Giáo trình Matlab toàn tập
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MatlabꢀtoꢁnꢀtËpꢀ
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cꢁiꢀꢀ®Ætꢀꢀ
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1.ꢀMATLABꢀforꢀWINꢀ
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YªuꢀcÇuꢀhÖꢀthèngꢀ
HÖꢀthèngꢀIBMꢀhoÆcꢀt−¬ngꢀthÝchꢀ100%ꢀvíiꢀbéꢀviꢀxöꢀlÝꢀ486ꢀIntelꢀcéngꢀvíiꢀbéꢀ®ångꢀxöꢀlÝꢀto¸nꢀ
häcꢀ 487ꢀ (ꢀ ngo¹iꢀ trõꢀ 486ꢀ DXꢀ ꢀ cãꢀ béꢀ xöꢀ lÝꢀ bªnꢀ trongꢀ ),ꢀ Pentiumꢀ hoÆcꢀ Pentiumꢀ Proꢀ
Processor.ꢀ
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MicrosoftꢀWindowꢀ95ꢀhoÆcꢀWindowꢀNT.ꢀ
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a)ꢀꢀæꢀCDꢀROMꢀ
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ꢀꢀꢀꢀꢂꢀꢀBéꢀ®iÒuꢀphèiꢀ®åꢀho¹ꢀ8ꢀbitꢀꢀvꢁꢀcardꢀmꢁnꢀh×nhꢀ(ꢀ256ꢀmꢁuꢀ®ångꢀthêiꢀ)ꢀ
ꢀꢀꢀꢀꢂꢀꢀKho¶ngꢀtrèngꢀ®Üaꢀ®ñꢀ®Óꢀcꢁiꢀ®Ætꢀvꢁꢀch¹yꢀc¸cꢀtuúꢀchän.ꢀSùꢀyªuꢀcÇuꢀ®Üaꢀcøngꢀthayꢀ®æiꢀtuúꢀ
theoꢀkÝchꢀcìꢀc¸cꢀpartitionꢀvꢁꢀc¸cꢀtÖpꢀtrîꢀgiópꢀhelpꢀ®−îcꢀcꢁiꢀ®ÆtꢀtrùcꢀtiÕpꢀtheoꢀtuúꢀchän.ꢀQu¸ꢀ
tr×nhꢀcꢁiꢀ®ÆtꢀsÏꢀth«ngꢀb¸oꢀchoꢀb¹nꢀbiÕtꢀtØꢀmØꢀvÒꢀdungꢀl−îngꢀ®ÜaꢀyªuꢀcÇu.ꢀVÝꢀdô:ꢀ
ꢀ PartitionꢀvíiꢀmétꢀliªnꢀcungꢀmÆtꢀ0ꢀcÇnꢀꢀ25ꢀMBꢀchoꢀriªngꢀMATLABꢀvꢁꢀ50ꢀMBꢀchoꢀc¶ꢀ
MATLABꢀvꢁꢀHELP.ꢀ
ꢀ Partitionꢀ víiꢀ liªnꢀ cungꢀ 64ꢀ KBꢀ cÇnꢀ 115ꢀ MBꢀ choꢀ riªngꢀ MATLABꢀ vꢁꢀ 250ꢀ MBꢀ choꢀ c¶ꢀ
MATLABꢀvꢁꢀHELP.ꢀ
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bꢀ)ꢀBéꢀnhí.ꢀ
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MicrosoftꢀWIndowꢀ95:ꢀ8ꢀMBꢀtèiꢀthiÓuꢀvꢁꢀ16ꢀMBꢀkhuyÕnꢀnghÞ.ꢀ
MicrosoftꢀWINꢀNTꢀ3.51ꢀhoÆcꢀ4.0:ꢀ12ꢀMBꢀtèiꢀthiÓuꢀvꢁꢀ16ꢀMBꢀkhuyÕnꢀnghÞ.ꢀ
ꢀꢀ
C¸cꢀkhuyÕnꢀnghÞꢀ
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Béꢀnhíꢀphôꢀvꢁoꢀ(Béꢀnhíꢀbæꢀsung:ꢀadditionalꢀMemory).ꢀ
VØꢀm¹chꢀt¨ngꢀtècꢀ®åꢀho¹ꢀbæꢀꢀtrîꢀchoꢀMicrosoftꢀWindow.ꢀ
M¸yꢀinꢀtrîꢀgiópꢀchoꢀMicrosoftꢀWindow.ꢀ
VØꢀm¹chꢀ©mꢀthanhꢀtrîꢀgiópꢀchoꢀMicrosoftꢀWindow.ꢀ
MicrosoftꢀWordꢀ7.0ꢀhoÆcꢀh¬nꢀꢀ(ꢀnÕuꢀb¹nꢀcãꢀýꢀ®ÞnhꢀsöꢀdôngꢀMATLABꢀꢀNoteBookꢀ).ꢀ
Tr×nhꢀbiªnꢀdÞchꢀWatcomꢀC,ꢀBorland,ꢀMicrosoftꢀ(x©yꢀdùngꢀfileꢀMEX).ꢀ
NetscapeꢀNavigatorꢀ2.0ꢀhoÆcꢀversionꢀcaoꢀh¬nꢀhoÆcꢀMicrosoftꢀInternetꢀExplorerꢀ3.0ꢀ®Óꢀ
ch¹yꢀMATLABꢀHelpꢀDesk.ꢀ
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Qu¸ꢀtr×nhꢀcꢁiꢀ®Æt
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ꢀꢀꢀꢀ1.ꢀꢀ§Ætꢀ®ÜaꢀvꢁoꢀæꢀCD.ꢀTrªnꢀWINꢀ95ꢀch−¬ngꢀtr×nhꢀSETUPꢀb¾tꢀ®Çuꢀch¹yꢀtùꢀ®éngꢀnÕuꢀnh−ꢀ
MATLABꢀchaꢀ®−îcꢀcꢁiꢀtõꢀtr−íc.ꢀCßnꢀkh«ng,ꢀnhÊnꢀ®ópꢀvꢁoꢀbiÓuꢀt−îngꢀsetup.exeꢀ®Óꢀb¾tꢀ®Çuꢀ
qu¸ꢀtr×nhꢀcꢁiꢀ®Æt.ꢀ
ꢀꢀꢀꢀ2.ꢀꢀꢀChÊpꢀnhËnꢀhayꢀbáꢀ®iꢀnh÷ngꢀkhuyÕnꢀc¸oꢀvÒꢀcÊpꢀ®¨ngꢀkÝꢀphÇnꢀmÒmꢀtrªnꢀmꢁnꢀh×nh.ꢀ
NÕuꢀchÊpꢀnhËnꢀb¹nꢀmíiꢀcãꢀthÓꢀb¾tꢀ®Çuꢀqu¸ꢀtr×nhꢀcꢁiꢀ®Æt.ꢀ
ꢀꢀꢀꢀ3.ꢀꢀꢀTrªnꢀCustumerꢀInformation,ꢀnhËpꢀvꢁoꢀtªnꢀb¹n,ꢀ®ÞaꢀchØꢀcñaꢀb¹n.ꢀTªnꢀkh«ngꢀ®−îcꢀqu¸ꢀ
30ꢀkÝꢀtù.ꢀNhÊnꢀnótꢀNEXT.ꢀ
ꢀꢀꢀꢀ4.ꢀꢀꢀNhÊnꢀvꢁoꢀc¸cꢀhépꢀtrèngꢀthꢁnhꢀphÇnꢀdÊuꢀ v ꢀnÕuꢀꢀnh−ꢀb¹nꢀmuènꢀtuúꢀchänꢀ®ãꢀvꢁꢀ
nhÊnꢀtiÕpꢀnÕuꢀb¹nꢀcãꢀýꢀ®Þnhꢀkh«ngꢀmuènꢀtuúꢀchänꢀ®ãꢀ(ꢀcãꢀthÓꢀthªmꢀvꢁoꢀsauꢀnꢁyꢀnÕuꢀmuènꢀ
2
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).ꢀTrªnꢀmꢁnꢀh×nhꢀhiÓnꢀthÞꢀꢀC:\MATLABꢀlꢁꢀth−ꢀmôcꢀ®ÝchꢀmÆcꢀ®Þnhꢀcñaꢀqu¸ꢀtr×nhꢀcꢁiꢀ®Æt.ꢀNÕuꢀ
b¹nꢀmuènꢀcꢁiꢀ®Ætꢀvꢁoꢀth−ꢀmôcꢀkh¸cꢀhoÆcꢀ®æiꢀtªnꢀth−ꢀmôcꢀth×ꢀb¹nꢀlùaꢀchänꢀBrowse.ꢀ
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MATLABꢀchoꢀMacintosh.ꢀ
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MATLABꢀchoꢀm¸yꢀMacintoshꢀꢀch¹yꢀ®−îcꢀtrªn:ꢀ
Mäiꢀm¸yꢀMacintoshꢀcãꢀcÊuꢀh×nhꢀ®ñꢀm¹nhꢀ(ꢀpowerꢀMacintoshꢀ).ꢀ
MäiꢀMacintoshꢀꢀ®−îcꢀtrangꢀbÞꢀꢀbéꢀviꢀxöꢀlÝꢀꢀ68040ꢀ(ꢀbéꢀ®ångꢀxöꢀlÝꢀto¸nꢀhäcꢀbªnꢀtrongꢀ).ꢀ
Mäiꢀm¸yꢀMacintoshꢀ®−îcꢀtrangꢀbÞꢀbéꢀviꢀxöꢀlÝꢀ68020ꢀhoÆcꢀ68030ꢀꢀvꢁꢀbéꢀ®ångꢀxöꢀlÝꢀto¸nꢀ
häcꢀꢀ68881ꢀhoÆcꢀ68882.ꢀ
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YªuꢀcÇuꢀtèiꢀthiÓuꢀ®Óꢀch¹yꢀMATLAB.ꢀ
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ꢀ§Üaꢀ cøngꢀ trèngꢀ tèiꢀ thiÓuꢀ 26ꢀ MB,ꢀ cÇnꢀ thªmꢀ 60ꢀ MBꢀ choꢀ hÖꢀ thèngꢀ tuúꢀ chonꢀ HELPꢀ trùcꢀ
tuyÕn.ꢀ
16ꢀMBꢀchoꢀph©nꢀvïngꢀbéꢀnhí.ꢀ
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æꢀCDꢀROM.ꢀ
ColorꢀQuickꢀDraw.ꢀꢀ
ꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂoOoꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢀ
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Ch−¬ng1ꢀ
GIíIꢀTHIÖUꢀchung
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ꢀꢀꢀꢀꢀꢀB©ygiêꢀ b¹nꢀ ®ꢃꢀ cꢁiꢀ ®Ætꢀ xong,ꢀ chóngꢀ taꢀ hꢃyꢀ xemꢀ MATLABꢀ cãꢀ thÓꢀ lꢁmꢀ ®−îcꢀ nh÷ngꢀ g×.ꢀ
TrongꢀphÇnꢀnꢁyꢀchóngꢀtaꢀsÏꢀtr×nhꢀbꢁyꢀmétꢀsèꢀnh÷ngꢀøngꢀdôngꢀcñaꢀnã;ꢀv×ꢀ®Óꢀtr×nhꢀbꢁyꢀtÊtꢀc¶ꢀ
nh÷ngꢀøngꢀdôngꢀcñaꢀMATLABꢀsÏꢀrÊtꢀdꢁiꢀvꢁꢀtènꢀthêiꢀgian.ꢀNÕuꢀb¹nꢀ®äcꢀquyÓnꢀh−íngꢀdÉnꢀ
nꢁy,ꢀb¹nꢀsÏꢀthÊyꢀMATLABꢀlꢁꢀng«nꢀng÷ꢀrÊtꢀm¹nhꢀ®Óꢀgi¶iꢀquyÕtꢀnh÷ngꢀvÊnꢀ®Òꢀquanꢀträngꢀvꢁꢀ
khãꢀkh¨nꢀcñaꢀb¹n.ꢀNãꢀsÏꢀrÊtꢀh÷uꢀÝchꢀkhiꢀb¹nꢀ®äcꢀphÇnꢀh−íngꢀdÉnꢀc¬ꢀb¶nꢀv×ꢀnãꢀsÏꢀcungꢀcÊpꢀ
choꢀb¹nꢀ nh÷ngꢀkiÕnꢀthøcꢀc¬ꢀb¶nꢀ ®Óꢀb¹nꢀ hiÓuꢀrâꢀMATLABꢀvꢁꢀph¸tꢀtriÓnꢀ®−îcꢀ nh÷ngꢀkh¶ꢀ
n¨ngꢀcñaꢀm×nhꢀsauꢀnꢁy.ꢀ
CãꢀlÏꢀc¸chꢀdÔꢀnhÊtꢀ®Óꢀh×ngꢀdungꢀvÒꢀMATLABꢀlꢁꢀnãꢀcãꢀ®Çyꢀ®ñꢀc¸cꢀ®Æcꢀ®iÓmꢀcñaꢀm¸yꢀ
tÝnhꢀc¸ꢀnh©n:ꢀgièngꢀnh−ꢀc¸cꢀm¸yꢀtÝnhꢀc¬ꢀb¶n,ꢀnãꢀlꢁmꢀtÊtꢀc¶ꢀc¸cꢀphÐpꢀtÝnhꢀto¸nꢀhäcꢀc¬ꢀb¶nꢀ
nh−ꢀcéng,ꢀtrõ,ꢀnh©n,ꢀchia;ꢀgièngꢀnh−ꢀm¸yꢀtÝnhꢀküꢀthuËt,ꢀnãꢀbaoꢀgåm:ꢀsèꢀphøc,ꢀc¨nꢀthøc,ꢀsèꢀ
mò,ꢀlogarithm,ꢀc¸cꢀphÐpꢀto¸nꢀl−îngꢀgi¸cꢀnh−ꢀsine,ꢀcosine,ꢀtang;ꢀnãꢀcòngꢀgièngꢀnh−ꢀm¸yꢀtÝnhꢀ
cãꢀkh¶ꢀn¨ngꢀlËpꢀtr×nh,ꢀcãꢀthÓꢀl−uꢀtr÷,ꢀt×mꢀkiÕmꢀl¹iꢀd÷ꢀliÖu,ꢀcòngꢀcãꢀthÓꢀt¹o,ꢀb¶oꢀvÖꢀvꢁꢀghiꢀtr×nhꢀ
tùꢀc¸cꢀlÖnhꢀ®Óꢀtùꢀ®éngꢀphÐpꢀto¸nꢀkhiꢀgi¶iꢀquyÕtꢀc¸cꢀvÊnꢀ®Ò,ꢀb¹nꢀcãꢀthÓꢀsoꢀs¸nhꢀlogic,ꢀ®iÒuꢀ
khiÓnꢀthùcꢀhiªnꢀlÖnhꢀ®Óꢀ®¶mꢀb¶oꢀtÝnhꢀ®óngꢀ®¾nꢀcñaꢀphÐpꢀto¸n.ꢀGièngꢀnh−ꢀc¸cꢀm¸yꢀtÝnhꢀhiÖnꢀ
®¹iꢀnhÊt,ꢀnãꢀchoꢀphÐpꢀb¹nꢀbiÓuꢀdiÔnꢀd÷ꢀliÖuꢀdíiꢀnhiÒuꢀd¹ngꢀnh−:ꢀbiÓuꢀdiÔnꢀth«ngꢀth−êng,ꢀmaꢀ
tr©nꢀ®¹iꢀsè,ꢀc¸cꢀhꢁmꢀtæꢀhîpꢀvꢁꢀcãꢀthÓꢀthaoꢀt¸cꢀvíiꢀd÷ꢀliÖuꢀth−êngꢀcòngꢀnh−ꢀ®èiꢀvíiꢀmaꢀtrËn.ꢀꢀꢀ
TrongꢀthùcꢀtÕꢀMATLABꢀcßnꢀøngꢀdôngꢀrÊtꢀréngꢀrꢃiꢀtrongꢀnhiÒuꢀlÜnhꢀvùcꢀvꢁꢀnãꢀcòngꢀsöꢀ
dôngꢀrÊtꢀnhiÒuꢀc¸cꢀphÐpꢀtÝnhꢀto¸nꢀhäc.ꢀVíiꢀnh÷ngꢀ®Æcꢀ®iÓmꢀ®ãꢀvꢁꢀkh¶ꢀn¨ngꢀth©nꢀthiÖnꢀvíiꢀ
ng−êiꢀsöꢀdôngꢀnªnꢀnãꢀdÔꢀdꢁngꢀsöꢀdôngꢀh¬nꢀc¸cꢀng«nꢀng÷ꢀkh¸cꢀnh−ꢀBasic,ꢀPascal,ꢀC.ꢀ
NãꢀcungꢀcÊpꢀmétꢀm«iꢀtr−êngꢀphongꢀphóꢀchoꢀbiÓuꢀdiÔnꢀd÷ꢀliÖu,ꢀvꢁꢀcãꢀkh¶ꢀn¨ngꢀm¹nhꢀmÏꢀ
vÒꢀ®åꢀho¹,ꢀb¹nꢀcãꢀthÓꢀt¹oꢀc¸cꢀgiaoꢀdiÖnꢀriªngꢀchoꢀng−êiꢀsöꢀdông(GUIs)ꢀ®Óꢀg¶iꢀquyÕtꢀnh÷ngꢀ
vÊnꢀ®Òꢀriªngꢀchoꢀm×nh.ꢀThªmꢀvꢁoꢀ®ãꢀMATLABꢀ®−aꢀraꢀnh÷ngꢀc«ngꢀcôꢀ®Óꢀgi¶iꢀquyÕtꢀnh÷ngꢀ
vÊnꢀ®Òꢀ®ÆcꢀbiÖt,ꢀgäiꢀlꢁꢀToolboxꢀ(hépꢀc«ngꢀcô).ꢀVÝꢀdôꢀStudentꢀEditionꢀcñaꢀMATLABꢀbaoꢀgåmꢀ
c¶ꢀToolboxꢀ®iÒuꢀkhiÓnꢀhÖꢀthèng,ꢀToolboxꢀxöꢀlÝꢀtÝnꢀhiÖu,ꢀToolboxꢀbiÓuꢀt−îngꢀto¸nꢀhäc.ꢀNgoꢁiꢀ
raꢀb¹nꢀcãꢀthÓꢀt¹oꢀToolboxꢀchoꢀriªngꢀm×nh.ꢀ
Víiꢀnh÷ngꢀkh¶ꢀn¨ngꢀm¹nhꢀmÏ,ꢀréngꢀlínꢀcñaꢀMATLABꢀnªnꢀnãꢀrÊtꢀcÇnꢀthiÕtꢀchoꢀb¹nꢀb¾tꢀ
®ÇuꢀtõꢀphÇnꢀc¬ꢀb¶n.ꢀSauꢀ®©yꢀchóngꢀtaꢀsÏꢀnghiªnꢀcøuꢀtõngꢀphÇn,ꢀvꢁꢀcuènꢀs¸chꢀnꢁyꢀsÏꢀgiópꢀ
3
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b¹nꢀhiÓuꢀ®−îcꢀchóng.ꢀTr−ícꢀtiªn,ꢀmétꢀc¸chꢀ®¬nꢀgi¶nꢀnhÊtꢀlꢁꢀchóngꢀtaꢀquanꢀniÖmꢀnh−ꢀlꢁꢀmétꢀ
m¸yꢀtÝnhꢀc¬ꢀb¶n,ꢀtiÕpꢀtheoꢀlꢁꢀnh−ꢀm¸yꢀtÝnhꢀküꢀthuËtꢀvꢁꢀnh−ꢀm¸yꢀtÝnhꢀcãꢀthÓꢀlËpꢀtr×nhꢀ®−îc,ꢀ
cuèiꢀcïngꢀlꢁꢀnh−ꢀm¸yꢀtÝnhꢀhiÖnꢀ®¹iꢀnhÊt.ꢀB»ngꢀc¸chꢀquanꢀniÖmꢀnꢁyꢀb¹nꢀsÏꢀdÔꢀdꢁngꢀhiÓuꢀ
®ù¬cꢀnh÷ngꢀc¸chꢀmꢁꢀMATLABꢀgi¶iꢀquyÕtꢀnh÷ngꢀvÊnꢀ®Òꢀth«ngꢀth−êngꢀvꢁꢀxemꢀMATLABꢀgi¶iꢀ
quyÕtꢀnh÷ngꢀvÊnꢀ®ÒꢀvÒꢀsèꢀphøcꢀmÒmꢀdÎoꢀnh−ꢀthÕꢀnꢁo.ꢀ
TuúꢀthuécꢀvꢁoꢀkiÕnꢀthøcꢀcñaꢀb¹n,ꢀb¹nꢀcãꢀthÓꢀt×mꢀthÊyꢀnh÷ngꢀphÇnꢀtrongꢀcuènꢀs¸chꢀh−ꢂ
íngꢀdÉnꢀnꢁyꢀhøngꢀthóꢀhayꢀbuånꢀtÎ...ꢀꢀ
Khiꢀb¹nꢀch¹yꢀch−¬ngꢀtr×nhꢀMATLAB,ꢀnãꢀsÏꢀt¹oꢀmétꢀhoÆcꢀnhiÒuꢀcöaꢀsæꢀtrªnꢀmꢁnꢀh×nhꢀcñaꢀ
b¹n,ꢀvꢁꢀcöaꢀsæꢀlÖnhꢀ(command)ꢀlꢁꢀcöaꢀsæꢀchÝnhꢀ®Óꢀb¹nꢀgiaoꢀtiÕpꢀvíiꢀMATLAB,ꢀcöaꢀsæꢀnꢁyꢀ
xuÊtꢀhiÖnꢀnhꢀh×nhꢀdíiꢀ®©y.ꢀ
C¸cꢀ kÝꢀ tùꢀ EDU>> ꢀ lꢁꢀ dÊuꢀ nh¾cꢀ cñaꢀ MATLABꢀ trongꢀ studentꢀ MATLAB.ꢀ Trongꢀ c¸cꢀ
versionꢀkh¸cꢀcñaꢀMATLAB,ꢀdÊuꢀnh¾cꢀ®¬nꢀgi¶nꢀchØꢀlꢁꢀ >> .ꢀKhiꢀcöaꢀsæꢀlÖnhꢀxuÊtꢀhiÖn,ꢀlꢁꢀ
cöaꢀsæꢀho¹tꢀ®éng,ꢀconꢀtráꢀxuÊtꢀhiÖnꢀbªnꢀph¶iꢀdÊuꢀnh¾cꢀnh−ꢀëꢀh×nhꢀd−íi.ꢀConꢀtráꢀvꢁꢀdÊuꢀ
nh¾cꢀnꢁyꢀcñaꢀMATLABꢀb¸oꢀr»ngꢀMATLABꢀ®angꢀ®îiꢀ®ÓꢀthùcꢀhiÖnꢀlÖnh.ꢀ
ꢀꢀꢀꢀꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀH×nhꢀ1.1ꢀꢀꢀꢀꢀCöaꢀsæꢀlÖnhꢀcñaꢀStudentꢀMATLABꢀ
ꢀ
1.1ꢀC¸cꢀphÐpꢀto¸nꢀ®¬nꢀgi¶nꢀ
ꢀ
Gièngꢀnh−ꢀm¸yꢀtÝnhꢀ®¬nꢀgi¶nꢀth«ngꢀth−êng,ꢀMATLABꢀcãꢀthÓꢀthùcꢀhiÖnꢀc¸cꢀphÐpꢀto¸nꢀ
®¬nꢀgi¶n,ꢀnh−ꢀvÝꢀdôꢀd−íiꢀ®©y:ꢀ
Maryꢀ®Õnꢀmétꢀcöaꢀhꢁngꢀv¨nꢀphßngꢀphÈmꢀvꢁꢀmuaꢀ4ꢀcôcꢀtÈy,ꢀ25ꢀxuꢀmétꢀcôc,ꢀ6ꢀtËpꢀvë,ꢀ52ꢀ
xuꢀmétꢀtËp,ꢀhaiꢀcuénꢀb¨ngꢀ®ꢁi,ꢀ99ꢀxuꢀmétꢀcuén.ꢀHꢃyꢀtÝnhꢀxemꢀMaryꢀmuaꢀbaoꢀnhiªuꢀvËt,ꢀvꢁꢀ
tængꢀsèꢀtiÒnꢀlꢁꢀbaoꢀnhiªu?ꢀ
NÕuꢀdïngꢀm¸yꢀtÝnhꢀth«ngꢀth−êng,ꢀtaꢀvꢁoꢀc¸cꢀsè:ꢀ
ꢀꢀꢀ4ꢀ+ꢀ6ꢀ+ꢀ2ꢀ=ꢀ12ꢀꢀ(ꢀvËt)ꢀ
ꢀꢀꢀ
ꢀ
ꢀ
ꢀꢀꢀ4x25ꢀ+ꢀ6x52ꢀ+ꢀ2x99ꢀ=ꢀ610ꢀ(xu)ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀH×nhꢀ1.2ꢀꢀꢀꢀꢀCöaꢀsæꢀlÖnhꢀcñaꢀMATLABꢀversionꢀ5.2ꢀ
ꢀ
TrongꢀMATLABꢀchóngꢀtaꢀcãꢀthÓꢀgi¶iꢀquyÕtꢀvÊnꢀ®ÒꢀnꢁyꢀtheoꢀnhiÒuꢀc¸ch.ꢀTr−ícꢀtiªnꢀgièngꢀnh−ꢀ
m¸yꢀtÝnhꢀëꢀtrªn,ꢀchóngꢀtaꢀcãꢀthÓꢀtÝnh:ꢀ
ꢀ
>>ꢀ4ꢀ+ꢀ6ꢀ+ꢀ2ꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀ12ꢀ
>>ꢀ4*25ꢀ+ꢀ6*52ꢀ+ꢀ2*99ꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀ610ꢀ
ꢀ
Chóꢀýꢀ r»ngꢀMATLABꢀ kh«ngꢀchóꢀýꢀ ®Õnꢀ nh÷ngꢀkho¶ngꢀtrèng,ꢀchoꢀtÊtꢀc¶ꢀc¸cꢀ phÇn,ꢀvꢁꢀ
phÐpꢀnh©nꢀcãꢀmøcꢀ®éꢀ−uꢀtiªnꢀcaoꢀh¬nꢀphÐpꢀcéng.ꢀVꢁꢀmétꢀchóꢀýꢀkh¸cꢀlꢁꢀMATLABꢀgäiꢀkÕtꢀ
qu¶ꢀansꢀ(viÕtꢀt¾tꢀcñaꢀanswer)ꢀchoꢀc¶ꢀhaiꢀphÐpꢀtÝnh.ꢀ
ꢀꢀ Nh−ꢀ®ꢃꢀnãiꢀëꢀtrªn,ꢀvÊnꢀ®ÒꢀtrªnꢀcãꢀthÓꢀgi¶iꢀquyÕtꢀb»ngꢀc¸chꢀchøaꢀc¸cꢀth«ngꢀtinꢀvꢁoꢀ
biÕnꢀcñaꢀMATLAB:ꢀ
ꢀ
>>ꢀerasersꢀ=ꢀ4ꢀ
erasers=ꢀ
ꢀꢀꢀꢀꢀꢀ4ꢀ
4
Updatesofts.com
Ebook Team
>>ꢀpadsꢀ=ꢀ6ꢀ
pads=ꢀ
ꢀꢀꢀꢀꢀꢀ6ꢀ
>>ꢀtapeꢀ=ꢀ2;ꢀ
>>ꢀitermsꢀ=ꢀerasesꢀ+ꢀpadsꢀ+ꢀtapeꢀ
iterms=ꢀ
ꢀꢀꢀꢀꢀꢀ12ꢀ
>>ꢀcostꢀ=ꢀerases*25ꢀ+ꢀpads*52ꢀ+ꢀtape*99ꢀ
cost=ꢀ
ꢀꢀꢀꢀꢀꢀ610ꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀëꢀ®©yꢀchóngꢀtaꢀt¹oꢀ3ꢀbiÕnꢀMATLAB:ꢀerases,ꢀpads,ꢀtapeꢀ®Óꢀchøaꢀsèꢀl−îngꢀmçiꢀlo¹iꢀvËt.ꢀ
Sauꢀkhiꢀvꢁoꢀc¸cꢀgi¸ꢀtrÞꢀchoꢀc¸cꢀbiÕnꢀnꢁy,ꢀMATLABꢀhiÓnꢀthÞꢀkÕtꢀqu¶ꢀraꢀmꢁnꢀh×nh,ꢀtrõꢀtr−êngꢀ
hîpꢀbiÕnꢀtape.ꢀDÊuꢀhaiꢀchÊmꢀ®»ngꢀsauꢀc©uꢀlÖnhꢀ >>ꢀtapeꢀ=ꢀ2; ꢀth«ngꢀb¸oꢀchoꢀMATLABꢀ
nhËnꢀgi¸ꢀtrÞꢀg¸nꢀnh−ngꢀkh«ngꢀhiÓnꢀthÞꢀraꢀmꢁnꢀh×nh.ꢀCuèiꢀcïngꢀkh¸cꢀvíiꢀgäiꢀkÕtꢀqu¶ꢀans,ꢀ
chóngꢀtaꢀyªuꢀcÇuꢀMATLABꢀgäiꢀkÕtꢀqu¶ꢀtængꢀsèꢀc¸cꢀvËtꢀlꢁꢀiterms,ꢀvꢁꢀtængꢀsèꢀtiÒnꢀlꢁꢀcost.ꢀT¹iꢀ
mçiꢀb−ícꢀMATLABꢀ®Òuꢀ®aꢀraꢀc¸cꢀth«ngꢀtin.ꢀV×ꢀcãꢀl−uꢀgi÷ꢀc¸cꢀbiÕnꢀnªnꢀchóngꢀtaꢀcãꢀthÓꢀyªuꢀ
cÇuꢀMATLABꢀtÝnhꢀgi¸ꢀtrÞꢀtrungꢀb×nhꢀchoꢀmçiꢀvËt:ꢀ
ꢀ
>>ꢀeverage_costꢀ=ꢀcost/itermsꢀ
everage_cost=ꢀ
ꢀꢀꢀꢀꢀꢀ50.8333ꢀ
ꢀ
Bëiꢀv×ꢀeverageꢀcostꢀcãꢀhaiꢀtõ,ꢀmꢁꢀMATLABꢀyªuꢀcÇuꢀbiÕnꢀchØꢀcãꢀmétꢀtõ,ꢀnªnꢀchóngꢀtaꢀdïngꢀ
dÊuꢀg¹chꢀd−íiꢀ®Óꢀnèiꢀhaiꢀtõꢀnꢁyꢀthꢁnhꢀmétꢀtõ.ꢀ
ꢀꢀNgoꢁiꢀc¸cꢀphÐpꢀtÝnhꢀtrªn,ꢀMATLABꢀcßnꢀcãꢀmétꢀsèꢀphÐpꢀtÝnhꢀc¬ꢀb¶nꢀkh¸cꢀnh−ꢀb¶ngꢀd−íiꢀ
®©y:ꢀ
ꢀ
PhÐpꢀtÝnhꢀ
PhÐpꢀcéng,ꢀaꢀ+ꢀbꢀ
BiÓuꢀt−îngꢀ
+ꢀ
VÝꢀdôꢀ
5ꢀ+ꢀ3ꢀ
7ꢀꢂꢀ4ꢀ
18*24ꢀ
PhÐpꢀtrõ,ꢀaꢀꢂꢀbꢀ
PhÐpꢀnh©n,ꢀa.bꢀ
PhÐpꢀchia,ꢀabꢀ
PhÐpꢀluüꢀthõa,ꢀabꢀ
ꢀ
ꢂꢀ
*ꢀ
/ꢀhoÆcꢀ\ꢀ
^ꢀ
56/8ꢀ=ꢀ8\ꢀ56ꢀ
5^2ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
ꢀꢀꢀ
Trongꢀc¸cꢀphÐpꢀto¸nꢀtrªnꢀcãꢀmøcꢀ®éꢀ−uꢀtiªnꢀkh¸cꢀnhau,ꢀkhiꢀtÝnhꢀtõꢀtr¸iꢀsangꢀph¶iꢀcñaꢀ
métꢀdßngꢀgåmꢀnhiÒuꢀlÖnhꢀth×ꢀphÐpꢀto¸nꢀluüꢀthõaꢀcãꢀmøcꢀ®éꢀ−uꢀtiªnꢀcaoꢀnhÊt,ꢀtiÕpꢀtheoꢀlꢁꢀ
phÐpꢀnh©nꢀvꢁꢀphÐpꢀchiaꢀcãꢀmøcꢀ®éꢀ−uꢀtiªnꢀb»ngꢀnhauꢀcuèiꢀcïngꢀlꢁꢀphÐpꢀcéngꢀvꢁꢀphÐpꢀtrõꢀ
còngꢀcãꢀmøcꢀ®éꢀ−uꢀtiªnꢀb»ngꢀnhau.ꢀꢀ
ꢀ
1.2ꢀꢀKh«ngꢀgianꢀlꢁmꢀviÖcꢀcñaꢀMATLABꢀ
ꢀ
ꢀꢀꢀꢀꢀCòngꢀnh−ꢀb¹nꢀlꢁmꢀviÖcꢀvíiꢀcöaꢀsæꢀLÖnh,ꢀMATLABꢀnhíꢀc¸cꢀlÖnhꢀb¹nꢀgâꢀvꢁoꢀcòngꢀnh−ꢀ
c¸cꢀgi¸ꢀtrÞꢀb¹nꢀg¸nꢀchoꢀnãꢀhoÆcꢀnãꢀ®−îcꢀt¹oꢀlªn.ꢀNh÷ngꢀlÖnhꢀvꢁꢀbiÕnꢀnꢁyꢀ®−îcꢀgäiꢀlꢁꢀl−uꢀgi÷ꢀ
trongꢀkh«ngꢀgianꢀlꢁmꢀviÖcꢀcñaꢀMATLAB,ꢀvꢁꢀcãꢀthÓꢀ®−îcꢀgäiꢀl¹iꢀkhiꢀb¹nꢀmuèn.ꢀVÝꢀdô,ꢀ®ÓꢀkiÓmꢀ
traꢀgi¸ꢀtrÞꢀcñaꢀbiÕnꢀtape,ꢀtÊtꢀc¶ꢀnh÷ngꢀg×ꢀb¹nꢀph¶iꢀlꢁmꢀlꢁꢀyªuꢀcÇuꢀMATLABꢀchoꢀbiÕtꢀb»ngꢀ
c¸chꢀ®¸nhꢀvꢁoꢀtªnꢀbiÕnꢀt¹iꢀdÊuꢀnh¾c:ꢀ
ꢀ
>>ꢀtapeꢀ
5
Updatesofts.com
Ebook Team
tape=ꢀ
ꢀꢀꢀꢀꢀꢀ2ꢀ
ꢀ
NÕuꢀb¹nꢀkh«ngꢀnhíꢀtªnꢀbiÕn,ꢀb¹nꢀcãꢀthÓꢀyªuꢀcÇuꢀMATLABꢀchoꢀdanhꢀs¸chꢀc¸cꢀbiÕnꢀb»ngꢀ
c¸chꢀd¸nhꢀlÖnhꢀwhoꢀtõꢀdÊuꢀnh¾cꢀlÖnh:ꢀ
ꢀ
>>ꢀwhoꢀ
Yourꢀvariablesꢀare:ꢀ
ansꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀcostꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀitermsꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀtapeꢀ
average_costꢀꢀꢀerasersꢀꢀꢀꢀꢀꢀꢀꢀpadsꢀ
ꢀ
ꢀꢀꢀꢀ
Chóꢀýꢀr»ngꢀMATLABꢀkh«ngꢀ®−aꢀraꢀgi¸ꢀtrÞꢀcñaꢀtÊtꢀc¶ꢀc¸cꢀbiÕn,ꢀnÕuꢀb¹nꢀmuènꢀbiÕtꢀgi¸ꢀ
trÞ,ꢀb¹nꢀ®¸nhꢀvꢁoꢀtªnꢀbiÕnꢀt¹iꢀdÊuꢀnh¾cꢀlÖnhꢀcñaꢀMATLAB.ꢀ
ꢀꢀꢀ§Óꢀgäiꢀl¹iꢀc¸cꢀlÖnhꢀb¹nꢀ®ꢃꢀdïng,ꢀMATLABꢀdïngꢀc¸cꢀphÝmꢀmòiꢀtªnꢀ(↑ꢀ↓ꢀ)ꢀtrªnꢀbꢁnꢀphÝmꢀcñaꢀ
b¹n.ꢀVÝꢀdôꢀ®Óꢀgäiꢀl¹iꢀlÖnhꢀb¹nꢀgâꢀvꢁoꢀlócꢀgÇnꢀhiÖnꢀt¹iꢀnhÊt,ꢀb¹nꢀnhÊnꢀphÝmꢀmòiꢀtªnꢀ↓,ꢀtiÕpꢀtôcꢀ
nhÊnꢀphÝmꢀnꢁy,ꢀnãꢀsÏꢀl¹iꢀgäiꢀtiÕpꢀlÖnhꢀtr−ícꢀ®ã,ꢀNÕuꢀb¹nꢀdïngꢀphÝmꢀmòiꢀtªnꢀ↑ꢀnãꢀsÏꢀgäiꢀl¹iꢀ
lÖnhꢀtõꢀlÖnhꢀ®Çuꢀtiªnꢀchoꢀ®ÕnꢀlÖnhꢀgÇnꢀhiÖnꢀt¹iꢀnhÊt.ꢀC¸cꢀphÝmꢀmòiꢀtªnꢀ←ꢀꢀvꢁꢀ→ꢀꢀcãꢀthÓꢀ
dïngꢀ®Óꢀthayꢀ®æiꢀvÞꢀtrÝꢀconꢀtráꢀtrongꢀdßngꢀlÖnhꢀt¹iꢀdÊuꢀnh¾cꢀcñaꢀMATLAB,ꢀnh−ꢀvËyꢀchóngꢀtaꢀ
cãꢀthÓꢀsöaꢀdßngꢀlÖnh,ꢀthªmꢀn÷a,ꢀchóngꢀtaꢀcãꢀthÓꢀdïngꢀchuétꢀcïngꢀvíiꢀbéꢀnhíꢀ®Ömꢀ®Óꢀc¾t,ꢀ
copy,ꢀd¸n,ꢀvꢁꢀsöaꢀv¨nꢀb¶nꢀt¹iꢀdÊuꢀnh¾cꢀcñaꢀdßngꢀlÖnh.ꢀ
ꢀ
1.3ꢀꢀBiÕnꢀ
ꢀ
ꢀꢀꢀꢀ
Gièngꢀnh−ꢀnh÷ngꢀng«nꢀng÷ꢀlËpꢀtr×nhꢀkh¸c,ꢀMATLABꢀcãꢀnh÷ngꢀquyꢀ®ÞnhꢀriªngꢀvÒꢀtªnꢀ
biÕn.ꢀTr−ícꢀtiªnꢀtªnꢀbiÕnꢀph¶iꢀlꢁꢀmétꢀtõ,ꢀkh«ngꢀchøaꢀdÊuꢀc¸ch,ꢀvꢁꢀtªnꢀbiÕnꢀph¶iꢀcãꢀnh÷ngꢀ
quyꢀtu©nꢀthñꢀnh÷ngꢀquyꢀt¾cꢀsau:ꢀ
ꢀꢀꢀꢀꢀꢀQuyꢀ®ÞnhꢀvÒꢀtªnꢀbiÕnꢀꢀꢀꢀꢀꢀꢀꢀ
TªnꢀbiÕnꢀcãꢀph©nꢀbiÖtꢀch÷ꢀhoaꢀch÷ꢀth−êng.ꢀꢀ
ꢀꢀꢀꢀꢀ
ꢀ
VÝꢀdô:ꢀIterms,ꢀiterms,ꢀitErms,ꢀvꢁꢀꢀITERMSꢀlꢁꢀc¸cꢀbiÕnꢀkh¸cꢀnhauꢀ
TªnꢀbiÕnꢀcãꢀthÓꢀchøaꢀnhiÒuꢀnhÊtꢀ31ꢀkÝꢀtù,ꢀꢀcßnꢀc¸cꢀkÝꢀtùꢀsauꢀkÝꢀtùꢀthøꢀ31ꢀbÞꢀlêꢀ®i.ꢀꢀ
VÝꢀdô:ꢀhowaboutthisveriablenameꢀ
TªnꢀbiÕnꢀb¾tꢀ®Çuꢀph¶iꢀlꢁꢀch÷ꢀc¸i,ꢀꢀtiÕpꢀtheoꢀcãꢀthÓꢀlꢁꢀch÷ꢀsè,ꢀsèꢀg¹chꢀd−íiꢀꢀ
VÝꢀdô:ꢀhow_about_this_veriable_name,ꢀX51483.ꢀa_b_c_d_eꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
KÝꢀtùꢀchÊmꢀc©uꢀkh«ngꢀ®−îcꢀphÐpꢀdïngꢀꢀv×ꢀnãꢀcãꢀnh÷ngꢀýꢀnghÜaꢀ®ÆcꢀbiÖtꢀ
Cïngꢀvíiꢀnh÷ngꢀquyꢀ®Þnhꢀtrªn,ꢀMATLABꢀcãꢀnh÷ngꢀbiÕnꢀ®ÆcꢀbiÖtꢀtrongꢀb¶ngꢀsau:ꢀ
ꢀ
ꢀ
C¸cꢀbiÕnꢀ®ÆcꢀbiÖtꢀ Gi¸ꢀtrÞꢀ
ansꢀ
TªnꢀbiÕnꢀmÆcꢀ®Þnhꢀdïngꢀ®Óꢀtr¶ꢀvÒꢀkÕtꢀqu¶ꢀ
ꢀ
ꢀpiꢀ=ꢀ3.1415..ꢀ
Epsꢀ
flopsꢀ
SèꢀnháꢀnhÊt,ꢀnh−ꢀvËyꢀdïngꢀcéngꢀvíiꢀ1ꢀ®Óꢀ®−îcsèꢀnháꢀnhÊtꢀlínꢀh¬nꢀ1ꢀ
SèꢀcñaꢀphÐpꢀto¸nꢀsèꢀthùcꢀ
infꢀ
NaNꢀhoÆcꢀnanꢀ
iꢀ(vꢁ)ꢀjꢀ
§ÓꢀchØꢀsèꢀv«ꢀcïngꢀnhꢀkÕtꢀqu¶ꢀcñaꢀ1/0ꢀ
Dïngꢀ®ÓꢀchØꢀsèꢀkh«ngꢀx¸cꢀ®Þnhꢀnh−ꢀkÕtꢀqu¶ꢀꢀꢀꢀꢀcñaꢀ0/0ꢀ
iꢀ=ꢀjꢀ=ꢀꢀ
narginꢀ
naroutꢀ
realminꢀ
realmaxꢀ
Sèꢀc¸cꢀ®èiꢀsèꢀ®aꢀvꢁoꢀhꢁmꢀ®−îcꢀsöꢀdôngꢀ
Sèꢀc¸cꢀ®èiꢀsèꢀhꢁmꢀ®aꢀraꢀ
SèꢀnháꢀnhÊtꢀcãꢀthÓꢀ®−îcꢀcñaꢀsèꢀthùcꢀ
SèꢀlínꢀnhÊtꢀcãꢀthÓꢀ®−îcꢀcñaꢀsèꢀthùcꢀ
6
Updatesofts.com
Ebook Team
ꢀ
ꢀꢀ Nh−ꢀb¹nꢀcãꢀthÓꢀt¹oꢀmétꢀbiÕnꢀcñaꢀMATLAB,ꢀvꢁꢀb¹nꢀcòngꢀcãꢀthÓꢀg¸nꢀl¹iꢀgi¸ꢀtrÞꢀchoꢀmétꢀ
hoÆcꢀnhiÒuꢀbiÕn.ꢀꢀ
VÝꢀdô:ꢀ
ꢀ
>>ꢀerasesꢀ=ꢀ4;ꢀ
>>ꢀpadsꢀ=ꢀ6;ꢀ
>>ꢀtapeꢀ=ꢀ2;ꢀ
>>ꢀitermsꢀ=ꢀeasesꢀ+ꢀpadsꢀ+ꢀtapeꢀ
iterms=ꢀ
ꢀꢀꢀꢀꢀꢀ12ꢀ
>>ꢀerasesꢀ=ꢀ6ꢀ
erases=ꢀ
ꢀꢀꢀꢀꢀꢀ6ꢀ
>>ꢀitermsꢀ
iterms=ꢀ
ꢀꢀꢀꢀꢀꢀ12ꢀ
ꢀ
ëꢀ®©yꢀchóngꢀtaꢀsöꢀdôngꢀl¹iꢀvÝꢀdôꢀtrªn,ꢀchóngꢀtaꢀt×mꢀ®−îcꢀsèꢀvËtꢀmꢁꢀMaryꢀ®ꢃꢀmuaꢀsauꢀ®ãꢀ
chóngꢀtaꢀthayꢀ®æiꢀsèꢀcôcꢀtÈyꢀlªnꢀ6,ꢀgi¸ꢀtrÞꢀnꢁyꢀsÏꢀ®Ìꢀlªnꢀgi¸ꢀtrÞꢀtr−ícꢀcñaꢀnãꢀlꢁꢀ4.ꢀKhiꢀb¹nꢀlꢁmꢀ
nh−ꢀvËy,ꢀgi¸ꢀtrÞꢀcñaꢀitermsꢀvÉnꢀkh«ngꢀthayꢀ®æi,ꢀv×ꢀMATLABꢀkh«ngꢀtÝnhꢀl¹iꢀitermsꢀvíiꢀgi¸ꢀtrÞꢀ
míiꢀcñaꢀerases.ꢀKhiꢀMATLABꢀthùcꢀhiÖnꢀmétꢀphÐpꢀtÝnh,ꢀnãꢀlÊyꢀgi¸ꢀtrÞꢀcñaꢀc¸cꢀbiÕnꢀhiÖnꢀthêi,ꢀ
nªnꢀnÕuꢀb¹nꢀmuènꢀtÝnhꢀgi¸ꢀtrÞꢀmíiꢀcñaꢀiterms,ꢀcost,ꢀaverage_cost,ꢀb¹nꢀgäiꢀl¹iꢀc¸cꢀlÖnhꢀtÝnhꢀ
c¸cꢀgi¸ꢀtrÞꢀ®ã.ꢀ
ꢀꢀꢀ
§èiꢀ víiꢀ c¸cꢀ biÕnꢀ ®Æcꢀ biÖtꢀ ëꢀ trªn,ꢀ nãꢀ cãꢀ s½nꢀ gi¸ꢀ trÞ,ꢀ nh−ꢀ vËyꢀ khiꢀ b¹nꢀ khëiꢀ ®éngꢀ
MATLAB;ꢀnÕuꢀb¹nꢀthayꢀ®æiꢀgi¸ꢀtrÞꢀcñaꢀnãꢀth×ꢀnh÷ngꢀgi¸ꢀtrÞꢀ®ÆcꢀbiÖtꢀbanꢀ®ÇuꢀsÏꢀbÞꢀmÊtꢀchoꢀ
®Õnꢀkhiꢀb¹nꢀxo¸ꢀbiÕnꢀ®ãꢀ®iꢀhoÆcꢀkhëiꢀ®éngꢀl¹iꢀMATLAB.ꢀDoꢀ®ãꢀb¹nꢀkh«ngꢀnªnꢀthayꢀ®æiꢀgi¸ꢀ
trÞꢀcñaꢀbiÕnꢀ®ÆcꢀbiÖt,ꢀtrõꢀkhiꢀnãꢀthùcꢀsùꢀcÇnꢀthiÕt.ꢀ
ꢀꢀꢀꢀ C¸cꢀbiÕnꢀtrongꢀkh«ngꢀgianꢀlꢁmꢀviÖcꢀcñaꢀMATLABꢀcãꢀthÓꢀbÞꢀxo¸ꢀkh«ngꢀ®iÒuꢀkiÖnꢀb»ngꢀ
c¸chꢀdïngꢀlÖnhꢀclear.ꢀVÝꢀdô:ꢀ
>>ꢀclearꢀerasesꢀ
ꢀꢀꢀꢀchØꢀxo¸ꢀmétꢀbiÕnꢀerasesꢀ
>>ꢀclearꢀcostꢀitermsꢀ
ꢀꢀꢀxo¸ꢀc¶ꢀhaiꢀbiÕnꢀcostꢀvꢁꢀitermsꢀ
>>ꢀclearꢀꢀcl*ꢀ
ꢀꢀꢀdÊuꢀ*ꢀ®ÓꢀchØꢀr»ngꢀxo¸ꢀtÊtꢀc¶ꢀc¸cꢀbiÕnꢀb¾tꢀ®Çuꢀb»ngꢀhaiꢀkÝꢀtùꢀcl.ꢀ
>>ꢀclearꢀ
ꢀ
xo¸ꢀtÊtꢀc¶ꢀc¸cꢀbiÕnꢀtrongꢀkh«ngꢀgianꢀlꢁmꢀviÖc!.ꢀB¹nꢀsÏꢀkh«ngꢀ®−îcꢀháiꢀ®Óꢀx¸cꢀnhËnꢀc©uꢀ
lÖnhꢀnꢁyꢀvꢁꢀtÊtꢀc¶ꢀc¸cꢀbiÕnꢀ®ꢃꢀbÞꢀxo¸ꢀkh«ngꢀthÓꢀkh«iꢀphôcꢀl¹i.ꢀ
CãꢀthÓꢀnãiꢀr»ngꢀdïngꢀlÖnhꢀclearꢀrÊtꢀnguyꢀhiÓm,ꢀv×ꢀvËyꢀkhiꢀdïngꢀlÖnhꢀnꢁyꢀb¹nꢀnªnꢀdïngꢀ®óngꢀ
vÞꢀtrÝ.ꢀ
ꢀ
1.4ꢀC©uꢀgi¶iꢀthÝchꢀ(comment)ꢀvꢁꢀsùꢀchÊmꢀc©uꢀ
ꢀ
ꢀꢀꢀꢀTÊtꢀc¶ꢀc¸cꢀv¨nꢀb¶nꢀ®»ngꢀsauꢀkÝꢀhiÖuꢀphÇnꢀtr¨mꢀ(%)ꢀ®Òuꢀlꢁꢀc©uꢀgi¶iꢀthÝch.ꢀVÝꢀdô:ꢀ
ꢀ
>>ꢀerasesꢀ=ꢀ4ꢀꢀꢀꢀ%ꢀSèꢀcôcꢀtÈy.ꢀ
erases=ꢀ
7
Updatesofts.com
Ebook Team
ꢀꢀꢀꢀꢀꢀ4ꢀ
ꢀ
BiÕnꢀerasesꢀ®−îcꢀg¸nꢀgi¸ꢀtrÞꢀlꢁꢀ4,ꢀcßnꢀtÊtꢀc¶ꢀkÝꢀhiÖuꢀphÇnꢀtr¨mꢀvꢁꢀv¨nꢀb¶nꢀ®»ngꢀsauꢀnãꢀ®Òuꢀ
bÞꢀlêꢀ®i.ꢀ§Æcꢀ®iÓmꢀnꢁyꢀgiópꢀchoꢀchóngꢀtaꢀdÔꢀtheoꢀdâiꢀc«ngꢀviÖcꢀchóngꢀtaꢀ®angꢀlꢁm.ꢀ
ꢀꢀꢀꢀNhiÒuꢀlÖnhꢀcãꢀthÓꢀ®Ætꢀtrªnꢀcïngꢀmétꢀhꢁng,ꢀchóngꢀc¸chꢀnhauꢀbëiꢀdÊuꢀphÈyꢀhoÆcꢀdÊuꢀchÊmꢀ
phÈy,ꢀnh−:ꢀ
ꢀ
>>ꢀerasesꢀ=ꢀ4,ꢀpadsꢀ=ꢀ6;ꢀtapeꢀ=ꢀ2ꢀ
erases=ꢀ
ꢀꢀꢀꢀꢀꢀ4ꢀ
tape=ꢀ
ꢀꢀꢀꢀꢀꢀ2ꢀ
dÊuꢀphÈyꢀ®ÓꢀyªuꢀcÇuꢀMATLABꢀhiÓnꢀthÞꢀkÕtꢀqu¶ꢀtrªnꢀmꢁnꢀh×nh;ꢀcßnꢀdÊuꢀchÊmꢀphÈyꢀlꢁꢀkh«ngꢀ
hiÓnꢀthÞꢀkÕtꢀqu¶ꢀtrªnꢀmꢁnꢀh×nh.ꢀ
>>ꢀaverage_costꢀ=ꢀcost/ꢀ...ꢀ
itermsꢀ
average_cost=ꢀ
ꢀꢀꢀꢀꢀꢀ50.83333ꢀ
ꢀ
Nh−ꢀvÝꢀdôꢀtrªn,ꢀtaꢀcãꢀthÓꢀdïngꢀdÊuꢀbaꢀchÊmꢀ(...)ꢀ®ÓꢀchØꢀc©uꢀlÖnhꢀ®−îcꢀtiÕpꢀtôcꢀëꢀhꢁngꢀd−íi,ꢀ
phÐpꢀtÝnhꢀthùcꢀhiÖnꢀ®−îcꢀkhiꢀdÊuꢀbaꢀchÊmꢀng¨nꢀc¸chꢀgi÷aꢀto¸nꢀtöꢀvꢁꢀbiÕn,ꢀnghÜaꢀlꢁꢀtªnꢀbiÕnꢀ
kh«ngꢀbÞꢀng¨nꢀc¸chꢀgi÷aꢀhaiꢀhꢁng:ꢀ
ꢀ
>>ꢀaverage_costꢀ=ꢀcost/ꢀit...ꢀ
ermsꢀ
???ꢀage_costꢀ=ꢀcost/itermsꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
ꢀMissingꢀꢀoperator,ꢀꢀcoma,ꢀorꢀsemicolon.ꢀ
ꢀ
gièngꢀnh−ꢀvËy,ꢀtr¹ngꢀth¸iꢀcñaꢀlêiꢀgi¶iꢀthÝchꢀkh«ngꢀthÓꢀtiÕpꢀtôc:ꢀ
ꢀ
>>ꢀ%ꢀꢀCommentsꢀcannotꢀbeꢀcontinuedꢀ...ꢀ
>>ꢀeitherꢀ
???ꢀUndefinedꢀfunctionꢀorꢀvariableꢀeither.ꢀ
ꢀ
B¹nꢀcãꢀthÓꢀdõngꢀch−¬ngꢀtr×nhꢀb»ngꢀc¸chꢀnhÊnꢀ®ångꢀthêiꢀCtrlꢀvꢁꢀC.ꢀ
ꢀ
1.5ꢀꢀSèꢀphøcꢀ
ꢀ
Métꢀtrongꢀnh÷ngꢀ®Æcꢀ®iÓmꢀm¹nhꢀmÏꢀnhÊtꢀcñaꢀMATLABꢀlꢁꢀlꢁmꢀviÖcꢀvíiꢀsèꢀphøc.ꢀSèꢀphøcꢀ
trongꢀMATLABꢀ®−îcꢀ®ÞnhꢀnghÜaꢀtheoꢀnhiÒuꢀc¸ch,ꢀvÝꢀdôꢀnh−ꢀsau:ꢀ
ꢀ
>>ꢀc1ꢀ=ꢀ1ꢀꢂꢀ2iꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀChÌnꢀthªmꢀkÝꢀtùꢀiꢀvꢁoꢀphÇnꢀ¶o.ꢀ
c1=ꢀ
ꢀꢀꢀꢀꢀꢀ1.0000ꢀꢂꢀ2.0000iꢀ
>>ꢀc1ꢀ=ꢀ1ꢀꢂꢀ2jꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀjꢀëꢀ®©yꢀt−¬ngꢀtùꢀnh−ꢀiꢀëꢀtrªn.ꢀ
c1=ꢀ
ꢀꢀꢀꢀꢀꢀ1.0000ꢀꢂꢀ2.0000iꢀ
>>ꢀc2ꢀ=ꢀ3*(2ꢂsqrt(ꢂ1)*3)ꢀ
c2=ꢀ
8
Updatesofts.com
Ebook Team
ꢀꢀꢀꢀꢀꢀ6.0000ꢀꢂꢀ9.0000iꢀ
>>ꢀc3ꢀ=ꢀsqrt(ꢂ2)ꢀ
c3=ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ0ꢀ+ꢀ1.4142iꢀ
>>ꢀc4ꢀ=ꢀ6ꢀ+ꢀsin(.5)*iꢀ
c4=ꢀ
ꢀꢀꢀꢀꢀꢀ6.0000ꢀ+ꢀ0.4794iꢀ
>>ꢀc5ꢀ=ꢀ6ꢀ+ꢀsin(.5)*jꢀ
c5=ꢀ
ꢀꢀꢀꢀꢀꢀ6.0000ꢀ+ꢀ0.4794iꢀꢀꢀ
ꢀ
TrongꢀhaiꢀvÝꢀdôꢀcuèi,ꢀMATLABꢀmÆcꢀ®Þnhꢀgi¸ꢀtrÞꢀcñaꢀiꢀ=ꢀjꢀ=ꢀꢀdïngꢀchoꢀphÇnꢀ¶o.ꢀNh©nꢀvíiꢀiꢀ
hoÆcꢀ jꢀ ®−îcꢀ yªuꢀ cÇuꢀ trongꢀ tr−êngꢀ hîpꢀ nꢁy,ꢀ sin(.5)iꢀ vꢁꢀ sin(.5)jꢀ kh«ngꢀ cãꢀ ýꢀ nghÜaꢀ ®èiꢀ víiꢀ
MATLAB.ꢀCuèiꢀcïngꢀvíiꢀc¸cꢀkÝꢀtùꢀiꢀvꢁꢀj,ꢀnh−ꢀëꢀtrongꢀhaiꢀvÝꢀdôꢀ®ÇuꢀëꢀtrªnꢀchØꢀlꢁmꢀviÖcꢀvíiꢀsèꢀ
cèꢀ®Þnh,ꢀkh«ngꢀlꢁmꢀviÖcꢀ®−îcꢀvíiꢀbiÓuꢀthøc.ꢀ
ꢀꢀꢀꢀ ꢀMétꢀsèꢀng«nꢀng÷ꢀyªuꢀcÇuꢀsùꢀ®iÒuꢀkhiÓnꢀ®ÆcꢀbiÖtꢀchoꢀsèꢀphøcꢀkhiꢀnãꢀxuÊtꢀhiÖn,ꢀtrongꢀ
MATLABꢀth×ꢀkh«ngꢀcÇuꢀnh−ꢀvËy.ꢀTÊtꢀc¶ꢀc¸cꢀphÐpꢀtÝnhꢀto¸nꢀhäcꢀ®Òuꢀthaoꢀt¸cꢀ®−îcꢀnh−ꢀ®èiꢀ
víiꢀsèꢀthùcꢀth«ngꢀth−êng:ꢀ
ꢀ
>>ꢀc6ꢀ=ꢀ(c1ꢀ+ꢀc2)/c3ꢀꢀꢀꢀꢀꢀꢀ%ꢀTõꢀc¸cꢀd÷ꢀliÖuꢀëꢀtrªnꢀ
c6=ꢀ
ꢀꢀꢀꢀꢀꢀꢂ7.7782ꢀꢂꢀ4.9497iꢀ
>>ꢀcheck_it_outꢀ=ꢀi^2ꢀꢀꢀꢀꢀꢀ%ꢀB×nhꢀph−¬ngꢀcñaꢀiꢀph¶iꢀlꢁꢀꢂ1ꢀ
check_it_out=ꢀ
ꢀꢀꢀꢀꢀꢀꢂ1.0000ꢀ+ꢀ0.0000iꢀ
ꢀ
trongꢀvÝꢀdôꢀnꢁyꢀchØꢀcßnꢀl¹iꢀphÇnꢀthùc,ꢀphÇnꢀ¶oꢀb»ngꢀkh«ng.ꢀChóngꢀtaꢀcãꢀthÓꢀdïngꢀhꢁmꢀreal
ꢀ
vꢁꢀimagꢀ®ÓꢀkiÓmꢀtraꢀtõngꢀphÇnꢀthùcꢀvꢁꢀ¶o.ꢀ
ꢀꢀꢀ
ꢀ
ChóngꢀtaꢀcãꢀthÓꢀbiÓuꢀdiÔnꢀsèꢀphøcꢀd¹ngꢀ®éꢀlínꢀvꢁꢀgãcꢀ(d¹ngꢀcùc):ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀMꢀꢀM.ejꢀ=ꢀa+biꢀ
ꢀ
ëꢀtrªnꢀsèꢀphøcꢀ®−îcꢀbiÓuꢀdiÔnꢀb»ngꢀ®éꢀlínꢀMꢀvꢁꢀgãcꢀ,ꢀquanꢀhÖꢀgi÷aꢀc¸cꢀ®¹iꢀl−îngꢀnꢁyꢀvꢁꢀ
phÇnꢀthùc,ꢀphÇnꢀ¶oꢀcñaꢀsèꢀphøcꢀbiÓuꢀdiÔnꢀd−íiꢀd¹ngꢀ®¹iꢀsèꢀlꢁ:ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀMꢀ=ꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ=ꢀtanꢂ1(b/ꢀa)ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀaꢀ=ꢀMcosꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀbꢀ=ꢀMsinꢀ
ꢀꢀ TrongꢀMATLAB,ꢀ®ÓꢀchuyÓnꢀtõꢀd¹ngꢀcùcꢀsangꢀd¹ngꢀ®¹iꢀsè,ꢀdïngꢀc¸cꢀhꢁmꢀreal,ꢀimag,ꢀ
vꢁꢀangle:ꢀ
ꢀ
>>ꢀc1ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀGäiꢀl¹iꢀc1ꢀ
c1=ꢀ
ꢀꢀꢀꢀꢀꢀ1.0000ꢀꢂꢀ2.0000iꢀ
>>ꢀM_c1ꢀ=ꢀabs(c1)ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀTÝnhꢀargumentꢀcñaꢀsèꢀphøcꢀ
M_c1=ꢀ
ꢀꢀꢀꢀꢀꢀ2.2361ꢀ
>>ꢀangle_c1ꢀ=ꢀangle(c1)ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀTÝnhꢀgãcꢀcñaꢀsèꢀphøcꢀtheoꢀradianꢀ
angle_c1=ꢀ
9
Updatesofts.com
Ebook Team
ꢀꢀꢀꢀꢀꢀꢂ1.1071ꢀ
>>ꢀdeg_c1ꢀ=ꢀangle_c1*180/ꢀpiꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀChuyÓnꢀtõꢀradianꢀsangꢀ®éꢀ
ꢀꢀꢀꢀꢀꢀꢂ63.4349ꢀ
>>ꢀreal_c1ꢀ=ꢀreal(c1)ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀTÝnhꢀphÇnꢀthùcꢀ
real_c1=ꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀ1ꢀ
>>ꢀimag_c1ꢀ=ꢀimag(c1)ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀTÝnhꢀphÇnꢀ¶oꢀ
imag_c1=ꢀ
ꢀꢀꢀꢀꢀꢀꢂ2ꢀ
ꢀ
ꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂoOoꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢀ
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
Ch−¬ng2ꢀ
ꢀ
C¸Cꢀ§ÆCꢀtÝnhꢀKÜꢀTHUËTꢀ
ꢀ
Gièngꢀnh−ꢀhÇuꢀhÕtꢀc¸cꢀm¸yꢀtÝnhꢀküꢀthuËt,ꢀMATLABꢀ®aꢀraꢀrÊtꢀnhiÒuꢀc¸cꢀhꢁmꢀto¸nꢀhäc,ꢀkÜꢀ
thuËtꢀth«ngꢀdông,ꢀngoꢁiꢀraꢀMATLABꢀcßnꢀcungꢀcÊpꢀhꢁngꢀtr¨mꢀc¸cꢀhꢁmꢀ®ÆcꢀbiÖtꢀvꢁꢀthuËtꢀ
to¸n,ꢀnãꢀrÊtꢀh÷uꢀÝchꢀ®Óꢀgi¶iꢀquyÕtꢀc¸cꢀvÊnꢀ®Òꢀkhoaꢀhäc.ꢀTÊtꢀc¶ꢀc¸cꢀhꢁmꢀnꢁyꢀ®−îcꢀliÖtꢀkªꢀ
trongꢀonlineꢀhelp,ꢀcßnꢀëꢀ®©yꢀchØꢀ®ÒꢀcËpꢀ®Õnꢀnh÷ngꢀhꢁmꢀth«ngꢀdôngꢀnhÊt.ꢀ
ꢀ
2.1ꢀC¸cꢀhꢁmꢀto¸nꢀhäcꢀth«ngꢀth−êngꢀ
ꢀ
ꢀꢀꢀ ꢀC¸cꢀhꢁmꢀ to¸nꢀ häcꢀ cñaꢀ MATLABꢀ ®−îcꢀ liÖtꢀ kªꢀ trongꢀ b¶ngꢀd−íiꢀ ®©y,ꢀ chóngꢀ ®Òuꢀ cãꢀ
chungꢀmétꢀc¸chꢀgäiꢀhꢁmꢀnh−ꢀvÝꢀdôꢀd−íiꢀ®©y:ꢀ
ꢀ
>>ꢀxꢀ=ꢀsqrt(2)/2ꢀ
x=ꢀ
ꢀꢀꢀꢀꢀꢀ0.7071ꢀ
>>ꢀyꢀ=ꢀsin(x)ꢀ
y=ꢀ
ꢀꢀꢀꢀꢀꢀ0.7854ꢀ
>>ꢀy_degꢀ=ꢀy*180/piꢀ
y_deg=ꢀ
ꢀꢀꢀꢀꢀꢀ45.0000ꢀ
ꢀ
Nh÷ngꢀlÖnhꢀnꢁyꢀ®Óꢀt×mꢀmétꢀgãcꢀ(tÝnhꢀb»ngꢀ®é)ꢀkhiꢀbiÕtꢀgi¸ꢀtrÞꢀhꢁmꢀsinꢀcñaꢀnãꢀlꢁꢀ/ꢀ2.ꢀ
TÊtꢀc¶ꢀc¸cꢀhꢁmꢀliªnꢀquanꢀ®ÕnꢀgãcꢀcñaꢀMATLABꢀ®ÒuꢀlꢁmꢀviÖcꢀvíiꢀradian.ꢀ
B¶ngꢀc¸cꢀhꢁm:ꢀ
ꢀ
C¸cꢀhꢁmꢀth«ngꢀth−êngꢀ
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abs(x)ꢀ
TÝnhꢀargumentꢀcñaꢀsèꢀphøcꢀxꢀ
Hꢁmꢀng−îcꢀcñaꢀcosineꢀ
acos(x)ꢀ
acosh(x)ꢀ
angle(x)ꢀ
asin(x)ꢀ
asinh(x)ꢀ
atan(x)ꢀ
atan2(x,ꢀy)ꢀ
atanh(x)ꢀ
ceil(x)ꢀ
Hꢁmꢀng−îcꢀcñaꢀhyperbolicꢀcosineꢀ
TÝnhꢀgãcꢀcñaꢀsèꢀphøcꢀxꢀ
Hꢁmꢀng−îcꢀcñaꢀsineꢀ
Hꢁmꢀng−îcꢀcñaꢀhyperbolicꢀsineꢀ
Hꢁmꢀng−îcꢀcñaꢀtangentꢀ
LꢁꢀhꢁmꢀarctangentꢀcñaꢀphÇnꢀthùcꢀcñaꢀxꢀvꢁꢀyꢀ
Hꢁmꢀng−îcꢀcñaꢀhyperbolicꢀtangentꢀ
XÊpꢀxØꢀd−¬ngꢀv«ꢀcïngꢀ
conj(x)ꢀ
cos(x)ꢀ
Sèꢀphøcꢀliªnꢀhîpꢀ
Hꢁmꢀcosineꢀcñaꢀxꢀ
cosh(x)ꢀ
exp(x)ꢀ
fix(x)ꢀ
Hꢁmꢀhyperbolicꢀcosineꢀcñaꢀxꢀ
Hꢁmꢀexꢀ
XÊpꢀxØꢀkh«ngꢀ
floor(x)ꢀ
gdc(x,ꢀy)ꢀ
imag(x)ꢀ
lcm(x,ꢀy)ꢀ
log(x)ꢀ
XÊpꢀxØꢀ©mꢀv«ꢀcïngꢀ
¦ícꢀsèꢀchungꢀlínꢀnhÊtꢀcñaꢀhaiꢀsèꢀnguyªnꢀxvꢁꢀꢀꢀyꢀ
Hꢁmꢀtr¶ꢀvÒꢀphÇnꢀ¶oꢀcñaꢀsèꢀphøcꢀ
BéiꢀsèꢀchungꢀnháꢀnhÊtꢀcñaꢀhaiꢀsèꢀnguyªnꢀxꢀvꢁꢀyꢀ
Logarithmꢀtùꢀnhiªnꢀ
log10(x)ꢀ
real(x)ꢀ
Logarithmꢀc¬ꢀsèꢀ10ꢀ
Hꢁmꢀtr¶ꢀvÒꢀphÇnꢀthùcꢀcñaꢀxꢀ
PhÇnꢀd−ꢀcñaꢀphÐpꢀchiaꢀx/ꢀyꢀ
HꢁmꢀlꢁmꢀtrßnꢀvÒꢀsèꢀnguyªnꢀtèꢀ
Hꢁmꢀ dÊu:ꢀ tr¶ꢀ vÒꢀ dÊuꢀ cñaꢀ argumentꢀ nh−:ꢀꢀ
sign(1.2)=1;ꢀsign(ꢂ23.4)=ꢂ1;ꢀsign(0)=0ꢀ
HꢁmꢀtÝnhꢀsineꢀcñaꢀxꢀ
rem(x,ꢀy)ꢀ
round(x)ꢀ
sign(x)ꢀ
sin(x)ꢀ
sinh(x)ꢀ
sqrt(x)ꢀ
tan(x)ꢀ
tanh(x)ꢀ
ꢀ
HꢁmꢀtÝnhꢀhyperbolicꢀsineꢀcñaꢀxꢀ
Hꢁmꢀkhaiꢀc¨nꢀbËcꢀhaiꢀ
Tangentꢀ
Hyperbolicꢀtangentꢀ
>>ꢀ4*atan(1)ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀꢀMétꢀc¸chꢀtÝnhꢀxÊpꢀxØꢀgi¸ꢀtrÞꢀcñaꢀpiꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀ3.1416ꢀ
>>ꢀhelpꢀatant2ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀYªuꢀcÇuꢀgiópꢀ®ìꢀ®èiꢀvíiꢀhꢁmꢀatan2ꢀ
ꢀ
ATAN2ꢀꢀꢀfourꢀquadrantꢀinverseꢀtangentꢀ
ꢀꢀꢀꢀꢀꢀATAN2(Y,ꢀX)ꢀisꢀtheꢀfourꢀquadrantꢀarctangentꢀofꢀtheꢀrealꢀpartsꢀofꢀtheꢀelementsꢀofꢀXꢀandꢀ
Y.ꢀꢀꢀꢀꢂpiꢀ<=ꢀATAN2(Y,ꢀX)ꢀ<=ꢀpiꢀꢀꢀꢀꢀꢀꢀꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀseeꢀalsoꢀATAN.ꢀ
>>ꢀ180/pi*atan(ꢂ2/ꢀ3)ꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀꢂ33.69ꢀ
>>ꢀ180/pi*atan2(2,ꢀꢂ3)ꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀ146.31ꢀ
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>>ꢀ180/pi*atan2(ꢂ2,ꢀ3)ꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀꢂ33.69ꢀ
>>ꢀ180/pi*atan2(2,ꢀ3)ꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀ33.69ꢀ
>>ꢀ180/pi*atan2(ꢂ2,ꢀꢂ3)ꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀꢂ146.31ꢀ
ꢀ
MétꢀsèꢀvÝꢀdôꢀkh¸c:ꢀ
ꢀ
>>ꢀyꢀ=ꢀsqrt(3^2ꢀ+ꢀ4^2)ꢀꢀꢀ%ꢀTÝnhꢀc¹nhꢀhuyÒnꢀcñaꢀtamꢀgi¸cꢀꢀpitagoꢀ3ꢂ4ꢂ5ꢀ
y=ꢀ
ꢀꢀꢀꢀꢀꢀ5ꢀ
>>ꢀyꢀ=ꢀrem(23,4)ꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀ23/4ꢀcãꢀphÇnꢀd−ꢀlꢁꢀ3ꢀ
y=ꢀ
ꢀꢀꢀꢀꢀꢀ3ꢀ
>>ꢀxꢀ=ꢀ2.6,y1ꢀ=ꢀfix(x),y2ꢀ=ꢀfloor(x),y3ꢀ=ꢀceil(x),y4ꢀ=ꢀround(x)ꢀ
x=ꢀ
ꢀꢀꢀꢀꢀꢀ2.6000ꢀ
y1=ꢀ
ꢀꢀꢀꢀꢀꢀ2ꢀ
y2=ꢀ
ꢀꢀꢀꢀꢀꢀ2ꢀ
y3=ꢀ
ꢀꢀꢀꢀꢀꢀ3ꢀ
y4=ꢀ
ꢀꢀꢀꢀꢀꢀ3ꢀ
>>ꢀgcd(18,81)ꢀꢀꢀꢀ%ꢀꢀ9ꢀlꢁꢀ−ícꢀsèꢀchungꢀlínꢀnhÊtꢀcñaꢀ18ꢀvꢁꢀ81ꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀ9ꢀ
>>ꢀlcm(18,81)ꢀꢀꢀꢀ%ꢀ162ꢀlꢁꢀbéiꢀsèꢀchungꢀlínꢀnhÊtꢀcñaꢀ18ꢀvꢁꢀ81ꢀ
ans=ꢀ
ꢀꢀꢀꢀꢀꢀ162ꢀ
ꢀ
VÝꢀdô:ꢀ¦ícꢀl−îngꢀchiÒuꢀcaoꢀcñaꢀng«iꢀnhꢁꢀ
ꢀꢀꢀVÊnꢀ®Ò:ꢀGi¶ꢀthiÕtꢀbiÕtꢀkho¶ngꢀc¸chꢀtõꢀngêiꢀquanꢀs¸tꢀ®Õnꢀng«iꢀnhꢁꢀlꢁꢀD,ꢀgãcꢀtõꢀngêiꢀquanꢀ
s¸tꢀ®Õnꢀng«iꢀnhꢁꢀlꢁꢀ ;ꢀchiÒuꢀcaoꢀcñaꢀngêiꢀquanꢀs¸tꢀlꢁꢀh.ꢀHáiꢀng«iꢀnhꢁꢀcaoꢀbaoꢀnhiªu?ꢀꢀ
ꢀ
ꢀꢀꢀGi¶iꢀph¸p:ꢀTaꢀbiÓuꢀdiÔnꢀkÝchꢀthøcꢀnh−ꢀh×nhꢀ2.1:ꢀ
ꢀ
ꢀꢀꢀꢀ
ꢀ
(kh«ngꢀthÊy)ꢀ
H×nhꢀ2.1ꢀ
ꢀ
Ng«iꢀnhꢁꢀcãꢀchiÒuꢀcaoꢀlꢁꢀHꢀ+ꢀh,ꢀHꢀlꢁꢀchiÒuꢀdꢁiꢀcñaꢀmétꢀc¹nhꢀcñaꢀtamꢀgi¸c,ꢀchiÒuꢀdꢁiꢀnꢁyꢀ
cãꢀthÓꢀtÝnhꢀ®−îcꢀb»ngꢀc«ngꢀthøcꢀquanꢀhÖꢀgi÷aꢀgãcꢀvꢁꢀc¹nhꢀcñaꢀtamꢀgi¸c:ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀtan()ꢀ=ꢀꢀꢀ
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ꢀ
Tõꢀ®ãꢀtaꢀcãꢀchiÒuꢀcaoꢀcñaꢀng«iꢀnhꢁꢀlꢁꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀhꢀ+ꢀHꢀ=ꢀhꢀ+ꢀD.tan()ꢀ
NÕuꢀhꢀ=2meters,ꢀDꢀ=50meters,ꢀvꢁꢀꢀlꢁꢀ60o,ꢀMATLABꢀsÏꢀ®aꢀraꢀkÕtꢀqu¶ꢀlꢁ:ꢀ
ꢀ
>>ꢀhꢀ=ꢀ2ꢀ
hꢀ=ꢀ
ꢀꢀꢀꢀꢀ2ꢀ
>>ꢀthetaꢀ=ꢀ60ꢀ
thetaꢀ=ꢀ
ꢀꢀꢀꢀ60ꢀ
>>ꢀDꢀ=ꢀ50ꢀ
Dꢀ=ꢀ
ꢀꢀꢀꢀ50ꢀ
>>ꢀbuiding_heightꢀ=ꢀh+D*atan(theta*pi/180)ꢀ
buiding_heightꢀ=ꢀ
ꢀꢀꢀ54.3599ꢀ
ꢀ
ꢀ
ꢀ
VÝꢀdôꢀsùꢀsuyꢀgi¶mꢀdoꢀph©nꢀrꢃꢀ
ꢀꢀꢀꢀVÊnꢀ®Òꢀ:ꢀSùꢀph©nꢀrꢃꢀph©nꢀtöꢀpoloniumꢀcãꢀchuꢀkúꢀph©nꢀrꢃꢀlꢁꢀ140ꢀngꢁy,ꢀtøcꢀlꢁꢀsauꢀ140ꢀ
ngꢁyꢀ th×ꢀ l−îngꢀ poloniunꢀ cßnꢀ l¹iꢀ lꢁꢀ 1/2ꢀ l−îngꢀ banꢀ ®Çu.ꢀ Háiꢀ nÕuꢀ banꢀ ®Çuꢀ cãꢀ 10ꢀ gramsꢀ
polonium,ꢀnãꢀsÏꢀcßnꢀl¹iꢀbaoꢀnhiªuꢀsauꢀ250ꢀngꢁy?ꢀ
ꢀꢀꢀꢀGi¶iꢀquyÕt:ꢀSauꢀ1ꢀchuꢀkúꢀph©nꢀrꢃꢀhoÆcꢀ140ꢀngꢁy,ꢀcßnꢀl¹iꢀ10x0.5ꢀ=ꢀ5ꢀgrams;ꢀsauꢀ2ꢀchuꢀkúꢀ
ph©nꢀrꢃꢀhoÆcꢀ280ꢀngꢁy,ꢀcßnꢀl¹iꢀ5x0.5ꢀ=ꢀ10x(0.5)2ꢀ=ꢀ2.5grams,ꢀtõꢀ®ãꢀtaꢀcãꢀkÕtꢀqu¶ꢀn»mꢀtrongꢀ
kho¶ngꢀ5ꢀvꢁꢀ2.5ꢀgrams,ꢀvꢁꢀtaꢀcãꢀc«ngꢀthøcꢀtÝnhꢀphÇnꢀcßnꢀl¹iꢀsauꢀkho¶ngꢀthêiꢀgianꢀbÊtꢀkú:ꢀ
ꢀ
ꢀꢀꢀꢀkhèiꢀl−îngꢀcßnꢀl¹iꢀ=ꢀkhèiꢀl−îngꢀbanꢀ®Çuꢀx(0.5)thêiꢀgian/ꢀchuꢀkú
ꢀ
vÝꢀdôꢀthêiꢀgianꢀlꢁꢀ250ꢀngꢁy,ꢀꢀvꢁꢀkÕtꢀqu¶ꢀMATLABꢀ®aꢀraꢀlꢁ:ꢀ
ꢀ
ꢀ
>>ꢀinitial_amountꢀ=ꢀ10;ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀKhèiꢀl−îngꢀbanꢀ®Çuꢀ
>>ꢀhalf_lifeꢀ=ꢀ140;ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀChuꢀkúꢀph©nꢀrꢃꢀ
>>ꢀtimeꢀ=ꢀ250;ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀThêiꢀgianꢀtÝnhꢀkhèiꢀl−îngꢀ
>>ꢀamount_leftꢀ=ꢀinitial_*0.5^(time/half_life)ꢀ
amount_left=ꢀ
ꢀꢀꢀꢀꢀꢀ2.9003ꢀ
ꢀ
VÝꢀdôꢀtÝnhꢀto¸nꢀvÒꢀlꢃiꢀxuÊtꢀꢀ
ꢀꢀꢀVÊnꢀ®Ò:ꢀB¹nꢀ®ångꢀýꢀmuaꢀ«t«ꢀmíiꢀvíiꢀgi¸ꢀ18,500ꢀdollars.ꢀNg−êiꢀb¸nꢀ«t«ꢀ®aꢀraꢀhaiꢀgi¶iꢀph¸pꢀ
vÒꢀtꢁiꢀchÝnhꢀlꢁ:ꢀthøꢀnhÊt,ꢀtr¶ꢀ2.9%ꢀlꢃiꢀxuÊtꢀcñaꢀsèꢀtiÒnꢀtrªnꢀtrongꢀvßngꢀ4ꢀn¨m.ꢀThøꢀhaiꢀlꢁꢀtr¶ꢀ
8.9%ꢀlꢃiꢀxuÊtꢀcñaꢀsèꢀtiÒnꢀtrªnꢀtrongꢀvßngꢀ4ꢀn¨mꢀvꢁꢀgi¸ꢀb¸nꢀ®−îcꢀgi¶mꢀ®iꢀmétꢀkho¶nꢀlꢁꢀ1500ꢀ
dollars.ꢀHáiꢀvíiꢀgi¶iꢀph¸pꢀnꢁoꢀth×ꢀb¹nꢀmuaꢀ®−îcꢀ«t«ꢀvíiꢀgi¸ꢀrÎꢀh¬n?ꢀ
ꢀꢀꢀGi¶iꢀph¸p:ꢀSèꢀtiÒnꢀtr¶ꢀhꢁngꢀth¸ngꢀlꢁꢀP,ꢀtrªnꢀtængꢀsèꢀtiÒnꢀlꢁꢀAꢀdollars,ꢀtØꢀsèꢀlꢃiꢀxuÊtꢀhꢁngꢀ
th¸ngꢀlꢁꢀR,ꢀtr¶ꢀtrongꢀMꢀth¸ng:ꢀ
ꢀꢀꢀꢀꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀPꢀ=ꢀAꢀ
ꢀ
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TængꢀsèꢀtiÒnꢀph¶iꢀtr¶ꢀsÏꢀlꢁ:ꢀTꢀ=ꢀPxMꢀ
Gi¶iꢀph¸pꢀMATLABꢀ®aꢀraꢀlꢁ:ꢀ
ꢀ
>>ꢀformatꢀbankꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀꢀDïngꢀd¹ngꢀhiÓnꢀthÞꢀng©nꢀhꢁngꢀ
>>ꢀAꢀ=ꢀ18500;ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀTængꢀsèꢀtiÒnꢀ
>>ꢀMꢀ=ꢀ12*4;ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀSèꢀth¸ngꢀph¶iꢀtr¶ꢀlꢃiꢀ
>>ꢀFRꢀ=ꢀ1500;ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀTiÒnꢀgi¶mꢀgi¸ꢀcñaꢀnhꢁꢀm¸yꢀ
>>ꢀ%ꢀꢀGi¶iꢀph¸pꢀthøꢀnhÊtꢀ
>>ꢀRꢀ=ꢀ(2.9/100)/12;ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀTØꢀlÖꢀlꢃiꢀxuÊtꢀhꢁngꢀth¸ngꢀꢀ
>>ꢀPꢀ=ꢀA*(R*(1+R)^M/((1+R)^Mꢀꢂꢀ1))ꢀꢀꢀ%ꢀKho¶nꢀtiÒnꢀph¶iꢀtr¶ꢀhꢁngꢀth¸ngꢀ
P=ꢀ
ꢀꢀꢀꢀꢀꢀ408.67ꢀ
>>ꢀT1ꢀ=ꢀP*Mꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀTængꢀgi¸ꢀtrÞꢀcñaꢀ«t«ꢀ
T1=ꢀ
ꢀꢀꢀꢀꢀꢀ19616.06ꢀ
>>ꢀꢀ%ꢀꢀGi¶iꢀph¸pꢀthøꢀhaiꢀ
>>ꢀRꢀ=ꢀ(8.9/100)/12;ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀTØꢀlÖꢀlꢃiꢀxuÊtꢀhꢁngꢀth¸ngꢀ
>>ꢀPꢀ=ꢀ(AꢂFR)*(R*(1ꢀ+ꢀR)^M/((1+R)^Mꢀꢂꢀ1))ꢀꢀ%ꢀTiÒnꢀph¶iꢀtr¶ꢀhꢁngꢀth¸ngꢀ
P=ꢀ
ꢀꢀꢀꢀꢀꢀ422.24ꢀ
>>ꢀT2ꢀ=ꢀP*Mꢀꢀꢀꢀꢀ%ꢀꢀTængꢀgi¸ꢀtrÞꢀcñaꢀ«t«ꢀ
T2=ꢀ
ꢀꢀꢀꢀꢀꢀ20267.47ꢀ
>>ꢀDiffꢀ=ꢀT2ꢀꢂꢀT1ꢀ
Diff=ꢀ
ꢀꢀꢀꢀꢀꢀ651.41ꢀ
ꢀ
Nh−ꢀvËyꢀtaꢀcãꢀgi¶iꢀph¸pꢀthøꢀnhÊtꢀgi¸ꢀrÎꢀh¬nꢀgi¶iꢀph¸pꢀthøꢀhai.ꢀ
ꢀ
VÝꢀdô:ꢀVÊnꢀ®Òꢀnångꢀ®éꢀacidꢀ
ꢀꢀꢀVÊnꢀ®Ò:ꢀNh−ꢀmétꢀphÇnꢀcñaꢀqu¸ꢀtr×nhꢀs¶nꢀxuÊtꢀbéꢀphËnꢀcñaꢀvËtꢀ®ócꢀt¹iꢀmétꢀnhꢁꢀm¸yꢀtùꢀ
®éng,ꢀbéꢀphËnꢀ®ãꢀ®−îcꢀnhóngꢀtrongꢀn−ícꢀ®Óꢀlꢁmꢀnguéi,ꢀsauꢀ®ãꢀnhóngꢀtrongꢀbånꢀ®ùngꢀdungꢀ
dÞchꢀacidꢀ®Óꢀlꢁmꢀs¹ch.ꢀTrongꢀtoꢁnꢀbéꢀcñaꢀqu¸ꢀtr×nhꢀnångꢀ®éꢀacidꢀgi¶mꢀ®iꢀkhiꢀc¸cꢀbéꢀphËnꢀ®ꢂ
−îcꢀlÊyꢀraꢀkháiꢀbånꢀacidꢀv×ꢀkhiꢀnhóngꢀbéꢀphËnꢀcñaꢀvËtꢀ®ócꢀvꢁoꢀbånꢀth×ꢀmétꢀl−îngꢀn−ícꢀcßnꢀ
b¸mꢀtrªnꢀvËtꢀ®ócꢀkhiꢀnhóngꢀëꢀbÓꢀtr−ícꢀcòngꢀvꢁoꢀtheoꢀvꢁꢀkhiꢀnhÊcꢀraꢀkháiꢀbånꢀmétꢀl−îngꢀacidꢀ
b¸mꢀtheoꢀvËt.ꢀ§Óꢀ®¶mꢀb¶oꢀchÊtꢀl−îngꢀth×ꢀnångꢀ®éꢀacidꢀph¶iꢀkh«ngꢀ®−îcꢀnháꢀh¬nꢀmétꢀl−îngꢀ
tèiꢀthiÓu.ꢀB¹nꢀhꢃyꢀb¾tꢀ®Çuꢀvíiꢀnångꢀ®éꢀdungꢀdÞchꢀlꢁꢀ90%ꢀth×ꢀnångꢀ®éꢀtèiꢀthiªuꢀph¶iꢀlꢁꢀ50%.ꢀ
L−îngꢀchÊtꢀlángꢀthªmꢀvꢁoꢀvꢁꢀlÊyꢀ®iꢀsauꢀmçiꢀlÇnꢀnhóngꢀdaoꢀ®éngꢀtrongꢀkho¶ngꢀtõꢀ1%ꢀ®Õnꢀ
10%.ꢀHáiꢀbaoꢀnhiªuꢀbéꢀphËnꢀcãꢀthÓꢀnhóngꢀvꢁoꢀbÓꢀdungꢀdÞchꢀacidꢀtr−ícꢀkhiꢀnångꢀ®éꢀcñaꢀnãꢀ
gi¶mꢀxuèngꢀd−íiꢀmøcꢀchoꢀphÐp?ꢀ
ꢀꢀꢀGi¶iꢀph¸p:ꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀBanꢀ®Çuꢀnångꢀ®éꢀacidꢀlꢁꢀꢀinitial_conꢀ=ꢀ90%ꢀ=ꢀacid/ꢀ(acidꢀ+ꢀwater)ꢀ
sauꢀlÇnꢀnhóngꢀthøꢀnhÊtꢀnångꢀ®éꢀacidꢀcßn:ꢀ
ꢀꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀconꢀ=ꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ=ꢀꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ=ꢀꢀ
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ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ=ꢀꢀ
ꢀ
acid ꢀlꢁꢀl−îngꢀacidꢀbanꢀ®ÇuꢀtrongꢀdungꢀdÞch,ꢀ water ꢀlꢁꢀl−îngꢀn−ícꢀbanꢀ®Çuꢀtrongꢀdungꢀ
dÞch,ꢀ lost ꢀlꢁꢀl−îngꢀphÇnꢀtr¨mꢀn−ícꢀthªmꢀvꢁo.ꢀSèꢀacidꢀcßnꢀl¹iꢀtrongꢀdungꢀdÞchꢀsauꢀlÇnꢀ
nhóngꢀthøꢀnhÊtꢀlꢁ:ꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀacid_leftꢀ=ꢀꢀ
ꢀ
NghÜaꢀlꢁ,ꢀkhiꢀnhóngꢀlÇnꢀthøꢀhaiꢀnångꢀ®éꢀdungꢀdÞchꢀsÏꢀlꢁ:ꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀconꢀ=ꢀꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ=ꢀꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ=ꢀꢀꢀ
ꢀ
TiÕpꢀtôcꢀqu¸ꢀtr×nhꢀnꢁy,ꢀsauꢀnꢀlÇnꢀnhóng,ꢀnångꢀ®éꢀacidꢀlꢁ:ꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀconꢀ=ꢀꢀ
ꢀ
NÕuꢀnångꢀ®éꢀacidꢀcßnꢀl¹iꢀlꢁꢀmøcꢀtèiꢀthiÓuꢀchÊpꢀnhËnꢀ®−îc,ꢀsèꢀlÇnꢀnhóngꢀcùcꢀ®¹iꢀsÏꢀlꢁꢀmétꢀ
sèꢀnguyªnꢀb»ngꢀhoÆcꢀnháꢀh¬nꢀn:ꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀnꢀ=ꢀꢀ
ꢀ
TrongꢀMATLABꢀgi¶iꢀph¸pꢀsÏꢀlꢁ:ꢀ
ꢀ
>>ꢀinitial_conꢀ=ꢀ90ꢀ
initial_con=ꢀ
ꢀꢀꢀꢀꢀꢀ90ꢀ
>>ꢀmin_conꢀ=ꢀ50ꢀ
min_con=ꢀ
ꢀꢀꢀꢀꢀꢀ50ꢀ
>>ꢀlostꢀ=ꢀ0.01;ꢀ
>>ꢀnꢀ=ꢀfloor(log(ꢀinitial_con/min_con)/log(1+lost))ꢀ
n=ꢀ
ꢀꢀꢀꢀꢀꢀ59ꢀ
ꢀ
Nh−ꢀvËyꢀcãꢀthÓꢀnhóngꢀ59ꢀlÇnꢀtr−ícꢀkhiꢀnångꢀ®éꢀacidꢀgi¶mꢀxuèngꢀd−íiꢀ50%.ꢀChóꢀýꢀhꢁmꢀ
floorꢀdïngꢀ®ÓꢀlꢁmꢀtrßnꢀsèꢀnꢀxuèngꢀsèꢀnguyªnꢀgÇnꢀnhÊt,ꢀvꢁꢀëꢀd©yꢀtaꢀcòngꢀcãꢀthÓꢀdïngꢀhꢁmꢀ
logarithmꢀc¬ꢀsèꢀ10ꢀvꢁꢀlogarithmꢀc¬ꢀsèꢀ2ꢀthayꢀchoꢀhꢁmꢀlogarithmꢀtùꢀnhiªnꢀëꢀtrªn.ꢀ
ꢀ
ꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂoOoꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢀ
ꢀ
ꢀ
15
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ch−¬ngꢀ3ꢀ
NH÷NGꢀ§ÆCꢀ§IÓMꢀCñAꢀCöAꢀSæꢀLÖNHꢀ
ꢀ
ꢀ
CöaꢀsæꢀlÖnhꢀ(comand)ꢀcñaꢀMATLABꢀcãꢀrÊtꢀnhiÒuꢀnh÷ngꢀ®Æcꢀ®iÓmꢀcÇnꢀchóꢀý,ꢀmétꢀsèꢀchóngꢀ
®ꢃꢀ®−îcꢀgiíiꢀthiÖuꢀëꢀch−¬ngꢀtr−íc,ꢀvꢁꢀsauꢀ®©yꢀchóngꢀtaꢀt×mꢀhiÓuꢀrâꢀh¬nꢀvÒꢀchóng.ꢀ
ꢀ
3.1ꢀQu¶nꢀlÝꢀkh«ngꢀgianꢀlꢁmꢀviÖcꢀcñaꢀMATLABꢀꢀ
ꢀ
ꢀꢀꢀꢀC¸cꢀd÷ꢀliÖuꢀvꢁꢀbiÕnꢀ®−îcꢀt¹oꢀlªnꢀtrongꢀcöaꢀsæꢀlÖnh,ꢀ®−îcꢀl−uꢀtrongꢀmétꢀphÇnꢀgäiꢀlꢁꢀkh«ngꢀ
gianꢀlꢁmꢀviÖcꢀcñaꢀMATLAB.ꢀMuènꢀxemꢀtªnꢀbiÕnꢀtrongꢀkh«ngꢀgianꢀlꢁmꢀviÖcꢀcñaꢀMATLABꢀtaꢀ
dïngꢀlÖnhꢀwho:ꢀ
ꢀ
>>ꢀwhoꢀ
ꢀ
Yourꢀvariablesꢀare:ꢀ
ꢀ
Dꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀhꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
buiding_heightꢀꢀꢀꢀꢀꢀthetaꢀ
ꢀ
C¸cꢀbiÕnꢀnꢁyꢀ®−îcꢀdïngꢀtrongꢀvÝꢀdôꢀ−ícꢀl−îngꢀchiÒuꢀcaoꢀng«iꢀnhꢁ.ꢀ§ÓꢀxemꢀchiꢀtiÕtꢀh¬nꢀvÒꢀ
c¸cꢀbiÕnꢀtaꢀdïngꢀlÖnhꢀwhos:ꢀ
ꢀ
>>ꢀwhosꢀ
ꢀNameꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀSizeꢀꢀꢀꢀꢀꢀꢀꢀꢀBytesꢀꢀClassꢀ
ꢀ
ꢀꢀDꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ1x1ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ8ꢀꢀdoubleꢀarrayꢀ
ꢀꢀbuiding_heightꢀꢀꢀ1x1ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ8ꢀꢀdoubleꢀarrayꢀ
ꢀꢀhꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ1x1ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ8ꢀꢀdoubleꢀarrayꢀ
ꢀꢀthetaꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ1x1ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ8ꢀꢀdoubleꢀarrayꢀ
ꢀ
Grandꢀtotalꢀisꢀ4ꢀelementsꢀusingꢀ32ꢀbytesꢀ
ꢀ
ꢀꢀꢀMçiꢀbiÕnꢀ®−îcꢀliÖtꢀkªꢀvíiꢀkÝchꢀcìꢀcñaꢀnã,ꢀsèꢀbytesꢀsöꢀdông,ꢀvꢁꢀc¸cꢀlípꢀcñaꢀchóngꢀ(class),ꢀ
trongꢀvÝꢀdôꢀ®ÆcꢀbiÖtꢀnꢁy,ꢀc¸cꢀbiÕnꢀ®Òuꢀlꢁꢀsèꢀ®¬n,ꢀcãꢀ®éꢀchÝnhꢀx¸cꢀhaiꢀsèꢀsauꢀdÊuꢀphÈy.ꢀLÖnhꢀ
whosꢀ®ÆcꢀbiÖtꢀcãꢀÝchꢀkhiꢀnghiªnꢀcøuꢀ®ÕnꢀphÇnꢀm¶ngꢀvꢁꢀc¸cꢀkiÓuꢀd÷ꢀliÖuꢀkh¸c.ꢀꢀ
ꢀꢀꢀꢀ
Ngoꢁiꢀc¸cꢀhꢁmꢀnꢁy,ꢀtrongꢀmôcꢀShowꢀWorkspaceꢀtrongꢀb¶ngꢀchänꢀfileꢀt¹oꢀraꢀcöaꢀsæꢀ
GUIꢀgäiꢀlꢁꢀWorkspaceꢀBrowser,ꢀnãꢀchøaꢀc¸cꢀth«ngꢀtinꢀt−¬ngꢀtùꢀnh−ꢀlÖnhꢀwhos.ꢀThªmꢀn÷aꢀ
nãꢀt¹oꢀchoꢀb¹nꢀkh¶ꢀn¨ngꢀxo¸,ꢀlꢁmꢀs¹chꢀc¸cꢀbiÕnꢀmꢁꢀb¹nꢀchän.ꢀCöaꢀsæꢀnꢁyꢀcòngꢀcãꢀthÓꢀt¹oꢀ
b»ngꢀc¸chꢀnhÊnꢀnótꢀWorkspaceꢀBrowser,ꢀtrªnꢀthanhꢀc«ngꢀcôꢀcñaꢀcöaꢀsæꢀlÖnh.ꢀ
ꢀꢀꢀꢀꢀ Nh−ꢀ ®ꢃꢀ tr×nhꢀ bꢁyꢀ ëꢀ trªn,ꢀ lÖnhꢀ clearꢀ cãꢀ thÓꢀ xo¸ꢀ biÕnꢀ tõꢀ kh«ngꢀ gianꢀ lꢁmꢀ viÖcꢀ cñaꢀ
MATLAB.ꢀꢀ
VÝꢀdô:ꢀ
>>ꢀclearꢀꢀhꢀꢀDꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀXo¸ꢀc¸cꢀbiÕnꢀhꢀvꢁꢀDꢀ
>>ꢀwhoꢀ
ꢀ
Yourꢀvariablesꢀare:ꢀ
ꢀ
buiding_heightꢀꢀꢀꢀꢀꢀthetaꢀ
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ꢀ
C¸cꢀtuúꢀchänꢀkh¸cꢀcñaꢀhꢁmꢀclearꢀchóngꢀtaꢀcãꢀthÓꢀt×mꢀhiÓuꢀthªmꢀb»ngꢀlÖnhꢀhelp:ꢀ
ꢀ
>>ꢀhelpꢀclearꢀ
ꢀ
ꢀCLEARꢀꢀClearꢀvariablesꢀandꢀfunctionsꢀfromꢀmemory.ꢀ
ꢀꢀꢀꢀCLEARꢀremovesꢀallꢀvariablesꢀfromꢀtheꢀworkspace.ꢀ
ꢀꢀꢀꢀCLEARꢀVARIABLESꢀdoesꢀtheꢀsameꢀthing.ꢀ
ꢀꢀꢀꢀCLEARꢀGLOBALꢀremovesꢀallꢀglobalꢀvariables.ꢀ
ꢀꢀꢀꢀCLEARꢀFUNCTIONSꢀremovesꢀallꢀcompiledꢀMꢂfunctions.ꢀ
ꢀꢀꢀꢀCLEARꢀMEXꢀremovesꢀallꢀlinksꢀtoꢀMEXꢂfiles.ꢀ
ꢀꢀꢀꢀCLEARꢀALLꢀremovesꢀallꢀvariables,ꢀglobals,ꢀfunctionsꢀandꢀMEXꢀlinks.ꢀ
ꢀꢀ
ꢀꢀꢀꢀCLEARꢀVAR1ꢀVAR2ꢀ...ꢀclearsꢀtheꢀvariablesꢀspecified.ꢀꢀTheꢀwildcardꢀ
ꢀꢀꢀꢀcharacterꢀ'*'ꢀcanꢀbeꢀusedꢀtoꢀclearꢀvariablesꢀthatꢀmatchꢀaꢀpattern.ꢀ
ꢀꢀꢀꢀForꢀinstance,ꢀCLEARꢀX*ꢀclearsꢀallꢀtheꢀvariablesꢀinꢀtheꢀcurrentꢀ
ꢀꢀꢀꢀworkspaceꢀthatꢀstartꢀwithꢀX.ꢀ
ꢀꢀ
ꢀꢀꢀꢀIfꢀXꢀisꢀglobal,ꢀCLEARꢀXꢀremovesꢀXꢀfromꢀtheꢀcurrentꢀworkspace,ꢀ
ꢀꢀꢀꢀbutꢀleavesꢀitꢀaccessibleꢀtoꢀanyꢀfunctionsꢀdeclaringꢀitꢀglobal.ꢀ
ꢀꢀꢀꢀCLEARꢀGLOBALꢀXꢀcompletelyꢀremovesꢀtheꢀglobalꢀvariableꢀX.ꢀ
ꢀꢀ
ꢀꢀꢀꢀCLEARꢀFUNꢀclearsꢀtheꢀfunctionꢀspecified.ꢀꢀIfꢀFUNꢀhasꢀbeenꢀlockedꢀ
ꢀꢀꢀꢀbyꢀMLOCKꢀitꢀwillꢀremainꢀinꢀmemory.ꢀ
ꢀꢀ
ꢀꢀꢀꢀCLEARꢀALLꢀalsoꢀhasꢀtheꢀsideꢀeffectꢀofꢀremovingꢀallꢀdebuggingꢀ
ꢀꢀꢀꢀbreakpointsꢀsinceꢀtheꢀbreakpointsꢀforꢀaꢀfileꢀareꢀclearedꢀwheneverꢀ
ꢀꢀꢀꢀtheꢀmꢂfileꢀchangesꢀorꢀisꢀcleared.ꢀꢀꢀ
ꢀꢀ
ꢀꢀꢀꢀUseꢀtheꢀfunctionalꢀformꢀofꢀCLEAR,ꢀsuchꢀasꢀCLEAR('name'),ꢀ
ꢀꢀꢀꢀwhenꢀtheꢀvariableꢀnameꢀorꢀfunctionꢀnameꢀisꢀstoredꢀinꢀaꢀx©u.ꢀ
ꢀꢀꢀꢀSeeꢀalsoꢀWHO,ꢀWHOS,ꢀMLOCK,ꢀMUNLOCK.ꢀ
ꢀ
ꢀꢀꢀꢀ ꢀCuèiꢀcïng,ꢀkhiꢀlꢁmꢀviÖcꢀtrongꢀkh«ngꢀgianꢀlꢁmꢀviÖcꢀcñaꢀMATLAB,ꢀnãꢀth−êngꢀthuËnꢀ
tiÖnꢀ®ÓꢀghiꢀhoÆcꢀinꢀmétꢀb¶nꢀsaoꢀc«ngꢀviÖcꢀcñaꢀb¹n,ꢀlÖnhꢀdiaryꢀghiꢀd÷ꢀliÖuꢀng−êiꢀdïngꢀ®−aꢀ
vꢁoꢀvꢁꢀcöaꢀsæꢀlÖnhꢀvꢁꢀ®−aꢀraꢀfileꢀv¨nꢀb¶nꢀd¹ngꢀmꢃꢀASCIIꢀcãꢀtªnꢀlꢁꢀdiaryꢀtrongꢀth−ꢀmôcꢀhiÖnꢀ
t¹i.ꢀ
ꢀ
>>ꢀdiaryꢀframeꢀꢀꢀ%ꢀghiꢀd÷ꢀliÖuꢀvaoꢀfileꢀframeꢀꢀ
>>ꢀdiaryꢀoffꢀꢀꢀꢀꢀ%ꢀꢀkÕtꢀthócꢀlÖnhꢀdiaryꢀvꢁꢀ®ãngꢀfileꢀ
ꢀ
ꢀꢀꢀꢀꢀ KhiꢀcöaꢀsæꢀlÖnhꢀ®−îcꢀchän,ꢀchänꢀprint...ꢀꢀtõꢀb¶ngꢀchänꢀfileꢀ®Óꢀinꢀmétꢀb¶nꢀcñaꢀcöaꢀsæꢀ
lÖnh,ꢀb¹nꢀcãꢀthÓꢀdïngꢀchuétꢀ®ÓꢀlùaꢀchänꢀphÇnꢀm×nhꢀmuènꢀghi,ꢀchänꢀPintꢀSelection...ꢀtõꢀb¶ngꢀ
chänꢀfile,ꢀ®ÓꢀinꢀmétꢀphÇnꢀv¨nꢀb¶nꢀ®ꢃꢀlùaꢀchän.ꢀ
ꢀ
3.2ꢀGhiꢀvꢁꢀphôcꢀhåiꢀd÷ꢀliÖuꢀ
ꢀ
ꢀꢀꢀꢀꢀ §Óꢀnhíꢀc¸cꢀbiÕnꢀMATLABꢀcãꢀthÓꢀghiꢀvꢁꢀgäiꢀl¹iꢀd÷ꢀliÖuꢀtõꢀfileꢀtrongꢀm¸yꢀtÝnhꢀcñaꢀb¹n.ꢀ
MôcꢀWorkspaceꢀas...ꢀtrongꢀb¶ngꢀchänꢀfileꢀmëꢀhépꢀchuÈnꢀhéiꢀtho¹iꢀ®ÓꢀghiꢀtÊtꢀc¶ꢀc¸cꢀbiÕnꢀ
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hiÖnꢀt¹i.ꢀGièngꢀnh−ꢀvËy,ꢀtrongꢀmôcꢀLoadꢀWorkspaceꢀtrongꢀb¶ngꢀchänꢀfileꢀmëꢀhépꢀhéiꢀtho¹iꢀ
®Óꢀgäiꢀl¹iꢀtÊtꢀc¶ꢀc¸cꢀbiÕnꢀmꢁꢀtaꢀ®ꢃꢀghiꢀl¹iꢀtõꢀkh«ngꢀgianꢀlꢁmꢀviÖcꢀtr−íc,ꢀnãꢀkh«ngꢀlꢁmꢀmÊtꢀ
c¸cꢀbiÕnꢀnꢁyꢀtrongꢀkh«ngꢀgianꢀlꢁmꢀviÖcꢀhiÖnꢀt¹i.ꢀKhiꢀtaꢀgäiꢀl¹iꢀc¸cꢀbiÕn,ꢀmꢁꢀc¸cꢀbiÕnꢀnꢁyꢀ
trïngꢀtªnꢀvíiꢀc¸cꢀbiÕnꢀtrongꢀkh«ngꢀgianꢀlꢁmꢀviÖcꢀcñaꢀMATLAB,ꢀnãꢀsÏꢀthayꢀ®æiꢀgi¸ꢀtrÞꢀcñaꢀc¸cꢀ
biÕnꢀtheoꢀgi¸ꢀtrÞꢀcñaꢀc¸cꢀbiÕnꢀgäiꢀraꢀtõꢀfile.ꢀ
ꢀꢀꢀꢀꢀ NÕuꢀb¶ngꢀchänꢀfileꢀkh«ngꢀthuËnꢀtiÖnꢀhoÆcꢀkh«ngꢀ®¸pꢀøngꢀ®−îcꢀnh÷ngꢀyªuꢀcÇuꢀcñaꢀ
b¹n,ꢀMATLABꢀcungꢀcÊpꢀhaiꢀlÖnhꢀsaveꢀvꢁꢀload,ꢀnãꢀthùcꢀhiÖnꢀmétꢀc¸chꢀmÒmꢀdÎoꢀh¬n,ꢀtrongꢀ
tr−êngꢀhîpꢀ®ÆcꢀbiÖt,ꢀlÖnhꢀsaveꢀchoꢀphÐpꢀb¹nꢀghiꢀmétꢀhoÆcꢀnhiÒuꢀh¬nꢀmétꢀbiÕnꢀtuyꢀtheoꢀsùꢀ
lùaꢀchonꢀcñaꢀb¹n.ꢀ
VÝꢀdô:ꢀ
>>ꢀsaveꢀ
ꢀ
ChøaꢀtÊtꢀc¶ꢀc¸cꢀbiÕnꢀtrongꢀMATLABꢀtheoꢀkiÓuꢀnhÞꢀph©nꢀtrongꢀfileꢀMATLAB.matꢀ
ꢀ
>>ꢀsaveꢀꢀdataꢀ
ꢀ
chøaꢀtÊtꢀc¶ꢀc¸cꢀbiÕnꢀtrongꢀMATLABꢀtheoꢀkiÓuꢀnhÞꢀph©nꢀtrongꢀfleꢀdata.mat.ꢀ
ꢀ
>>ꢀsaveꢀꢀdataꢀꢀerasersꢀꢀpadsꢀꢀtapeꢀꢀꢀꢂasciiꢀ
ꢀ
Ghiꢀc¸cꢀbiÕnꢀerasers,ꢀpads,ꢀtapeꢀtrongꢀd¹ngꢀmꢃꢀASCIIꢀ8ꢀsèꢀtrongꢀfileꢀdata.ꢀFileꢀd¹ngꢀmꢃꢀ
ASCIIꢀcãꢀthÓꢀsöaꢀ®æiꢀb»ngꢀbÊtꢀcøꢀch−¬ngꢀtr×nhꢀso¹nꢀth¶oꢀv¨nꢀb¶nꢀnꢁo,ꢀchóꢀýꢀr»ngꢀfileꢀASCIIꢀ
kh«ngꢀcãꢀphÇnꢀmëꢀréngꢀꢀ.mat.ꢀ
ꢀ
>>ꢀsaveꢀꢀdataꢀꢀerasersꢀꢀpadsꢀꢀtapeꢀꢀꢂasciiꢀꢀꢀꢂdoubleꢀ
ꢀ
Ghiꢀc¸cꢀbiÕnꢀerasers,ꢀpads,ꢀtapeꢀd¹ngꢀASCIIꢀ16ꢀsèꢀtrongꢀfileꢀdata.ꢀ
LÖnhꢀloadꢀcòngꢀdïngꢀvíiꢀcóꢀph¸pꢀt−îngꢀtù.ꢀ
ꢀ
3.3ꢀKhu«nꢀd¹ngꢀhiÓnꢀthÞꢀsèꢀ
ꢀ
ꢀꢀꢀꢀꢀꢀ KhiꢀMATLABꢀhiÓnꢀthÞꢀkÕtꢀqu¶ꢀd¹ngꢀsè,ꢀnãꢀtu©nꢀtheoꢀmétꢀsèꢀquyꢀ®Þnhꢀsau:ꢀ
MÆcꢀ®Þnh,ꢀnÕuꢀkÕtꢀqu¶ꢀlꢁꢀsèꢀnguyªnꢀth×ꢀMATLABꢀhiÓnꢀthÞꢀnãꢀlꢁꢀmétꢀsèꢀnguyªn,ꢀkhiꢀkÕtꢀqu¶ꢀlꢁꢀ
métꢀsèꢀthùcꢀth×ꢀMATLABꢀhiÓnꢀthÞꢀsèꢀxÊpꢀxØꢀvíiꢀbènꢀch÷ꢀsèꢀsauꢀdÊuꢀphÈy,ꢀcßnꢀc¸cꢀsèꢀd¹ngꢀ
khoaꢀhäcꢀth×ꢀMATLABꢀhiÓnꢀthÞꢀcòngꢀgièngꢀnh−ꢀtrongꢀc¸cꢀm¸yꢀtÝnhꢀkhoaꢀhäc.ꢀ
ꢀꢀꢀꢀ B¹nꢀ cãꢀ thÓꢀ kh«ngꢀ dïngꢀ d¹ngꢀ mÆcꢀ ®Þnh,ꢀ mꢁꢀ t¹oꢀ métꢀ khu«nꢀ d¹ngꢀ riªngꢀ tõꢀ môcꢀ
Preferences,ꢀtrongꢀb¶ngꢀchänꢀfile,ꢀcãꢀthÓꢀmÆcꢀ®ÞnhꢀhoÆcꢀ®¸nhꢀd¹ngꢀxÊpꢀxØꢀt¹iꢀdÊuꢀnh¾c.ꢀ
ChóngꢀtaꢀdïngꢀbiÕnꢀaverage_costꢀ(ꢀtrongꢀvÝꢀdôꢀtr−íc)ꢀlꢁmꢀvÝꢀdô,ꢀd¹ngꢀsèꢀnꢁyꢀlꢁ:ꢀ
ꢀꢀ
LÖnhꢀcñaꢀMATLABꢀ
formatꢀshortꢀ
formatꢀlongꢀ
Average_costꢀ
50.833ꢀ
ChóꢀthÝchꢀ
5ꢀsèꢀ
16ꢀsèꢀ
50.83333333333334ꢀ
5.0833e+01ꢀ
5.083333333333334e+01ꢀ 16ꢀsèꢀvíiꢀsèꢀmòꢀ
formatꢀshortꢀeꢀ
formatꢀlongꢀeꢀ
formatꢀshortꢀgꢀ
5ꢀsèꢀvíiꢀsèꢀmòꢀ
50.833ꢀ
chÝnhꢀ x¸cꢀ h¬nꢀ formatꢀ shortꢀ
hoÆcꢀꢀformatꢀshortꢀeꢀ
chÝnhꢀ x¸cꢀ h¬nꢀ formatꢀ longꢀꢀ
hoÆcꢀformatꢀlongꢀeꢀ
hÖꢀc¬ꢀsèꢀ16ꢀ
formatꢀlongꢀgꢀ
formatꢀhexꢀ
50.83333333333333ꢀ
40496aaaaaaaaaabꢀ
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formatꢀbankꢀ
formatꢀ+ꢀ
formatꢀratꢀ
ꢀ
50.83ꢀ
+ꢀ
305/ꢀ6ꢀ
haiꢀsèꢀhÖꢀ10ꢀ
d−¬ng,ꢀ©mꢀhoÆcꢀb»ngꢀkh«ngꢀ
d¹ngꢀph©nꢀsèꢀ
MétꢀchóꢀýꢀquanꢀträngꢀlꢁꢀMATLABꢀꢀkh«ngꢀthayꢀ®æiꢀsèꢀkhiꢀ®Þnhꢀl¹iꢀkhu«nꢀd¹ngꢀhiÓnꢀthÞꢀ®−îcꢀ
chän,ꢀmꢁꢀchØꢀthayꢀ®æiꢀmꢁnꢀh×nhꢀthayꢀ®æi.ꢀ
ꢀ
ꢀ
ꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂoOoꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢀ
ꢀ
ꢀ
Ch−¬ngꢀ4ꢀ
ScriptꢀꢀM_filesꢀ
ꢀ
MétꢀvÊnꢀ®Òꢀ®¬nꢀgi¶nꢀlꢁ,ꢀyªuꢀcÇuꢀcñaꢀb¹nꢀt¹iꢀdÊuꢀnh¾cꢀcñaꢀMATLABꢀtrongꢀcöaꢀsæꢀlÖnhꢀlꢁꢀ
nhanhꢀvꢁꢀhiÖuꢀqu¶.ꢀTuyꢀnhiªnꢀv×ꢀsèꢀlÖnhꢀt¨ngꢀlªn,ꢀhoÆcꢀkhiꢀb¹nꢀmuènꢀthayꢀ®æiꢀgi¸ꢀtrÞꢀcñaꢀ
métꢀhoÆcꢀnhiÒuꢀbiÕnꢀvꢁꢀthùcꢀhiÖnꢀl¹iꢀmétꢀsèꢀlÖnhꢀvíiꢀgi¸ꢀtrÞꢀmíi,ꢀnÕuꢀcøꢀ®¸nhꢀlÆpꢀl¹iꢀt¹iꢀdÊuꢀ
nh¾cꢀcñaꢀMATLABꢀth×ꢀsÏꢀtrëꢀlªnꢀbuånꢀtÎ,ꢀdoꢀvËyꢀMATLABꢀcungꢀcÊpꢀmétꢀgi¶iꢀph¸pꢀchoꢀvÊnꢀ
®Òꢀnꢁyꢀlꢁ:ꢀnãꢀchoꢀphÐpꢀb¹nꢀthayꢀthÕꢀc¸cꢀlÖnhꢀcñaꢀMATLABꢀb»ngꢀmétꢀfileꢀv¨nꢀb¶nꢀ®¬nꢀgi¶n,ꢀ
vꢁꢀ yªuꢀ cÇuꢀ MATLABꢀ mëꢀ fileꢀ vꢁꢀ thùcꢀ hiÖnꢀ lÖnhꢀ chÝnhꢀ x¸cꢀ nh−ꢀ lꢁꢀ ®¸nhꢀ t¹iꢀ dÊuꢀ nh¾cꢀ cñaꢀ
MATLABꢀt¹iꢀcöaꢀsæꢀlÖnh,ꢀnh÷ngꢀfileꢀnꢁyꢀgäiꢀlꢁꢀscriptꢀfile,ꢀhoÆcꢀ®¬nꢀgi¶nꢀlꢁꢀM_file.ꢀDanhꢀtõꢀ
"script"ꢀ®ÓꢀchØꢀr»ngꢀthùcꢀtÕꢀMATLABꢀ®äcꢀtõꢀfileꢀkÞchꢀb¶nꢀt×mꢀthÊyꢀtrongꢀfile.ꢀDanhꢀtõꢀ"M_file"ꢀ
®ÓꢀchØꢀr»ngꢀtªnꢀscriptꢀfileꢀ®ãꢀph¶iꢀkÕtꢀthócꢀb»ngꢀphÇnꢀmëꢀréngꢀlꢁꢀ'.m'ꢀnhꢀvÝꢀdôꢀexample1.m.ꢀ
ꢀꢀꢀꢀ §Óꢀt¹oꢀmétꢀscriptꢀM_file,ꢀchänꢀNewꢀtrongꢀb¶ngꢀchänꢀfileꢀvꢁꢀchänꢀM_file.ꢀThñꢀtôcꢀnꢁyꢀ
sÏꢀt¹oꢀraꢀmꢁnꢀh×nhꢀso¹nꢀth¶o,ꢀvꢁꢀb¹nꢀcãꢀthÓꢀ®¸nhꢀ®−îcꢀc¸cꢀlÖnhꢀcñaꢀMATLABꢀtrongꢀ®ã.ꢀVÝꢀ
dôꢀd−íiꢀ®©yꢀlꢁꢀc¸chꢀlÖnhꢀtrongꢀvÝꢀdôꢀ−ícꢀl−îngꢀchiÒuꢀcaoꢀng«iꢀnhꢁꢀëꢀtr−íc:ꢀ
ꢀ
functionꢀexample1ꢀ
ꢀꢀꢀꢀꢀꢀ%ꢀꢀexample1.mꢀꢀVÝꢀdôꢀ−ícꢀl−îngꢀchiÒuꢀcaoꢀng«iꢀnhꢁꢀ
hꢀ=ꢀ2ꢀ
thetaꢀ=ꢀ60ꢀ
Dꢀ=ꢀ50;ꢀ
building_heightꢀ=ꢀhꢀ+ꢀD*tan(theta*pi/180)ꢀ
ꢀ
B¹nꢀcãꢀthÓꢀghiꢀvꢁꢀl−uꢀgi÷ꢀfileꢀnꢁyb»ngꢀc¸chꢀchänꢀSaveꢀtõꢀb¶ngꢀchänꢀfile.ꢀKhiꢀb¹nꢀghiꢀlªnꢀ
fileꢀchóꢀýꢀph¶iꢀ®¸nhꢀtªnꢀfileꢀtrïngꢀvíiꢀtªnꢀhꢁmꢀ(example)ꢀkh«ngꢀcÇnꢀ®¸nhꢀvꢁoꢀphÇnꢀmëꢀréng,ꢀ
MATLABꢀtùꢀg¸nꢀvꢁoꢀchoꢀnã.ꢀKhiꢀ®ãꢀtõꢀdÊuꢀnh¾cꢀtaꢀcãꢀthÓꢀ®¸nh:ꢀ
ꢀ
>>ꢀexample1ꢀ
h=ꢀ
ꢀꢀꢀꢀꢀꢀ2ꢀ
theta=ꢀ
ꢀꢀꢀꢀꢀꢀ60ꢀ
building_height=ꢀ
ꢀꢀꢀꢀꢀꢀ54.3599ꢀ
ꢀꢀꢀ
KhiꢀMATLABꢀdiÔnꢀgi¶iꢀc¸cꢀtr¹ngꢀth¸iꢀcñaꢀexample1ꢀëꢀtrªn,ꢀnãꢀsÏꢀ®−îcꢀnãiꢀküꢀh¬nꢀëꢀ
ch−¬ngꢀsau,ꢀnh−ngꢀmétꢀc¸chꢀng¾nꢀgän,ꢀMATLABꢀdïngꢀc¸cꢀtr¹ngꢀth¸iꢀcñaꢀbiÕnꢀMATLABꢀ
hiÖnꢀt¹iꢀvꢁꢀt¹oꢀlªnꢀc¸cꢀlÖnhꢀcñaꢀnã,ꢀb¾tꢀ®Çuꢀb»ngꢀtªnꢀM_file.ꢀNghÜaꢀlꢁ,ꢀnÕuꢀexample1ꢀkh«ngꢀ
ph¶iꢀlꢁꢀbiÕnꢀhiÖnꢀt¹i,ꢀhoÆcꢀmétꢀlÖnhꢀMATLABꢀx©yꢀdùngꢀlªn,ꢀMATLABꢀmëꢀfileꢀexample1.mꢀ
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(nÕuꢀnãꢀt×mꢀthÊy)ꢀvꢁꢀtÝnhꢀgi¸ꢀtrÞꢀc¸cꢀlÖnhꢀt×mꢀthÊyꢀchØꢀkhiꢀchóngꢀtaꢀvꢁoꢀc¸cꢀth«ngꢀsèꢀchÝnhꢀx¸cꢀ
t¹iꢀdÊuꢀnh¾cꢀcñaꢀcöaꢀsæꢀlÖnh.ꢀNh−ꢀ®ꢃꢀthÊyꢀlÖnhꢀtrongꢀM_fileꢀtruyꢀcËpꢀ®ÕnꢀtÊtꢀc¶ꢀc¸cꢀbiÕnꢀ
trongꢀkh«ngꢀgianꢀlꢁmꢀviÖcꢀcñaꢀMATLAB,ꢀvꢁꢀtÊtꢀc¶ꢀc¸cꢀbiÕnꢀtrongꢀM_fileꢀtrëꢀthꢁnhꢀmétꢀphÇnꢀ
cñaꢀkh«ngꢀgianꢀlꢁmꢀviÖc.ꢀB×nhꢀth−êngꢀc¸cꢀlÖnhꢀ®äcꢀtrongꢀM_fileꢀkh«ngꢀ®−îcꢀhiÓnꢀthÞꢀnh−ꢀlꢁꢀ
nãꢀ®−îcꢀtÝnhꢀtrongꢀcöaꢀsæꢀlÖnh,ꢀnh−ngꢀlÖnhꢀechoꢀonꢀyªuꢀcÇuꢀMATLABꢀhiÓnꢀthÞꢀhoÆcꢀlÆpꢀl¹iꢀ
lÖnhꢀ®èiꢀvíiꢀcöaꢀsæꢀlÖnhꢀnh−ꢀchóngꢀtaꢀ®ꢃꢀ®äcꢀvꢁꢀtÝnh.ꢀTiÕpꢀtheoꢀb¹nꢀcãꢀthÓꢀ®o¸nꢀ®−îcꢀlÖnhꢀ
echoꢀoffꢀlꢁmꢀg×.ꢀGièngꢀnh−ꢀvËy,ꢀlÖnhꢀechoꢀlÆpꢀl¹iꢀbëiꢀchÝnhꢀnãꢀlꢁmꢀthayꢀ®æiꢀchÝnhꢀtr¹ngꢀth¸iꢀ
cñaꢀnã.ꢀ
ꢀꢀꢀꢀꢀ
Víiꢀ®Æcꢀ®iÓmꢀnꢁyꢀcñaꢀM_fileꢀb¹nꢀcãꢀthÓꢀthayꢀ®æiꢀl¹iꢀnéiꢀdungꢀcñaꢀfile,ꢀvÝꢀdôꢀb¹nꢀcãꢀthÓꢀ
mëꢀM_fileꢀexample1.mꢀthayꢀ®æiꢀl¹iꢀc¸cꢀgi¸ꢀtrÞꢀcñaꢀh,ꢀD,ꢀhoÆcꢀtheta,ꢀghiꢀl¹iꢀfileꢀ®ãꢀvꢁꢀyªuꢀcÇuꢀ
MATLABꢀtÝnhꢀl¹iꢀlÖnhꢀtrongꢀfile.ꢀThªmꢀn÷a,ꢀb»ngꢀc¸chꢀt¹oꢀM_file,ꢀc¸cꢀlÖnhꢀcñaꢀb¹nꢀ®−îcꢀl−uꢀ
trªnꢀ®ÜaꢀvꢁꢀcãꢀthÓꢀøngꢀdôngꢀvÒꢀsauꢀkhiꢀb¹nꢀcÇn.ꢀ
ꢀꢀꢀ
ꢀNh÷ngꢀøngꢀdôngꢀcñaꢀchØꢀdÉnꢀcñaꢀMATLABꢀgiópꢀchóngꢀtaꢀhiÓuꢀ®−îcꢀkhiꢀdïngꢀscriptꢀ
fileꢀnh−ꢀtrongꢀexample1.m,ꢀchØꢀdÉnꢀchoꢀphÐpꢀb¹nꢀl−uꢀgi÷ꢀcïngꢀc¸cꢀlÖnhꢀtrongꢀscriptꢀfile,ꢀv×ꢀ
vËyꢀb¹nꢀnhíꢀ®−îcꢀnh÷ngꢀlÖnhꢀ®ãꢀlꢁmꢀg×ꢀkhiꢀb¹nꢀnh×nꢀl¹iꢀfileꢀsauꢀ®Êy.ꢀThªmꢀn÷a,ꢀdÊuꢀchÊmꢀ
phÈyꢀ®»ngꢀsauꢀc©uꢀlÖnhꢀkh«ngꢀchoꢀhiÓnꢀthÞꢀkÕtꢀqu¶,ꢀtõꢀ®ãꢀb¹nꢀcãꢀthÓꢀ®iÒuꢀchØnhꢀscriptꢀfileꢀ®aꢀ
raꢀnh÷ngꢀkÕtꢀqu¶ꢀcÇnꢀthiÕt.ꢀ
ꢀꢀꢀ V×ꢀnh÷ngꢀøngꢀdôngꢀcñaꢀscriptꢀfile,ꢀMATLABꢀcungꢀcÊpꢀmétꢀsèꢀhꢁmꢀ®ÆcꢀbiÖtꢀcãꢀÝchꢀkhiꢀ
b¹nꢀsöꢀdôngꢀtrongꢀM_file:ꢀ
ꢀ
C¸cꢀhꢁmꢀM_fileꢀ
disp(ans)ꢀ
echoꢀ
HiÓnꢀthÞꢀc¸cꢀkÕtꢀqu¶ꢀmꢁꢀkh«ngꢀhiÖnꢀtªnꢀbiÕnꢀ
§iÒuꢀkhiÓnꢀcöaꢀsæꢀlÖnhꢀlÆpꢀl¹iꢀc¸cꢀlÖnhꢀcñaꢀscriptꢀfileꢀ
SöꢀdôngꢀdÊuꢀnh¾cꢀ®Óꢀ®aꢀd÷ꢀliÖuꢀvꢁoꢀ
Traoꢀ®iÒuꢀkhiÓnꢀt¹mꢀthêiꢀchoꢀbꢁnꢀphÝmꢀ
Dõngꢀl¹iꢀchoꢀ®Õnꢀkhiꢀng−êiꢀdïngꢀnhÊnꢀmétꢀphÝmꢀbÊtꢀ
kúꢀ
inputꢀ
keyboardꢀ
pauseꢀ
pause(n)ꢀ
waitforbuttonpressꢀ
Dõngꢀl¹iꢀnꢀgi©yꢀ
Dõngꢀ l¹iꢀ choꢀ ®Õnꢀ khiꢀ ng−êiꢀ dïngꢀ nhÊnꢀ chuétꢀ hoÆcꢀ
phÝm.ꢀ
ꢀ
ꢀꢀ KhiꢀlÖnhꢀcñaꢀMATLABꢀkh«ngꢀkÕtꢀthócꢀb»ngꢀdÊuꢀchÊmꢀphÈy,ꢀkÕtꢀqu¶ꢀcñaꢀlÖnhꢀ®−îcꢀ
hiÓnꢀthÞꢀtrªnꢀcöaꢀsæꢀlÖnhꢀcïngꢀvíiꢀtªnꢀbiÕn.ꢀ§«iꢀlócꢀnãꢀthuËnꢀtiÖnꢀkhiꢀkh«ngꢀchoꢀhiÖnꢀtªnꢀ
biÕn,ꢀtrongꢀMATLABꢀꢀtaꢀdïngꢀlÖnhꢀdispꢀ®ÓꢀthùcꢀhiÖnꢀviÖcꢀnꢁy:ꢀ
ꢀ
>>ꢀhꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀC¸chꢀtruyÒnꢀthèngꢀ®ÓꢀhiÖnꢀkÕtꢀqu¶ꢀ
h=ꢀ
ꢀꢀꢀꢀꢀꢀ2ꢀ
>>ꢀdisp(h)ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ%ꢀHiÖnꢀkÕtꢀqu¶ꢀkh«ngꢀcãꢀtªnꢀbiÕnꢀ
ꢀꢀꢀꢀꢀꢀ2ꢀ
ꢀ
ꢀꢀꢀ ꢀ§Óꢀgiópꢀb¹nꢀso¹nꢀth¶oꢀscriptꢀfileꢀkhiꢀtÝnhꢀto¸nꢀchoꢀnhiÒuꢀtr−êngꢀhîp,ꢀlÖnhꢀinputꢀchoꢀ
phÐpꢀb¹nꢀt¹oꢀc©uꢀnh¾cꢀ®Óꢀvꢁoꢀd÷ꢀliÖuꢀ®−îcꢀanꢀtoꢁn.ꢀVÝꢀdôꢀexample1.mꢀvíiꢀnh÷ngꢀphÇnꢀ®−ꢂ
îcꢀsöa:ꢀ
ꢀ
functionꢀexample1ꢀ
ꢀꢀꢀꢀꢀꢀ%ꢀꢀexample1.mꢀꢀVÝꢀdôꢀ−ícꢀl−îngꢀchiÒuꢀcaoꢀng«iꢀnhꢁꢀ
hꢀ=ꢀ2ꢀ
thetaꢀ=ꢀ60ꢀ
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