Biomatematika 1Parciális deriváltak 1

Dr. Bugyi Beata - 2018. 10. 09.

1 VA ' Ltozds FV f ( x )

KOALAµ ( a) = of

TF1 ←V on

'ltoza 's a' nah mette 'Re

ATL da ?→ DV → DERNA ' Usb- p

a

a - nak uelgtelen his vaktoza 's a

dV(a)-= ( a 3)

'

=3 of ( ×" )

'en . x

" "

da

DVC a) = 3 at da TELFES DIFFERENCE 't

I-

Vz azI INTEGRA'

Us 's

§,

duca ) = fba ' da

Ae

2 valuate 's FV fl X, y )

HE NEERv ( rib ) = Tv

" he fcx , y )=2 - x ?yO

ht / dr is DV

dh ?→ du→ DERIVING

p"

OSSZETEIT"

,,EGYSIERU

"

BB"

Mit ismeriink ?

adr= vahtozo

' h=A'ubNDb ( Im ) he

V ( nih ) - Trib Is hIT2r OVCrih )- - PA KUDUS

2 r the( RIESZ VEGES )

r -_ At WANDO'

( Am ) h=VAktozoV Crib ) DERNA '

4-Vcr ,

he )=IrZh Itv2 #-),

dV( wth )=hT2rdr t ITV2 dh TELFES DIFFERENUAK- -

rmiatti he mialti

valltoza 's ooiltoza 's

PARUAIUS DERNA "LT ( RESZLEG.ES )

fcx , Yet )2 fcxifiz )1- X #shtozd

-

Y,

2- = DUAN Do' (

d X. )y,z

↳ y =vahtozoofcxiyiz)

x ,z= A UANDO' ( Ty )x,z

↳ z = vahtozo Ofcxiyiz)Y

,X -

- A' LLAN pot (F) yix

dffxiyiz ) -18×1)yµdxt¥)×,zdyt¥f¥ydZTELFES DIFFERENCIA 't

Pl :

fcx , y ) = 3×2 it xujt.ly-

↳

←¥"H)y=6xtry to

y ,= 4 3x

"

t x . 4 t (4)2

→

6xt4t0Ls@oEtJx.otxtry

X = 4 3. (4)"

t 4 y t y'

→ 0 t 4 t 2g

TERM DINAMIKA

IDEA 'Ll s GAZ n=1 uuol

pV=rniRT R - 8.31 ( Haulk )- ⇐I

'= - i. x' =

IV ,T

= -1-

pvalltoza 's ahah mette 'Re ye

a , per ) -netc

ftp.e-nrtff-a/---nvrI-12

2, pet ) = TITO ( ffs)jTIi

- TI-

146

dpc Vi )=MRT

( x ) ! y

- - dvt YI DT TELFESDIFFERENCIA 't✓ 2

- -

Op Op⇐ It lot Iv

net moledp = ? V : Am ' -22ms dV=1m3 T= 273k

R = 8:34t.tn#.kT=273k dirt dp = - nYdV= - 1ms,

✓ = t.ms ( 1ms )2= - 2268 .

63 Pa

dpd

dp= ? V=1m3 T : 273 K - 274k

dt-tkdttdp-Y-dt-EHnolk-ek.im's

= t 8.31 Pa

dpt

dip = ? V : Am '→ 2ms dV= 1ms T : 2.73K → 274k dt= 1k

dip = -ERI du t

HI AT =- 2268.63Pa t 8.31 Pa

✓ 2 ✓

LAt SD Eton and Mounds

BELSO"

ENERGIA,

MINT TELFES DIFFERED CIA 't

d U = d. Q - dry 1 THT # TEL Eivind PIA ds = # → dp=TdS

MUN KA dw =p DV

dy = Tds - pd TEVES DIFF.

u s v

MCs ,V ) → du = (%-) v

dst DV TEVES DIFF.

-

Dee( £1 = T

ou( Tv ),

= - p

D= VAHID'S 100 Kes INTERVAL UM

ENTALPIA Mutassuk neg L hogg P = a' U. It = do ,

& too

THEUtpv ( f . + g)'

= f 't gldp - O

DH = city t dCp¥)z

C f. g)'

e ft g tf g'

IF "otETEvdm = @t dip - V t P' DV

I due da - dw

du = da

-pd/VtdYpVtp¢Vd@=da - pdv

Odm = da

=