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1. If I give you the function g equals u of
v
.
2. what it will look like in terms of u and
v
.
3. to
v
. Then we know by the ordering principle
4. to that using first the chain rule to pass from u
v
to that
5. That's confusing-- from u to
v
. Then there
6. and
v
, they are linear formulas in terms of x and y.
7. these formulas for partials of f with respect to u and
v
.
8. the mind what's my name's your name big
V
cuz you're so huge notification ninja
9. We actually defined two vertices, u and
v
10.
v
11.
v
and we had to do it for every value of k between 0
12. We are expressing how w reacts to changes in u and
v
,
13. partial f over partial u partial y over partial
v
.
14. cross product r cross
v
? Well, it's the direction that's
15. So we reattach
v
. And if I do this,
16. constant in terms of u and
v
. So, I can take the constant out.
17. So -- So if the gradient vector is perpendicular to
v
,
18. Well, what is
v
?
v
is xy.
19. I didn't change u, I didn't change
v
,
20. Do the components of
v
add to zero?
21. prime, then you are safe. If you know it as u prime
v
22. r, and
v
delta t, magnitude of the cross product.
23. z and y, but another set of variables, here u and
v
.
24. to look at,
v
here, and you sum these things
25. roughly (
v
sub x delta x) (
v
sub y delta y).
26. to
v
they uses at most k edges.
27. There's some last edge from u to
v
,
28. Well, if we set y equals one, that tells us that u and
v
are
29. Under both legs of the
V
, from front to back.
30. velocity,
v
, equals dr/dt is tangent -- --
31. this or is it bronze what color is this
V
copper copper yeah really cool sore
32. maybe there and
v
goes somewhere, maybe here.
33. What you got there
V
?
34. I can multiply that second guy,
v
. So this was u
35. That means R is perpendicular to
v
.
36. What happens when x equals zero? Well, both u and
v
are zero.
37. how delta u delta
v
relate to delta x delta y,
38. double integral over some mysterious region of
v
du dv.
39. by changing variables to u equals x and
v
equals xy.
40. and
v
. And you know x and y are
41. integrand in terms of u and
v
. OK, so we were integrating x
42. a function of variables, which are u and
v
.
43. That is
v
du over dt. And partial of f with respect
44. ninjas here okay ninja up in the next injustice 2 character is
V
does not be
45. Well, that tells us u and
v
are going to be 0.
46. u and
v
. U and
v
themselves are actually
47. I'm gonna finish him by leaving the sword sheath and one after
V
frozen
48.
v
. But, if you fix a point,
49. UV prime is U prime
V
plus UV prime.
50. you get some balls you put it in the freezer and then you throw it up
V
are
51. of u and
v
coordinates, OK?
52. and x varies just becomes
v
equals zero.
53. So we have to pay n degree of
v
time,
54. substitution? So, in terms of u and
v
,
55. We actually defined two vertices, u and
v
56. equals one. So, that means u=
v
is my
57. delta u delta
v
is, sorry, approximately equal to
58. back to injustice to
V
Sub Zero awesome character he uses ice dad gears you mean
59. So there's going to be indegree of
v
different choices
60. So, it's
v
divided by a magnitude of
v
.
61. for each value of
v
, if I fix a value of
v
,
62. Knives. The F changes to a
V
. Just like 'life', 'lives'.
63. of change with respect to
v
, if I keep u constant,
64. to here okay but its value for stuff is still
V
okay so the width remains the
65. terms of u and
v
. Well, it's easy.
66. that's actually
v
=0. So, we'll start at
v
equals
67. if there is a path from u to
v
.
68. copy this area control C now I going to word here instead of pressing Ctrl
V
69. Well, we know what
v
cross
v
is because, remember,
70. yeah we can buy food and stuff where you going there
V
she's walking or she's
71. and y over b be
v
. So, we'll have two new
72. if you clear denominators for
v
squared then you will see
73. (u,
v
) over partial xy) times dx dy.
74. then the change in u and the change in
v
will correspond to,
75. This is all combinations, all combinations of u,
v
,
76. better watch out where
V
is gonna take a deuce on you that just means you're
77. Now if I drew all combinations of u,
v
, w, the original w,
78. should we get some more females for this group
V
no I mean for Justin but not for
79. Over here, we're taking a min over n degree of
v
things.
80. magnitude of the vector,
V
.
81. OK, so, if you know that uv prime equals u prime
v
plus uv
82. from back to front under two legs of a
V
.
83.
v
over partial of x, y.
84. and the next Teen Titan we or Justin out is Raven what I think Raven looks like
V
85. we can write this as dr/dt cross
v
plus r cross dv/dt,
86. And, it's obtained using the partial derivatives of u and
v
87. Veel dank! Thank you very much! Veel dank! Remember
v
is pronounced as fay in Dutch therefore
88.
v
. Anyway, so, whatever the reason
89. you is partial of u and
v
with respect to x and y,
90. this with respect to
v
? Here we need to know how to
91. draw what it looks like in terms of u and
v
.
92. what happens when I change
v
. That is the definition of a
93. Well, we have deleted
v
. So we have to reattach
v
again.
94. and
v
, then that means that f becomes
95. So
v
and w are the same.
96. OK? So, this one here should be
v
97. but a Cockney person may not use the "the", they will use an "f" sound or a "
v
" sound
98. So
V
and I made this over on her channel
99. that's like taller than
V
you guys probably remember that one now as you
100. so, it's called usually
V
, so,
V
here stands for velocity
101. oh I can zoom using
V
102. the equation of this uv coordinate is u equals
v
.
103. a function of u and
v
. And then we can ask ourselves,
104. So, to pick up and knit, you go in from the front to the back under both legs of the
V
,
105. Let's call them u and
v
. I am going to stay with these
106. If I tell you R cross
v
is constant, you might be expected
107. Suppose I have vectors u,
v
and w.
108. And so that means R dot
v
is zero.
109. replace x and y by new coordinates, u and
v
.
110. OK, so What we want to understand is how u and
v
vary