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1. So that'll be u and then
v
, let's take 0, I think,
2. y is
v
over u. So, let me actually add an
3. does w lie in the plane of u and
v
?
4. should we get some more females for this group
V
no I mean for Justin but not for
5. and
v
then it would be the same thing.
6. in fact, that the length of this cross product r cross
v
7. is partials of u and
v
with respect to x and y.
8. So we have to pay n degree of
v
time,
9. copy this area control C now I going to word here instead of pressing Ctrl
V
10. y sub
v
. We have a lot of partials in
11. That's confusing-- from u to
v
. Then there
12. And, that's
v
equals one. So,
v
goes from zero to one.
13. matrix |u sub x, u sub y,
v
sub x,
14. cross product r cross
v
? Well, it's the direction that's
15. right here is made for
V
it looks like a transforming you guys notice this is
16. a function of u and
v
. And then we can ask ourselves,
17. calculation about a derivative of the cross-product R cross
v
.
18. So -- So if the gradient vector is perpendicular to
v
,
19. but a Cockney person may not use the "the", they will use an "f" sound or a "
v
" sound
20. substitution? So, in terms of u and
v
,
21. variables, u and
v
, they depend on a single
22. how delta u delta
v
relate to delta x delta y,
23. u plus some number times
v
plus some number times w.
24. There's some last edge from u to
v
,
25. by changing variables to u equals x and
v
equals xy.
26. UV prime is U prime
V
plus UV prime.
27. we should figure out what dx dy will become in terms of u and
v
.
28. Sorry. If u and
v
are dependent on yet
29. anymore
V
what happened to oh you sound just like her though for everybody
30. points two jumps to the left of
V
here's the first jump that's the magnitude of
31. I can multiply that second guy,
v
. So this was u
32. snowflake what we're trying to beautify my ninja yep ins
V
she's always trying
33. both equal to x. So, in terms of u and
v
,
34. that r cross
v
equals a constant vector, OK?
35. it means we are going to slice by
v
equals constant.
36. we can write this as dr/dt cross
v
plus r cross dv/dt,
37. and that
v
equals 1x 0y. So that's how I would find it.
38. our planet moves by
v
delta t, OK?
39. It goes all the way up to vk, which is the last vertex,
v
.
40.
v
. Anyway, so, whatever the reason
41. change in y). And, the change in
v
will be
42. do you get if you take all combinations of u,
v
, and w?
43. Subscribe to
V
actually I know what it says it says give this video a thumbs up
44. Be sure to put in code while clay for a 10% off your order
v
. When you order all those things
45.
v
. That will be x sub u times du
46. variables, u and
v
, and we'll try to redo our
47. that's like taller than
V
you guys probably remember that one now as you
48. So we reattach
v
. And if I do this,
49. if there is a path from u to
v
.
50. delta r, is approximately equal to
v
51. That is
v
du over dt. And partial of f with respect
52. OK, so u equals
v
. Now, we have the two other
53. of
v
, what are the bounds for u? So, I'm traveling on my curve,
54. I didn't change u, I didn't change
v
,
55.
v
sub y|, the matrix that I had up there.
56. the length of the cross products r cross
v
measures the rate at
57. big
V
that's my superhero name alright notification ninja and whatever your
58. way past haha what do you think of that weapon there
V
huh cool in here just
59. from back to front under two legs of a
V
.
60. know how x and y depend on u and
v
.
61. velocity vector. So, this is
v
cross
v
plus r
62. This side we said is y equals one becomes u equals
v
.
63. Well, if we set y equals one, that tells us that u and
v
are
64. We actually defined two vertices, u and
v
65. and
v
, and it can try to take partial
66.
v
equals 2. So, I want (1,2).
67. What does it mean that I'm keeping
v
constant.
68. r. The other one is
v
delta t.
69. Well, we know what
v
cross
v
is because, remember,
70. what happens when I change
v
. That is the definition of a
71. And, what is xy in terms of u and
v
?
72. So df over dt should be f sub q du over dt plus f sub
v
plus dv
73. terms of u and
v
. Well, it's easy.
74. If I take all combinations of u,
v
, w*,
75. And, u and
v
will be some functions of x and y.
76. to
v
is going to be just u, dv over dt.
77. Yes? If u and
v
themselves depended
78. also exists a path from u to
v
.
79. integral in terms of u and
v
. So, how do we do the
80. ninja name is
V
wants to know what your ninja name is so let her know down below
81. and
v
. And you know x and y are
82. But, it becomes much easier in terms of u and
v
.
83. to
v
they uses at most k edges.
84.
V
I'm not gonna hit your face. How many videos have we filmed together too many and I have not cut off your face
85. it means d by dt of r cross
v
is the zero vector.
86. OK, so given any vector tangent -- -- let's call that vector
v
87. I'm just going to pack this shade right on the outer '
V
'
88. better watch out where
V
is gonna take a deuce on you that just means you're
89. So
v
and w are the same.
90. single form because we are saying r cross
v
has constant
91. We are expressing how w reacts to changes in u and
v
,
92. replace x and y by new coordinates, u and
v
.
93. you is partial of u and
v
with respect to x and y,
94. (u,
v
) over partial xy) times dx dy.
95. bounds for u and
v
in the new integral so that we know how to
96. zero, then delta u and delta
v
will
97. y equals 0, you get u equals 3;
v
equals 1.
98. So the value for m is $50,000, and at 6%
V
is only $883,000.
99. OK, so What we want to understand is how u and
v
vary
100.
V
hasn't seen that show enough so and I just like put those over my shoulder like this
101. If I tell you R cross
v
is constant, you might be expected
102. Do the components of
v
add to zero?
103. What happens when x equals zero? Well, both u and
v
are zero.
104. We actually defined two vertices, u and
v
105. Well, we have deleted
v
. So we have to reattach
v
again.
106. wave your hand
V
there you are okay all right so Vy who's the first person we
107. When
v
and u are the same, when
v
and w are the same,
108. draw what it looks like in terms of u and
v
.
109. So let
v
be a leaf of the tree.
110. and x varies just becomes
v
equals zero.
111. I'm gonna finish him by leaving the sword sheath and one after
V
frozen
