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2AC NOTES ( ADVANCED CALCULUS)
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These are comprehensive study notes and tutorials for MAM2000W in the first semester covering 2 modules: 2AC - Advanced Calculus 2LA - Linear Algebra
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Advanced Calculus, advanced
GOALS FOR FuLdPAT: B THJ Owi! (4) 7
Domain
Continutty
Differca liability
Integral ol vector function/ /.4)'
Parametric curves
VECTOR FunctioNs
ad:
vector function of a single variable sisad a function o Of , the le
type: 7: [a,b1 A R (n22)
This is as :
L Shorthand :
The dom ain ot a function is the ol reals uh
are delined at t.
Dom CP) : Dom Coal g Dom Cr21 .
Det: 7 Ce) has a limit at of Cach camponent in hos
at to
C cost tec-20.24
trample :
lim lim
cost
-1.0,
, (owTINu y + Di fERENTIAB
c ) is (ontinuouSał eJry Ita )=(to)
o
n(
CE) is d:Afeentiobl at
t I
fi is
Cach
componentm
diffeceatable at to *
f.
'C ) = (7 'Cto) 'Cto)J.
|NT ALS DFvECT R uNC TI0NS
The Intergra of over lo, is
justthe tegls o
allthe
Komponeat betúeee:L ,b te d u n o d o sv
d :
E omple:
S ) dt sa d) S ı5t
( 4 |d
5
(A 1J (0( ▇ ) e( : (. np
.*,
. d 3:
*(
, RATRIC URES
The vector unction () a,63 Rn BS dehine dby
notot ton : C
The Same curue canbe Cx pressed by d kren vector tunctron5.
E mple : ) = (s t (ost) o
CsimĄ6 cOs 4 ) Co, 1e
goph uve
4 C ) = CHCt), l))
4 = F Ct) = gCt)
elimiate ma1a g subjctoftheformula
enc le p ac the equationS
\dent y inlecepts
Eomp e: P e) =Comt , Cost) C n
p Sist y* cost
:: *y Sh ł cos
ły unit crrcle
C: 0 =I C0, )
= o = -| Lo - Je
whe yo
cost 0 Co, )a
ı
=Stat = S =
,0▇
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