Vector Calculus Summary Sheets

MathematicssummaryNetes
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cylindrical coordinates
x r cos 0 rsin O Z where 2EIR OC 0,21T and r 20
yz
Spherical coordinates
x z KoosOsimo rsinos.no rcos0 where OE 0,21T ELOTE
y and r 20
N
inner product
For a KEIRN g b
Zaibia e kg
4 21 23 3.4 20
2 g
a
qformoelladt faa fataif.ae length ohednaefenyearmperoggetproarieti


oe table Hallllkll CandySchwartzInequality
Netballshell Hall TriangleInequality


For ab EIR Habll Hellkklleoso
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t NoteRight
cross thandkuted
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a

T
IIE.EE kx
hxi J
gaxb

, b
ParametricRepresentationof a Cunypath
Ela
E Ct xlt 2LTD here E 1127112 and TE IR
yet
t t l EY for t EEO I y Lt cost sint t f atELO 2K



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y mum
tangentvector to curve C

aEI
drqi.tt 4dyhtfih It
scalatalueofundion
ri e
let IRN IR all thepoints ERNsattying TEFIFeneiwea.ed
fi
f I c Ine CEIR isthe levelsetd value c

8797 2 HITEII
f grad f f z f PRODUCTRULE
WORKSHERE

For a plane E thx thetangentplaneat Ko yo tho yallis
y
Z fGogo tffixoyotfcxxoltffylxo.myyo 2 20 t Df I Xo