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Calculus Chapter 3 R50,00   Add to cart
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  3. University Of The Witwatersrand (wits)
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Calculus Chapter 3
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This chapter includes notes on Quadric Surfaces, Directional Derivatives, Potential Functions, and Stationary Points. Each section includes multiple worked examples. Notes were taken on an iPad

Last document update: 5 year ago

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Document information

  • August 18, 2019
  • August 20, 2019
  • 24
  • 2018/2019
  • Study guide

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Content preview

{
HAP TER 3

ALC ULUS
SCALAR & VECTOR FIELDS

,Revision of basic
✓



graphs
→
y=kx2 Parabola

→
ax÷+y÷=1 Ellipse

→
say
.




g÷=1 Hyperbola )(




Surfaces in 3- dimensions
.



•
( a. b. c)
{ FLAT SURFACES }
axtbxtcx =D
7-

normal =(a , b. c)




problems
*
In all analyse the surface by 2D cuts
we
taking
which be done by letting X. then Z
equal same
can
y
constant and
seeing what graphs we
get .

, { 't
}
'

EQUATIONS OF THE FORM Z
=
ax by




-1
At b →
z=3x2t5yZ

'

yc=k :
Z =
3k -1542 ③
Tiara bola
5y2=z -

zkz




gang
:
rn
:




k
3x45y2=k elliptic parabalood
:
Z
-




At b -
→ Z =
2×2 -




YZ


a
a-
:




y
-

-
k .fi?ahI.-z5TmoParaboea
:

Did arabola
,
fizzle
!
Zz } ,
Hyperbolic paraboloid
k k 2×2 ye pity perboea
' = -




Z
=




b-
parabolic
at o
sa vera
-




-
cylinder

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