ! , - ! : � > %0 A .�� @ � % ) � 4 0 - ) B=0 ) !K% + % 0 > @�) �B ) B � - B > ! ,#> ( 4�! 0 - ) B %

� ) B *+\ > , ) %�) �?!�� 4 B 1 0 - ) B ) ��% > C > , ! �C ! , - ! : � > % �0 [ � 1 . ) B *+\ > , )=) �� 4 B 1 0 - ) B ) �) B >�C ! , - ! : � >0 ��� .�$ * � ) 0�. , ! * / ) ��!K� 4 B 1 0 - ) B

M=Q

Page 36: MATLAB Primer Third Edition

� � � ��R �� �����Q � O���V S���� .�$ � - B > ! ,#* � ) 0� .�]�� .�] � ) . ( � ) .K% 1 ! � >?* � ) 0A � 895 � .�]� % > @=- � ) .K% 1 ! � >?* � ) 0A � 895 � .�]�- % > @=- � ) .K% 1 ! � >?* � ) 0��� � * , ! 2D)�� � > * 8 ( H2* ) � + . ) B %��.�� # 1 * ) � ! , 1 ) ) , * - B�! 0 >;* � ) 0��# 1 : ! ,#. , ! * /A $ # 5 1 A % 0 ! - , % 0 > * * � ) 0� 1 1 .�1 ��# 1 > , , ) , : ! ,#* � ) 0��5 A $ / - % 0 ) . , ! @ * � ) 01 .�A � ! B . � >�/ - % 0 ) . , ! @ * � ) 06 .�89��#�A A 1 ) @=*�! % %�* � ) 00 � # $ ��� 1 � > ! 0 / > ,�* � ) 00 ��� .�$ * � ) 0�� 4 B 1 0 - ) B

� O���V S��K��� �� � �� ��$ 5 $ � � . , ! * / 0 - 0 � >�� # ��� � E ( ! E - %'� ! : > �-�� # ��� � + ( ! E - %'� ! : > �[ � # ��� � \ ( ! E - %'� ! : > ��� ) , 9 ( H2* � ) 0 %]�1 5 7 . , - *+� - B > %$ � �$ 0 > E 0�! B B ) 0 ! 0 - ) B]�$ � �$ @=) 4 % >?* � ! 1 > @=> B 0�) �0 > E 0]�5 B�� � $ . , ! * / - 1 ! ��- B * 4 0?� , ) @ @=) 4 % >

�� ���O�R�T� ���� ��� ���� �3��O�R � �� �� �������� �����O� �Q��] � 1 � 1 , > ! 0 >K) . 4 , > � . , ! * /+2#- B * ) 2 �]�6 0 . > 0�/�! B * � >�0 ) 1 4 , , > B 0') . 4 , >6 � 0 1 � > ! , 1 4 , , > B 0') . 4 , >6 � .�A � 1 � ) % >�) . 4 , >��.�� 7 / ) � * 1 4 , , > B 0�. , ! * /5 A ��.�� 7 , > 0 4 , B / ) � *+% 0 ! 0 4 %A � ����� .�$ 1 , > ! 0 >3! E > %#- B=0 - � > * * ) % - 0 - ) B %# �� A 1 , > ! 0 >3! E > %#- B+! , : - 0 , ! , +=* ) % - 0 - ) B %]�6 # . > 0�/�! B * � >�0 ) 0 ) 1 4 , , > B 0�! E > %# �5 A 1 ) B 0 , ) ��! E - %?% 1 ! � - B . ! B *+! * * > ! , ! B 1 >6 # �5 A 1 ) B 0 , ) �&* % > 4 * ) 1 ) � ) ,�! E - %?% 1 ! � - B .

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Page 37: MATLAB Primer Third Edition

� O���V S�����O����� �V �D������� � �O����R��1 5 B$ * , - B 0#. , ! * / ) ,?% ! C >?. , ! * / 0 )�)�� >��1 5 B$ .���$ 1 ) B ) . 4 , >K� ) 1 ! ��* , - B 0 > ,'* > � ! 4 � 0 %.�1 5 � B$ % > 0�*�! * > ,�) , - > B 0 ! 0 - ) B

��S�O�R R � ��R �� �����Q � O���V S�89� A � 9 ( H2@=> % /+% 4 , � ! 1 >89� A ��6 1 ) @ : - B�! 0 - ) B @=> % / � 1 ) B 0 ) 4 ,�* � ) 089� A ��[ 9 ( H2@=> % /+2#- 0 / \ > , )=* � ! B >A � 1 0 9 ( HJ% /�! * > *I% 4 , � ! 1 >A � 1 0 6 1 ) @ : - B�! 0 - ) B3% 4 , � ! 1 > � 1 ) B 0 ) 4 ,#* � ) 0A � 1 0 � 9 ( HJ% /�! * > *I% 4 , � ! 1 >K2#- 0 / � - . / 0 - B .��� .�$ � * � ) 0?� - B > %�! B * * ) - B 0 %#- B 9 ( HJ% *�! 1 >��� � � * , ! 2D)�� � > * 9 ( H * ) � + . ) B %�- B 9 ( HJ% *�! 1 >6 .�B$ . � 1 1 ) B 0 ) 4 ,#* � ) 06 .�B$ . � 1 � 9 ( H 1 ) B 0 ) 4 ,#* � ) 06 � # ��� � 1 ) B 0 ) 4 ,#* � ) 0#> � > C ! 0 - ) B � ! : > � %6 .�B$ . � 1 6 1 ) B 0 ) 4 ,#* � ) 0 1 ) @=* 4 0 ! 0 - ) B � 4 % > * : + �&�2L"1��26"? ��?6 .�� .�1 * % > 4 * ) 1 ) � ) , � 1 / > 1 , > , : ) ! , *��#* � ) 0��� 5 @ � 1 ( 4 - C > ,#* � ) 05 89# ]��Y* - % * � ! + - @+! . >" # $ � 1 0 # � � 2'! 0 > , � ! � ��* � ) 0A � 5 6 � C ) � 4 @=> 0 , - 1 C - % 4�! � - \ ! 0 - ) B * � ) 0

� � � O���V S��KV V R ��O������R@ 5 � " 9 ( H2. , ! * /+C - > 2#* ) - B 0?% * > 1 - ) 1 ! 0 - ) B@ 5 � " 8�$ ^C - > 220 , ! B % � ) , @+! 0 - ) B @+! 0 , - 1 > %��5 7�7� B @=> % /=/ - * * > B+� - B >?, > @=) C ! � @=) * >A ��#�75 B�] 1 ) � ) ,'% /�! * - B . @=) * ># �5 A ! E - %?% 1 ! � - B . ! B *+! * > ! , ! B 1 >6 # �5 A * % > 4 * ) 1 ) � ) ,�! E - %?% 1 ! � - B .A ��� 6 � � # 1 % * > 1 4 � ! ,�, > M > 1 0 ! B 1 >75 � � A � * - ��4 % >;, > M > 1 0 ! B 1 >A � 1 0 B�.�1 8 % 4 , � ! 1 >;B ) , @+! � %6 .�� .�1 89# � 1 ) � ) ,'� ) ) , 4 *=0 ! : � > � % > > : > � ) 2 ���1 5 ]��$ � B : , - . / 0 > B ) ,'*�! , , > B 1 ) � ) ,#@+! *A ��5 B�89# � % * - B 1 ) � ) ,�@+! *1 ]������ .�$ * � ) 0 1 ) � ) , @+! *��A @ � 1 ]�� / % C=0 ) , . : 1 ) � ) ,�@+! * 1 ) B C > , % - ) B1 ]�� � ��A @ , . : 0 ) / % C 1 ) � ) ,�@+! * 1 ) B C > , % - ) B

M/M

Page 38: MATLAB Primer Third Edition

�� �Q �OJ����V����A @ / 4 > ( % ! 0 4 , ! 0 - ) B ( C ! � 4 > � * > � ! 4 � 0 � � $ C ! , - ! B 0�) � 30D I]�1 # - � - B > ! ,#. , ! + ( % 1 ! � >��.�$ : � ! 1 , ( , > * ( + > � � ) 2?( 2#/ - 0 >6 .�.��_% /�! * > %�) � 1 + ! BI! B * @+! . > B 0 !��.�B�� . , ! + ( % 1 ! � >�2#- 0 /=0 - B . >?) � : � 4 >6 .������ 1 � - B > ! , 1 ) * * > ,�0 ) B >��5 B�/ *�! % 0 > �% /�! * > %�) �* - B ,��# ] ! � 0 > , B�! 0 - B . , > * 7 2#/ - 0 > 7 : � 4 > 7 ! B * : � ! 1 ,

� � �KP � R�����A ����� 1 � . > B > , ! 0 >K% * / > , >6 -�� 5 B�7� 1 . > B > , ! 0 > 1 + � - B * > ,��� # /A . > B > , ! 0 >K* > @=)�% 4 , � ! 1 >

�9 ��� R����������K�� ��� �� ��89. @ 5 � 5 B - B - 0 - ! � - \ >#@=) C - >?� , ! @=>�@=> @=) , +]�� $ 0 1 # 89� . > 0#@=) C - >?� , ! @=>89. @ 5 � * � ! + , > 1 ) , * > * @=) C - >?� , ! @=> %

�������Q R � O���V S� ���)�KP � R�������] � 1 � 1 , > ! 0 >K) . 4 , >�2#- B * ) 2# �� A 1 , > ! 0 >3! E > %� 5 B�� 1 , > ! 0 >�� - B >$ � �$ 1 , > ! 0 > 0 > E 0��# $ 6 � 1 , > ! 0 > *�! 0 1 /A � 1 0 #�6 � 1 , > ! 0 >�% 4 , � ! 1 >5 89# ]�� 1 , > ! 0 > - @+! . >� 5 6 .�B$ 1 .�� 1 , > ! 0 >�4 % > ,�- B 0 > , � ! 1 > 1 ) B 0 , ) �� 5 89� B � 1 , > ! 0 >�4 % > ,�- B 0 > , � ! 1 >?@=> B 4

�������Q R � O���V S� ��� �KV R O�� �� ���A � $ % > 0�) : " > 1 0�* , ) * > , 0 - > %]�� $ . > 0#) : " > 1 0�* , ) * > , 0 - > %1 � A � $ , > % > 0?) : " > 1 0#* , ) * > , 0 - > %7� � � $ � * > � > 0 >;) : " > 1 071 # " B�. " M�4 % / * > B * - B . . , ! * / - 1 %#> C > B 0 %

M2�

Page 39: MATLAB Primer Third Edition

� V ��O� R ��� ��O� �D��������� ���A �?75 # ]�A % *�! , % > @+! 0 , - EK� ) , @=> *�� , ) @Z* - ! . ) B�! � %A ��� -�� % *�! , % > - * > B 0 - 0 + @+! 0 , - EA ��1 # B�7BY% *�! , % > , ! B * ) @ @+! 0 , - EA ��.�B�� A , > * � ! 1 >;B ) B \ > , )=> B 0 , - > %�2#- 0 /=) B > %A ��1 # B�7�A -�8 % *�! , % >�% + @=@=> 0 , - 1 , ! B * ) @ @+! 0 , - EA �0 � B ! * * � +3� 4 B 1 0 - ) B=0 ) B ) B \ > , ) > B 0 , - > %

A ��# 1 A � 1 , > ! 0 >�% *�! , % >;@+! 0 , - E 1 ) B C > , 0'� 4 � ��@+! 0 , - E 0 )�% *�! , % >0 � � � 1 ) B C > , 0�% *�! , % >;@+! 0 , - E 0 )�� 4 � � @+! 0 , - E��B�7 ) B * - B * - 1 > %�) �B ) B \ > , )=> B 0 , - > %A �?6 .�B @ � 1 $ 1 ) B C > , 0'� , ) @Z% *�! , % >;@+! 0 , - E > E 0 > , B�! �� ) , @+! 0

5 A A ��# 1 A � 0 , 4 >;- �@+! 0 , - E - %'% *�! , % >B�B�[ B 4 @ : > ,#) �B ) B \ > , ) > B 0 , - > %B�.�B�[ � 1 .�A B ) B \ > , )=> B 0 , - > %B�[ 89# ! @=) 4 B 0�) ��% 0 ) , ! . >K! � � ) 1 ! 0 > *3� ) ,#B ) B \ > , )=> B 0 , - > %A ��# � � .6 ! � � ) 1 ! 0 >?@=> @=) , +�� ) ,#B ) B \ > , ) > B 0 , - > %

A �- C - % 4�! � - \ >�% *�! , % - 0 + % 0 , 4 1 0 4 , >]���� .�$ * � ) 0#. , ! * / 7 ! %#- B�� . , ! * / 0 / > ) , + �

6 .�� 898 7 1 ) � 4 @=B=@=- B - @�4 @�* > . , > >6 .�� ��� 1 8 ) , * > , 1 ) � 4 @=B % : ! % > * ) B B ) B \ > , ) 1 ) 4 B 0789��� 1 8 H�4 � @+! . > ( & > B * > � % ) / B * > 1 ) @=* ) % - 0 - ) B1 # B�7��� 1 8 , ! B * ) @ * > , @34 0 ! 0 - ) B3C > 1 0 ) ,A -�89898 7 % + @=@=> 0 , - 1 @=- B - @�4 @�* > . , > >A -�891 6 8 , > C > , % > (?4 0 / - � � ( & 1 <?> >?) , * > , - B .

6 .�B�7� A $ > % 0 - @+! 0 > 3 ( B ) , @ 1 ) B * - 0 - ) BB�.�1 89� A $ > % 0 - @+! 0 > 8 ( B ) , @A ��1 # B�/ % 0 , 4 1 0 4 , ! �, ! B ,

A ��# � ]�89� B$ � ) , @ � > ! % 0'% ( 4�! , > %�! 4 . @=> B 0 > * % + % 0 > @A ����# 1 8 A % > 0�*�! , ! @=> 0 > , %?� ) ,'% *�! , % >;@+! 0 , - E , ) 4 0 - B > %A -�8$�0 #�6 $ % + @ : ) � - 1 � ! 1 0 ) , - \ ! 0 - ) BI! B�! � + % - %A ��# 1 A � 0 � B % *�! , % >3! 4 E - � � ! , +K� 4 B 1 0 - ) B %�! B *=*�! , ! @=> 0 > , %

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