ラプラス変換と微分方程式

6/16のPFIセミナーで使用した資料です。セミナーはこちら https://www.youtube.com/watch?v=0hFsLowTL_U

Transcript

1. ϥϓϥεม׵ͱඍ෼ํఔࣜ 2016-06-16@PFI/PFNηϛφʔ
2. • ాதେี (TANAKA Daisuke) • Ξχϝ ໿1000ຊ/೥
 ຊ ໿300࡭/೥ (࠷ۙݮͬͨ) • PFNͰ͸Go͔Pythonɺͨ·ʹC++ɺ࠷ۙ͸Scala
 झຯͰ͸Javaਪ͠
3. Contents 1. ඍ෼ํఔࣜʹΑΔϞσϧԽ 2. ϥϓϥεม׵ͱཧ࿦ 3. ա౉Ԡ౴ 4. प೾਺Ԡ౴ 5. ·ͱΊ 6. ͓·͚
4. Contents 1. ඍ෼ํఔࣜʹΑΔϞσϧԽ 2. ϥϓϥεม׵ͱཧ࿦ 3. ա౉Ԡ౴ 4. प೾਺Ԡ౴ 5. ·ͱΊ 6. ͓·͚
5. ͍͖ͳΓͰ͕͢ɺ্ਤ ͷԠ౴ΛٻΊͳ͍͞
6. ཧ૝త༰ྔཁૉ ֤ཁૉͷجຊతੑ࣭ ઢܗ఍߅ ཧ૝ΠϯμΫλϯε
7. Kirchhoffͷୈ2๏ଇΑΓ ίϯσϯαͷੑ࣭ΑΓ ্ࣜΑΓ Λফڈͯ͠ 1࣍஗Εܥ
8. (ඍ෼ํఔࣜΛղ͍ͯ) a RADII + vote ) = via cR=T en ' ce , §tEB#**Ea eftd ' - e# t.to ) %k£i= at 2 eek dvd0¥ t Ek . # now = e¥ . # vice ) dd*e¥ ' votes ) = e¥ # Vice ) FYTRZFFE's in Eh vote ) = / e# . ± via + A ( At EEBEZIH vile 1=Es GE ) ease = Eh . Es + A Uottl = Es + A Eek vote = o ) = o -43 e , A = - Es JY = Es G - e- th )
9. ଓ͚ͯɺ্ਤ ͷԠ౴ΛٻΊͳ͍͞
10. Kirchhoffͷୈ2๏ଇΑΓ ΑΓ Λফڈͯ͠ 2࣍஗Εܥ
11. t.com#+RcduE4nd+v.tI - with Rd 4=12 =3 , 1€ =wn thee daff +25W . dhdeth.tw?vot4=w:viHi#jEHEffEmte25w.mtwi=onFFEb m = - w . (5+-157) ; ) 3>1 a IBPE WE , = A E Wales 'H#t+Bew . ( sT#lt+=↳ v.EC = 07=0 A A + B = - Es . - . D DUFF ) = - w.tn#IjA.-wnHfiT)B=o...D 1 . 2 D; BITE - us¥#A=t£t*¥Ks ~°kl=Es{ i - Ek- ns.#)ewnlsHeet + ( it *#)e-wdsH#c } } ; ;) 3- athas whet = theft Be ) + Es vote = 0 ) = At Es =o FY A = - Es drolet = - wn A + B = 0 Ey B = - cones For vote 1 = Es { 1- ( 1 twat ) Eat } (ඍ෼ํఔࣜΛղ͍ͯ…) iii ) 0<5 < 1 ae¥s€ vote ) = E wise ( A coat context + Bsintwndtei ) THE vote ) = A + Es to a) A = - Es du.tt#= - wig A - wife Bt Es -057 B =[t# vote 1 = e→*fATB ' sinfwn HI ) Et tai ' AE ) + Es = Efi . TETE sincwaeio ) } # Wd ⇒ # win , of = Earth
13. ͞Βʹଓ͚ͯɺ্ਤ ͷԠ౴ΛٻΊͳ͍͞
14. Kirchhoffͷୈ2๏ଇͱ͔ॾʑΛۦ࢖ͯ͠ ͜ͷඍ෼ํఔࣜ͸ղ͖ͨ͘ͳ͍…
15. Contents 1. ඍ෼ํఔࣜʹΑΔϞσϧԽ 2. ϥϓϥεม׵ͱཧ࿦ 3. ա౉Ԡ౴ 4. प೾਺Ԡ౴ 5. ·ͱΊ 6. ͓·͚
16. ϥϓϥεม׵ • ࣌ؒؔ਺ Λੵ෼֩ ( ͸ෳૉ਺ )ʹ ΑΓෳૉؔ਺ ʹࣸ૾͢Δੵ෼ม׵ͷҰछ • Ͱఆٛ͞Εͨ࣌ؒؔ਺ ( Ͱ ͱ͢Δ)ͷϥϓϥεม׵Λ࣍ͷΑ͏ʹఆٛ͢Δ • ͦͯ͜͠ͷม׵ Λ࣍ͷΑ͏ʹද͢
17. ϔϰΟαΠυͷ֊ஈؔ਺ • ҎԼͷؔ਺ͷϥϓϥεม׵͸ Lena ] =ftEHe→ de =[e5]Y = 's εςοϓؔ਺ˠεςοϓԠ౴
18. ݮਰؔ਺ • ҎԼͷؔ਺ͷϥϓϥεม׵͸ £ [ e- at ] =f+ Fiat . Estate e- Gt a) -# sea TY = six , [ Re 1st a ) > ° ] ϥϓϥεม׵දͰgoogleઌੜʹฉ͚͹޾ͤʹͳΕΔ
19. ࣮ඍ෼ͷ๏ଇ • ॳظ஋͕θϩ͢ͳΘͪ ͷ࣌ʹ͸ɺ࣌ؒྖ ҬͰ Λn֊ඍ෼͢Δ͜ͱ͸ɺs-ྖҬͰ͸ ʹ Λ͔͚Δ͜ͱʹ૬౰͢Δ
20. ϥϓϥεม׵ͷॾ๏ଇ Ճ๏ੑ ࣮ඍ෼ ࣮ੵ෼ ࣌ؒਪҠ ਖ਼ଇੑ
21. ϥϓϥεٯม׵ • ͕༩͑ΒΕͨ࣌ɺͦͷϥϓϥεม׵͕ ͱ ͳΔΑ͏ͳ ΛٻΊΔૢ࡞Λɺϥϓϥεٯม׵ ͱ͍͏ɻ • ্هͷࣜ͸࢖Θͣɺల։ఆཧΛ༻͍Δ͜ͱ͕ଟ͍
22. ϥϓϥεม׵ɾٯม׵Λ࢖͏
23. T d%dETt vote )=viH zap '#H¥ standoff ]+£[ vote ] - £[Esu#g¥eaaa#a¥t -↳IT{sVo( s ) - vote ) }=sTV°G ) uTV°( s ) + Vols ) =Es/¥T .io#vEFEiVols1=s(in*zEiHBFK-EsEts* ) 57052 '3E¥#Eey 1 / V.lt/=Es( 1 - EYT ) ←ඍ෼ํఔࣜΛղ͍ͨͷ ͱಉ݁͡Ռ
24. ఻ୡؔ਺ • ͋Δཁૉ͋Δ͍͸ܥͷೖྗͱग़ྗͱͷؔ܎͸ɺҰൠ ʹ·ͣඍ෼ํఔࣜʹΑͬͯهड़͞ΕΔɻ • ΛҎԼͷΑ͏ʹఆٛ͠ɺ఻ୡؔ਺ͱݺͿ • ఻ୡؔ਺Λ࢖͏͜ͱʹΑͬͯɺෳࡶͳೖྗͱग़ྗͷ ؔ܎͕ࣜ؆୯ͳ୅਺ؔ܎ʹΑͬͯද͢͜ͱ͕Ͱ͖Δ
25. Contents 1. ඍ෼ํఔࣜʹΑΔϞσϧԽ 2. ϥϓϥεม׵ͱཧ࿦ 3. ա౉Ԡ౴ 4. प೾਺Ԡ౴ 5. ·ͱΊ 6. ͓·͚
26. ୅දతͳೖྗ • εςοϓೖྗ㲗εςοϓԠ౴ • Πϯύϧεೖྗ㲗ΠϯύϧεԠ౴ • ϥϯϓೖྗ㲗ϥϯϓԠ౴
27. εςοϓԠ౴
28. ΠϯύϧεԠ౴
29. ϥϯϓԠ౴
30. ϥϓϥεม׵ɾٯม׵Λ࢖͏
31. ೖྗʹΑͬͯ Λม͑Δ →ϥϓϥεม׵දΛ࢖ͬͯ࣌ ؒྖҬʹ໭͢ St RAZR , ah = 11dLTeh.cedhdEIe25undngtEttwn2voH-wnvit4.r-1x3tIfnnr5x7zEszFtEFstg.L@HeIfssVCs1-svolotj-Tilot1-s2VoCs1SfdvdoFf-sV.cs1-v.CotI-sV.cs1LEv.CeD-VoCs1.LEhiHT-Vils1lxlFCsst25wnstWnY.V . Is ) - willies ) wilts ) Vo ( s ) = t.se#Wi
32. εςοϓԠ౴
33. Contents 1. ඍ෼ํఔࣜʹΑΔϞσϧԽ 2. ϥϓϥεม׵ͱཧ࿦ 3. ա౉Ԡ౴ 4. प೾਺Ԡ౴ 5. ·ͱΊ 6. ͓·͚
34. प೾਺Ԡ౴ • ೖྗ͕Ұఆप೾਺ͷਖ਼ݭ೾ঢ়৴߸ͩͬͨ৔߹ͷɺೖ ग़ྗͷৼ෯ൺٴͼҐ૬ͷͣΕͱप೾਺ͷؔ܎ʹ஫໨ ͢Δɻ ཁૉ ͋Δ͍͸ܥ ೖྗ ग़ྗ
35. प೾਺఻ୡؔ਺ • ೖྗ͸ ͱද͢͜ͱ͕Ͱ͖Δɻ͜ͷೖྗʹର͢ Δग़ྗͷఆৗԠ౴੒෼Λ ͱ͓͘ɻ͜Ε͸ ఻ୡؔ਺ Ͱ ͱஔ͍ͨ΋ͷʹ૬౰͢Δɻ • ͜ͷ Λप೾਺఻ୡؔ਺ͱݺͿ • ৼ෯ൺ͕ ɺҐ૬ͷͣΕ͕
 ͭ·Γɺৼ෯ൺͱҐ૬ΛٻΊ͚ͨΕ͹प೾਺఻ୡؔ ਺ʹ஫໨͢Ε͹ྑ͍
36. ਖ਼ݭ೾ • ҎԼͷؔ਺ͷϥϓϥεม׵͸ gz+2SW=Wnsin WE = Eliot - e- jay rita 3155 L[ As 'm we ]=#h{ stein ] - £[ e- Ft ] } = Ijnlstjw - sijw) AN = sz-=
37. ͷ৔߹ͷ Ԡ౴ΛٻΊΔ
38. Vols ) = Vols ) . e.SI = siestas .nl#.zEdK'E*E = at ,iiw¥ . Este i⇒{ she - III } ] ( 57°52 FEECFYEE # nr ) WT vote I = Aif .me#t,.dw*lsinwt-wTcorwtA . ' .tn#=eeYITe*' µ+l@# sinotte ) 0= - team ' ( WT ) ৼ෯ൺ Ґ૬ →ϩʔύεϑΟϧλ
39. प೾਺఻ୡؔ਺͔Β௚઀ٻ ΊΒΕΔ 'f+i=⇒/IiiIT ) = - tan ' ( WT )
40. ఻ୡؔ਺ ͱ͓͘ͱ Ґ૬ Ґ૬ਐΊճ࿏
41. ϑʔϦΤม׵ • ΠϯύϧεԠ౴Λ࢖ͬͯɺ೚ҙͷೖྗ ʹର͢Δ Ԡ౴ ΛٻΊΔࣜ
 
 
 ೖྗ͕ ͷ৔߹ͷԠ౴͸ɺ
 
 
 Λߟྀͯ͠
42. ϑʔϦΤม׵ • ΠϯύϧεԠ౴Λ ϑʔϦΤม׵΋ͷ͕प೾਺఻ ୡؔ਺ ࣌ؒྖҬ s-ྖҬ प೾਺ྖҬ ϥϓϥεม׵ ϥϓϥεٯม׵ ϑʔϦΤม׵ ϑʔϦΤٯม׵
43. Contents 1. ඍ෼ํఔࣜʹΑΔϞσϧԽ 2. ϥϓϥεม׵ͱཧ࿦ 3. ա౉Ԡ౴ 4. प೾਺Ԡ౴ 5. ·ͱΊ 6. ͓·͚
44. ·ͱΊ • ඍ෼ํఔࣜͰϞσϧԽ͞ΕͨܥΛɺϥϓϥεม׵Λ ࢖͏͜ͱʹΑΓɺ୅਺ͷൣғͰܭࢉՄೳ • ϥϓϥεੵ෼ͷଘࡏ৚݅ʹ஫ҙ • ෳࡶͳܥͩͱద༻͕ਏ͘ͳͬͨΓ͢Δ • प೾਺఻ୡؔ਺ʹΑΓप೾਺ಛੑ͕ܭࢉՄೳ
45. ࠓ೔࿩͞ͳ͔ͬͨ͜ͱ • ఻ୡؔ਺ͱϒϩοΫઢਤ
 प೾਺఻ୡؔ਺ͱϕΫτϧي੻ɾϘʔυઢਤ • ϑΟʔυόοΫ੍ޚܥͷಛੑͱԠ౴ɺͦͷ҆ఆ౓ • Χεέʔυ੍ޚܥ
 ϑΟʔυϑΥϫʔυ੍ޚܥ • 1ೖྗ1ग़ྗҎ֎ͷܥ
46. Contents 1. ඍ෼ํఔࣜʹΑΔϞσϧԽ 2. ϥϓϥεม׵ͱཧ࿦ 3. ա౉Ԡ౴ 4. प೾਺Ԡ౴ 5. ·ͱΊ 6. ͓·͚
47. ͜ͷ Ԡ౴͸
48. ͱɺղ͚ͳ͍...
49. 3࣍CRճ࿏