Course 18.ppt

KULIAH 18 Persamaan Diferensial Parsial Persamaan Laplace pada SK Sikusiku

Indikator Ketercapaian 

menyelesaikan distribusi suu tunak dalam sistem koordinat siku-siku !D

$eckpoint 

"entukan

den#an beberapa cara

$ura Pendapat 

Se#i empat tanpa sumber panas



%#m distribusi suu di dalam pelat se#i empat & T = 0

T=0

T=0

T = 100

Pierre-Simon 'ar(uis de Laplace %orn

23 March 1749 Beaumont-en-Auge, Normandy, France

Died

5 March 1827 (aged 77) ar!", France

)ationality

French

*ields *ields

A"tronomer  and Mathemat!c!an

Kno+n for

#or$ !n %e&e"t!a& Mechan!c" 'a&ace" e*uat!on 'a&ac!an 'a&ace tran"+orm 'a&ace d!"tr!ut!on 'a&ace" demon 'a&ace ean"!on .oung/'a&ace e*uat!on 'a&ace numer  'a&ace &!m!t 'a&ace !n0ar!ant 'a&ace r!nc!&e

,a+abnya Pers. Laplace !D



%#m menyelesaikan pers Laplace&

$ura Pendapat 

1

%#m solusi PD% berikut ini& 2

d  Y 

Y  dy 1

2

=

or

2

k 

Y  dy

2

dy

2

−

2

2

or

Y ′′ − k  Y  = 1

2

or

Y ′′ + k  Y  = 1

k  Y  = 

2

2

d  Y 

d 2Y 

= −

k  or 2

d  Y  dy

2

+

k  Y  = 

2

!a&og 

%#m menyelesaikan Pers Laplace !D&

!a&og 

/unakan Pemisaan 0ariabel

nteract!0e - !a&ogue 

Ho+ do +e sole 2D3 +it a #ien boundary condition&

nteract!0e - !a&ogue

nteract!0e - !a&ogue

nteract!0e - !a&ogue

nteract!0e - !a&ogue

nteract!0e - !a&ogue

UH soal 1 y

14

4 4

144 4

5

%onus "657 y& y 4

a

4

"o 1

4

5

%onus 

Soal-soal 18 9 1

#or$ !n a!r  

*ind your best partner



3ac pair discusses te distribution of temperature inside plate.

re"entat!on 

Participant +o cosen randomly e5plains o+ to find distribution of temperature inside plate

&ate 2 

Use separation of ariable

&ate 2 

Laplace e(uation

&ate 2 

$omparin# to semi-infinite plate7 +at +ill be te difference for rectan#ular plate&

Pelat se#iempat s semi takin##a

UH18 soal !

nteract!0e !a&ogue 

Ho+ do +e find steady state temperature distribution inside tis plate&

nteract!0e !a&ogue

618 "oa& 3 

Soal-soal 18

Se#iempat tetap dan adiabatis

e+&ect!on 

2ne of student e5presses is:er learnin# outcome and process of teacin# learnin# today