BIOMATEMATIKA 1DERIVÁLTAK ALKALMAZÁSAI 1

Dr. Bugyi Beàta

2018. 09. 24.

MAG'

ASABB REND "U DE RIVA'

LINK

52A BADESES

yet)=5t4m

) vet ) -ftp.#tI--ddtftI=lot(ms )P

IGA 2- Otts,

HOGY aft) -

- toffs ) - swans'o⑦Yi5iiEYiiAnsTBswAt Th

. Atos at PILLAWATNYI at → O

act )= -00

apctjghiyoff-do.lt#v'

C t )atdt

v VA 'uTozA 's A' NAK MERTEKE

Detritus' lads Ap ( t ) = Clot )'

= to ( Fa )

@2A 'M X ) !Rs 'M

yet ) dyL= oft) # dof# = ap Ct )

1.

DERI VA' ht 1 . DERIV A

' ht

2. DERI VAIUapCt ) = y I)

ape t ) =def#¥

MOLEKULAHARMONIKUSREZGO"

MOZGA 'S§ REZGESEKR

^

foekvenaa Infractionsyc t ) = Afsin wt

⑧t

spektrosrhdpiaamplitude This rfrekvencia ( 25ft) →

0pct )=dT¥=( Asinwtf-A.coswt.ro^ Mt "

aplt )=ddft=( Aw coswt ) ! Cslnx ) '=cosx

= Aw ( - sinwt.ro )= - Awrdsinwt ( sink ) '= cos .

• Date cos 2X . 2

sinx = - 1 sinx=1( cosx ) I

- sixyet ) ymw= - A yMax=tA ( costa ) !

. sinEX.

act ) amN=Aw"

aMax=- Aw

"

.IT#=.sin2x.2cost - 1 wsx=l

N ( t ) NMIN - - Aw NMs×=tAW

< E' MI AI REA Kab K A TERM 'Ek( Ek )↳ DERIV A' LA 's freakin

'

sebesselg , integral alak )↳ INTEGRA '

Us 's ( act ) fiiggoehy)↳ DIFFERENCE I All EGYEN LET ( oeakcioseberseg ,

difference'

a' h's

alak )REA KU d SE BESS ¥ G = RATE

A ( t ) = kiindula 's i anyag koncentracioja

lil Assed "

¥a aeons

"

A ( t ) vattozasanak.me/rteke=dAC# =RATE

sebessdge dt

2MHzC g ) - Nzlg ) :* Hz.C g ) Ao = A- ( t =DWOLFRAM

k= SEBESS # Gt

E N' Hg ] = # At UANDO' ( ELA 'M)

A C its = Ato - fat Ek ]= -Mi-

←REND

RATE Csi KKEN

↳ draft ) t o

- - - = - k = - k A ( t ) → NUMB REND "U-

It =1 DIFFERING At US F.

↳ d#=( so - bet ) ! ( to )'

- ( kt )'=o - k= - k = strandeddt T p

SZA 'M senior . × INTEGRAL F.

Act )=Ao - let d= - ¥ - k¥9

jarod 't

Ao

, -m⇐ - &

?¥'

-

- - t, OIt- -

it :p.

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O O

FIVE 2¥51 IDB Tn ,z Aft -_ IT=AIA(t ) = to - let

f- = Faiz

AE = Ao - ktTyz

The Ae2k

RADIO AKAU BOMUA 'S

ng? F --→ ! tf; E ] ⇐ A ikea. 38¥

.1Ao= to org

⇒ k 'tA ( t ) Ao Ck] -

- Yen- -

←ELSE REND.lt

RATE

↳= - ks"Ct ) D # F. F .

↳ d.gg#.e=CAo.e-ktj!- (E)' =e× the

= Ao ( e-ht

. c- a ) ) - ( E of"

) '=E°. to .ro )w Th

= - ke Ao e-ht INT .

F

( doo . e" ) ! too . ex

2. Cy He kg) Cszttezcg ) [ Ey't't ]⇒⇐A

a=÷**kt EJ=,÷An

AC ¥. =--n÷oktt1-

gMAISOD REN DUN

RATE

↳ df¥f = - baht ) DIFF.

F.

t.nu#fE.I--.xi-ex-H--ix-=.**I=fsxte5YIAo . ( - l . ( Sok - ttt )

-

? so b) = aaltok = - 143×+15?(3xte )!

= ↳= - if .3xte5 ? 3

( so ht th )-

INT . F.

REMUS GAZ N=1wlR Leni .vERz# US

.

Blu ) . * Gaza 'w*wbd O KOTERMA

8.31 m=o

AEs → a -

- 364L?hPa→-_⇐Hata .to#ukmeg -

noel

kritikusaihapotlroz b - 0.0424mF Otattoo

pm , The,

Vk . O

1.) ERINTO"

m -_ o → DERNA 'T dPd{I=O pl ( v )=O

2. , d) to → (pl C v ) = o ) '=o pl' ( v ) = o

PC = - RF v - is - au#

¥1Ex

-

2)'

⇐

-2×-3-

,!£Like)=[

RT C v - b5'

I'

- Eav-I a II I !

-

= RT ( -1 ( v -BJ'

) - af-z v-3)=

- t ( x - 254×-2 )I

= - 1 ( x - 25 ? ( I - o ) =

= - t

E)= O = - 1 (

yo-

⑥- 2

-b)2

v3 b

*'

ah .

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p" It (2¥ )

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,⇐- rt a ↳¥12.53 !

¥5) If2. ex -352 ) !a -4

✓ €2. 5)C x - 35.4×-3,1= 2. C- 3) . x

= 2 . ( - 2) ( x - 3) -3¥

[ P''

cu ) = Est - FF ]=o