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1. the chain rule will tell us how the value of
w
changes.
2. So there's
w
.
3. function, which is coming from, any time div
w
is zero,
4. So who
w
still be visiting him and stuff? He's just not going to be staying at my place anymore? He was actually
5. C &
W
Semi
6. Now if I drew all combinations of u, v,
w
, the original
w
,
7. We know that the change in
w
is approximately equal to 4 delta x
8. Ruby:
W
-What do you mean?
9. of
w
dot product with the velocity vector dr/ds.
10. and the third guy,
w
*.
11. that dw/dt is, we start with partial
w
over
12. Well, you can think of
w
as just another variable that is
13.
W
- Director Clapper, I want to ask you...
14. Well, let's think of
w
as a function of three variables.
15. And, what do you do? En, what doet u? It's onlt
w
a t,
w
a t, wat. En, what doet u? En,
16. Then, a2, that's partial
w
partial y, and a3,
17.
w
equals c. So, it's zero because
w
of t
18. be a1. That's partial
w
partial x.
19. If I take all combinations of u, v,
w
*,
20. A transpose
w
equal zero, so now in the continuous case,
21. I make this together so watch for that at the end of this video
w
it up
22. u plus some number times v plus some number times
w
.
23. partial
w
over partial x or partial
w
over partial y,
24. the equation
w
of x, y, z equals some constant,
25. formula is that while the change in
w
is caused by changes in x,
26. that I change u a little bit, how does
w
change?
27.
W
- The government persuaded
28. All combinations of u, v,
w
.
29. maybe I can rewrite it as
w
dot v, and that should be,
30. As an FYI, that period was calculated using an arbitrary round value for
w
, the relevant
31. This is the
w
that gave me problems.
32. The combinations of u, v,
w
*, how do I produce them?
33. Yes? What kind of object is
w
?
34. So v and
w
are the same.
35. Suppose I have vectors u, v and
w
.
36. So, the rate of change of the value of
w
as I move along this
37. and now it's also the
w
.
38. All combinations of u, v,
w
* is the same as saying all vectors
39. which directions
w
changes the fastest,
40. 'They wentto(
w
)anamazing place.'
41. dw/ds in the direction of I hat is, sorry, gradient
w
dot I hat,
42.
w
equals c. I have a curve on that,
43. of
w
at some point, x, y, z.
44. x plus
w
is a function of t, and take its derivative.
45. setting the function,
w
, equal to a constant.
46. Well, if I set
w
equal to some constant, c, that means I look
47. saw", it's a bit different, "a-
w
", "saw".
48. do you get if you take all combinations of u, v, and
w
?
49. And once again you have the semi vowel (
w
)
50. gradient of
w
dot product with velocity vector dr/dt.
51. direction of u is gradient
w
dot u.
52. They almost sound like a
W
."
53. So, I will take
w
equals a1 times x plus a2 times y plus a3
54. that this is
w
sub x, times dx over dt plus -- Well,
55. partial
w
over partial u and partial
w
over partial v in
56. "o" and "e", "o" and "u", and "e" and "
w
".
57. the divergence of this
w
?
58. substitute.
W
as a function of t.
59. but I changed
w
to minus one, what does that mean?
60. En, wat doet u? It's
w
a t,
w
a t. Ik ben een student. student.
61. If taking all combinations of u, v,
w
62. And now, over on this side, I had the divergence of
w
63. and I call it
w
. I call its value
w
so that I
64. Let's call it
w
for now. Let's say I have quantity
w
as
65.
w
sub y is x squared times dy over dt plus
w
sub z,
66. going to give the connection between v and
w
.
67. I'm going to take three vectors, u, v and
w
,
68. what is dw/ds? What's the rate of change of
w
69. And, what is the magnitude of
w
? Well, it's actually the
70. When v and u are the same, when v and
w
are the same,
71. well, what should it be? What happens to the value of
w
72. two names,
w
and f. I mean
w
and f are really the
73. And that led me to
w
being, what we just said, ds/dy,
74.
w
equals c is a circle, x^2 y^2 = c.
75. for y into the formula for f then
w
becomes a function of u
76. partial
w
partial z. Now, what is the levels of this?
77. That's the rate of change of
w
with respect to u if I forget
78. Do the components of
w
*, now that you've fixed it correctly,
79. I could use any curve drawn on the level of
w
equals c.
80. my
w
here is pretty much what I called f before.
81. are probably toast. Partial
w
over partial x,
82. points towards higher values of
w
.
83. This is the divergence of
w
, of course.
84. If v is the same as
w
, then how is the potential function,
85. how
w
depends on x and y. If we don't know that then we
86. So
w
is, since these are the same,
w
is now [du/dx, du/dy].
87. And a female sheep is called a ewe, e-
w
-e.
88. and they "wa", go like a "
w
". So... And the "mail", m-a-i-l,
89. So this is
w
star maybe, a different
w
.
90. not people I hate, care about. D
W
Smithfield from Rhode Island, Jar key is like a little
91. WH words can pronounced “hw” or just “
w
”.
92. that's just gradient
w
dot product with the unit vector u.
93. Let's call it
w
of t as t increases.
94. But if this theory is right, and
w
is not exactly equal to -1, the force acting to expand
95. and
w
* happened to fall in that plane.
96. increase of
w
at the given point.
97. My
w
, I'm going to make that into
w
.
98. It's
w
a t, so it's a mistake. Sorry. I am a student. Yes. Ik ben een student.
99.
w
equals c. So, let's think about what that
100.
w
equals c. So that means v can be any
101. And the same v. But I'm going to change
w
.
102. this is the level set,
w
equals four,
103. I just make a simple
W
sound -ww.
104. So in the beginning when we were working with u, v,
w
,
105.
W
- My view is that if you're going to protect
106. That's the same as the length of gradient
w
times the length
107. just moments ago I spoke with George
W
Bush and congratulated him on becoming
108. where
w
equals x^2 y^2 - z^2. And so, we know that the
109. There in the same plane.
w
* gave us nothing new.
110. which measure how
w
changes if I move in the direction of the x
111. So, the gradient of
w
is a vector formed by putting
112. which is wx,maybe I should write, partial
w
of partial x.
113. These three, u, v, and
w
* I would call dependent.
114. Remember
w
was x^2y z. x was t, so you get t squared,
115. to the level,
w
equals c because it's tangent
116. direction of u is gradient
w
dot product of u.
117. And then, we plug that into
w
. And then we take the derivative.
118. The "d", "r", and the "
w
", they're consonants, and the "e" is a vowel.
119. So, the direction of gradient
w
is the direction of fastest
120. surface when
w
doesn't change, so, when this becomes zero,
121. tell you how sensitive
w
is to changes in each variable.
122. delta
w
equals zero, and its tangent plane
123. partial
w
partial x is 2x. And partial
w
partial y is 2y.
124. does
w
lie in the plane of u and v?
125. partial
w
over partial y should be required.
126. We are expressing how
w
reacts to changes in u and v,
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