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Maths 214 Advanced Calculus notes for A1 (2024) R100,00   Add to cart
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Maths 214 Advanced Calculus notes for A1 (2024)
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The only document you’ll need to pass your A1. Comprehensive notes made from class, the textbook and from an amazing YouTube channel (Alexandra Niedden). This document includes a concise explanation on everything from chapters 12.6, 13.1, 13.2, 14.1, 14.2, 1.7, 14.3, 14.4 with lots of examples to...

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  • March 18, 2024
  • 30
  • 2023/2024
  • Class notes
  • Dr heymann
  • All classes

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12 6
.
Cylinders & Quadric Surfaces

Cylinders : sufface that consists of all lines 1) to a


given line &
pass through a
given plane curve

(in 3 space >only two
variables)
Ex #1 :
z =
x2 Z

-


I


parabolic Cylinder
>

y




x




Ex # 2 :
y2 + z2 =
1


Y




Z




Quadric Surfaces :
graphs of 2nd degree equations in 3 variables



AX2 By 2 2z2 Dxy + Eyz + Fxz Iz J 0
+ + Gx Hy + =
+ + + +




Ex #3 :
z =
x2 + y2 zI0

Traces :




1 1 z =
0 :
0 =
x + y2
-
z =
1 : 1 =
x + y2
I
z =
4 :
4 = x +
y2

, 4
1
Intercepts Traces
:
+ + = 1


20 , =c)

#Zellises
0,


ellipsoid Co I b
, ,
0) s

c = a
,
0
. 0




· -



E E 03
=# I hyperb
2 =
+ 10, 0 , i


3 Laxis z =
#ellipse

C
a cone




A
R
O
T 4 e
(0 0 03
3
#
z = + , ,
x =




⑤ Laxis x + y2
y =
# - Parabolas
z z = #
ellipse
: =




- ⑰
elliptic
paraboloid
-




3
- = #2
4 +
hyperba e
-



Hyperboloid ellipse
O
z =
# >
-




of one


- sheet




N
, +
same as 4


>
-




is



& hyperboloid
of 2 sheets




↓ !

⑥
E
# parabaSola
z = -




2




Hyperbolick)
Paraboloid C
&I&
I
<
I
-
&

, Techniques : exercises to show how to determine general shape


4y2 x
+ 0)
Ex # (0
intercepts 0,
=
: ,




Laxis
Traces :
Y = 0 : 0 =
x +
4




=:= + elligee
N
T




D. ellistie D




L
~




Ex#5 : 462 + 4y2 + 22 +
8y -
47 = -

4



1 .
complete the square


46 + 4(y2 + 2y + 1) + z2 -
42 + 4 = -
4 + 4 + 4

4x +
4(y + 1)2 + (z- 2)2 = 4 * we want this to =1


x +
(y + 1) + (z -

2) = 1

4



intercepts : (0, 0, 2)

Co, -1
, o) all traces are ellipses

·


ellipsoid
· ·

-




·

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