Orthogonal unit vectors in ℝ 3 Consider the vectors I = 〈 1 / 2 , 1 / 2 〉 and J = 〈 − 1 / 2 , 1 / 2 〉 . 67. Express I and J in terms of the usual unit coordinate vectors i and j . Then write i and j in terms of I and J .
Orthogonal unit vectors in ℝ 3 Consider the vectors I = 〈 1 / 2 , 1 / 2 〉 and J = 〈 − 1 / 2 , 1 / 2 〉 . 67. Express I and J in terms of the usual unit coordinate vectors i and j . Then write i and j in terms of I and J .
Orthogonal unit vectors in
ℝ
3
Consider the vectors
I
=
〈
1
/
2
,
1
/
2
〉
and
J
=
〈
−
1
/
2
,
1
/
2
〉
.
67. Express I and J in terms of the usual unit coordinate vectors i and j. Then write i and j in terms of I and J.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
Chapter 13 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
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