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