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Class notes

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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  • January 23, 2023
  • 85
  • 2022/2023
  • Class notes
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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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