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WTW258: LU 2.4: TRIPLE INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES Lecture notes R80,00   Add to cart

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WTW258: LU 2.4: TRIPLE INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES Lecture notes

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Lecture notes were made while watching the recorded lectures assigned to watch. These notes include theory (theorems) and worked out examples from the lecturer. These specific notes cover Triple integrals in cylindrical and spherical coordinates.

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  • July 13, 2022
  • 8
  • 2021/2022
  • Class notes
  • Ms l mostert
  • All classes
All documents for this subject (24)
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lexisparks
2. 4 .
Cylindrical coordinates
easier way to do triple integrals
C- onto
FIB If projecting
^

r Maish

yt plane
-




then cylindrical
< o↳¥ac ,yi◦, ≥
coordinates : of r.ly , 2- )
( r , o, t ) ( x
,
r
, A)
-



JE r To > y
rosa
E-
rsino v
1-
Eff Lf projecting f- onto
✗ t plane
-




cyl .
Coard :

,
NZ
( rcoslt, y , rsino) r.cn,z)
↑&
E ↓
e
r ) 2C









*mµµyµµµgµµmµµµ,÷
To write triple integral it -0 .




cylindrical coordinates


Describe projection onto plane i. to .

polar coordinates

describe 2- it -0 .

rand 0


change function f- In ,y,t) to
gcrcosoyrsino ) ,
t

, Example
cytcoord for
① give iterated integrals in .




the solid bounded by
fffxytdv and C- region
E
z=✓xÑ and 7--3
① ①
curve of intersection
3

⊖ 2- =


✓TÑ3
① ①
y

21yd
-
9
A ↑

↳ci
L
enter one
a from this
perspective

in plane
projection
xy _





^ ① Cartesian → ② cylindrical
3
R
0Erk3

←# 3 ≤ * 13
-




1- • ≤ 21T
-


✓ ≤
yytvq.TO


Eye ≤ *≤ 3 → VÑy≤ 2- ≤ 3


③ RT ≤ 2- ≤ s


fffnytdv

r ≤ 2- ≤ 3
>

Crusoe)CrsinMZ]r

if.it/Fj#rcoso)crsinos2-Jrdtdrdo
'



'
'


fir > 2-




?⃝

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