BME350 WNE Biotransport Processes Problem Set 2 Exercise hello there I will post 5 math and physics questions, it should take you that longlook at it befor

BME350 WNE Biotransport Processes Problem Set 2 Exercise hello there I will post 5 math and physics questions, it should take you that longlook at it before BME 350
Biotransport Processes
Issued: Thursday, January 24, 2019
Due: Tuesday, February 5, 2019
Problem Set #2
PART 1:
First Order Differential Equations
The function y(t) obeys the differential equation
3
dyt  1
 yt   2u 1 t 
dt
2
for both negative and positive times.
Given the initial condition y(0) = 0 you are required to find an expression for y(t) for t > 0.
Recall that the function u-1(t) is a unit step function, defined by
u-1(t) = 0 ; t < 0 u-1(t) = 1 ; t > 0 or t = 0.
i)
Write down the differential equation for t > 0.
ii)
Solve the differential equation in i).
iii)
Provide a rough sketch of the solution.
1
PART 2:
Continuity in three dimensional Cartesian coordinates
In three dimensional Cartesian coordinates the continuity equation is of the form

C x, y, z, t 
   x, y, z, t   
t
where



 x, y, z, t    x x, y, z, t i   y x, y, z, t  ˆj   z x, y, z, t k
and

 x, y, z, t   y x, y, z, t   z x, y, z, t 
   x, y, z, t   x


.
x
y
z
Outline a derivation of this equation.
PART 3:
Exercise 3.18 From Weiss
PART 4:
Problems 3.1 and 3.2 From Weiss
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