18.03 Problem Set 7: Part II Solutions
Part I points: 26. 6, 27. 10, 28. 12.
1
I.26. et sin(3t) = 2i e(1+3i)t e(13i)t , so L[et sin(3t)] =
1
1
1
1 (s + 1 + 3i) (s + 1 3i)
3
=
=
.
2+9
2i s (1 + 3i) s (
18.03 Problem Set 7
I encourage collaboration on homework in this course. However, if you do your homework
in a group, be sure it works to your advantage rather than against you. Good grades for
homew
18.03 Problem Set 5, Second Half
The rst half of this problem set was handed out on March 12 and is available on the
web.
I encourage collaboration on homework in this course. However, if you do your
18.03 Problem Set 5, First Half
The second half will be available by Monday, March 29.
I encourage collaboration on homework in this course. However, if you do your homework
in a group, be sure it wor
18.03 Problem Set 3: First Half
This is the rst two problems of PS3. The rest will be available on February 26.
I encourage collaboration on homework in this course. However, if you do your homework
i
18.03 Problem Set 4: Part II Solutions
Part I points: 13. 3, 14. 8, 15. 5, 16. 4.
5+4i
13. (a) [4] z + 2z = e(3+4i)t has solution zp = e(3+4i)t /(3 + 4i) + 2) = 25+16 e3t (cos(4t) +
5
4
i sin(4t) so
18.03 Problem Set 4
I encourage collaboration on homework in this course. However, if you do your homework
in a group, be sure it works to your advantage rather than against you. Good grades for
homew
18.03 Problem Set 1
I encourage collaboration on homework in this course. However, if you do your homework
in a group, be sure it works to your advantage rather than against you. Good grades for
homew
:
2
3
5
27
ex +y +z
x12 y15
: f(x, y, z) = ex
f(x, y, z) =
i,j,k0
2 +y3 +z5
1
i+j+k f
i !j !k ! x i y j z k
f(x, y, z) =
(x, y, z) = (0, 0, 0)
Taylor
x iy jz k.
(x,y,z)=(0,0,0)
1
(x2 + y3 + z5
18.03 Problem Set 9
I encourage collaboration on homework in this course. However, if you do your homework
in a group, be sure it works to your advantage rather than against you. Good grades for
homew