Mathematical Methods in Mechanical and Aerospace Engineering
ENG EML 5060

Fall 2016
Assignment 2 Mathematical
Methods in Mechanical and
Aerospace Engineering
EML5060_CMB16Fall
1st Semester of 201617
1. Verify the Divergence Theorem, = + + in D region, a unit cube defined by
0 1, 0 1 and 0 1.
( ) = div
( ) = ( ) + + ( )
1
6
1 (): = 1,
Mathematical Methods in Mechanical and Aerospace Engineering
ENG EML 5060

Fall 2016
Assignment 2 Mathematical
Methods in Mechanical and
Aerospace Engineering
EML5060_CMB16Fall
1st Semester of 201617
1. Temperature function: (. . ) = 2 + 2 + 2 , flow of heat = , flux of heat out of
sphere of radius a 2 + 2 + 2 = 2 ? (surface area of sph
Mathematical Methods in Mechanical and Aerospace Engineering
ENG EML 5060

Fall 2016
Assignment 2 Mathematical
Methods in Mechanical and
Aerospace Engineering
EML5060_CMB16Fall
1st Semester of 201617
1. Buoyancy force on a floating object = , fluid pressure = (, , ),
weight of object is = , use Divergence Theorem to prove: + = 0.
() =
Mathematical Methods in Mechanical and Aerospace Engineering
ENG EML 5060

Fall 2016
Assignment 2 Mathematical
Methods in Mechanical and
Aerospace Engineering
EML5060_CMB16Fall
1st Semester of 201617
1. The natural extension of Gauss law ( ) = 4, (, , ) is charge
density per volume.
a. Show: div = 4
( ) = div = 4 div = 4
b. is an irrot
Mathematical Methods in Mechanical and Aerospace Engineering
ENG EML 5060

Fall 2016
Assignment 12 Mathematical
Methods in Mechanical and
Aerospace Engineering
EML5060_CMB16Fall
1st Semester of 201617
1. Tangent plan to 5 2 2 + 4 2 = 8 at (2,4,1):
(, , ) = 5 2 2 + 4 2 8
is orthogonal to at any point of (, , ) which is on the .
(, , )
Mathematical Methods in Mechanical and Aerospace Engineering
ENG EML 5060

Fall 2016
Assignment 12 Mathematical
Methods in Mechanical and
Aerospace Engineering
EML5060_CMB16Fall
1st Semester of 201617
1. Temperature function (, ) = 5 + 2 2 + 2 ,
starting point is (4,2),
direction to cool off ASAP?
(, ) = (, )
(, ) =
+
@(4,2)
= 4 ,
=