{
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
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
