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Samenvatting Calculus 1; Calculus, Early Transcendentals, ISBN: 9781292022178
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Samenvatting MST1: Calculus 1. Alle stof die in de colleges in het studiejaar 2021/2022 behandeld is.
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MST, Calculus 1 Aantekeningen/samenvatting
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Followedieburggraaf
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CA1, Hoorcollege 0
Partieel afleiden
Aanpak Getallen voorbeeld Rekenvoorbeeld
"" "
T =
-
100 .
p .
v 1- =
100 -
p .
V
"
fl 31=4
T=21④
Y & "
als p =
7 en ✓ =3 → 1- =
2100 Ten V bl ven onveranderd
b"" als p =
7.1 en ✓ =3 →
2T
toename : 30 av
= 100 V
✗
3
Ingevulde afgeleiden verm .
met verschil
?
Wat als f 13,1 ) Regels voor
je gaat afleiden in p geeft toename
benaderen door
'
variabelen
f. (3) f.
+ 13) -
13,1 -3 )
•
Een van de twee of meer 100.3 .
0,1 =
30
variabel alle
bl ft anderen worden
constant es .
Toename is benadering
doorgaans
•
een
ijij
, Hoorcollege / +2
Complexe getallen
Wat z n complexe getallen ? Rekenregels complexe getallen Complex toegevoegde
.↳+a,„„.↳§
>
-2+2-2=(4+9) ( b. bzli Atbi 2- bi
5- ax tbxz-cxt.cl
+ + 2- → = a-
↳
geeft b complexe getallen alt d 2- , Z, = (a azltlb , bzli
- -
-
,
> „ „
p pen z .
.
z, =
a. a. + µ ,
Algemeen geldt
☒
a. + bii.az bzi -
2- :
2-2 =
,
aztbzi az-bz.IO
2- .
E = aztb' =/2-12
✗
De modulus
De
lengte vector De polaire
n
van z vorm van
{
/ 2- / = 92+62 2- Modulus 12-1=5 . . . . . . .
. . . .. . . . _ ⇐ atbi
§
"
en argument 0
µ
"
:
kwadratische v91 oplossen
complex getal
Yair
in de vorm van
„ze
2- = atbi .
azztbz + ( = 0 adhv Soscastoa :
met b ; reële getallen te delen door Sin 0=7 sino
a,
y=r
a
→ -
I! -1 zzt dz
i ; Imaginair getal → te = 0 (oso -
-
¥ → ✗ = r .
coso
nlm .
2+3 ,
& opsplitsen
'
fan @ =
¥
.
-4 tzi
( 2- + Id ) -
⇐ d) te = 0
d. omschr ven tot
sta famard Dit geeft functie voorschrift
0 >
Re
2- = ✗ +
yi
2- = r .
Kos @ + i sino )
. -
i
. -2 -
ZI .
3- zi
-
Abc -
Formule
Bewerkingen op polaire getallen
Overgangen
Isin (0,1-02))
-2 , .
2-2=51 Nl ( Oslo .
, +02 ) +
polair cartd-isohcartetis.ch Polair
Z % Kosto
→ →
= ,
-
9) + isinloi -
0211
rsino r aztbz ,
y
= =
✗ = rcoso toen @ =
¥
Waarom willen dit ?
t d
we
2- =
rlcosotis.in 01
Wiskunde ☐ tips en tricks cosotisino-e.io 2- = reio-rlcosotis.in 0 )
dus 2- = r.e.io
Neem elke 2- =/ reign "
"
2-
rn ( ei )
>
Z geeft z = .
ik " ion
-02 ) r
¥ h
@
.
=
e.
12-4=12-13
=
'
Arglz ) =3 .
Arglz)
zij
ijij
ij ijijij
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