ChBE 521
Homework 5
due Wednesday, October 12
1. Beers 3.A.2 2. Beers 3.A.3 3. Beers 3.B.4 4. Consider the boundary value problem D d2 c = 0, dx2 c(0) = c(1) = 0.
The eigenvalues for this equation are n = n2 2 , and the eigenfunctions are n (x) = 2 sin(nx
ChBE 521
Homework 4
due Wednesday, September 30
1. Characterize the solution structure to the equation x3 px r = 0 Use graphical approaches (i.e. geometrical approaches) to determine the bifurcation points. 2. Consider a chemostat at steady state describe
ChBE 521
Homework 3
due Wednesday, September 16
1. Numerically solve the equation d2 c = c, dx2 subject to the boundary conditions c(0) = 1, dc dx = 0.
x=1
0 x 1,
Choose N large enough so that you do not observe any change in the solution. 2. Numerically
ChBE 521
Homework 2
due Wednesday, September 9
1. Show that (a) (AB )T = B T AT , (b) AT A is symmetric, (c) AA = 0 is possible but AT A = 0 is not possible (unless A = 0). (d) (AB )1 = B 1 A1 2. How would you t in the least squares sense an m-dimensional
ChBE 521
Homework 1
due Monday, August 31
1. Plot the function f (x, y ) = sin(2x) sin(2y ) on [2, 2] [2, 2]. 2. Beers, 1.A.1 3. Beers, 1.A.2 4. Beers, 1.A.3
1
ChBE 521
Homework 8
due Monday, November 30
1. Consider a game involving two six-sided dice. Plot the probability of observing each total value (with 2,3,.,12 on the horizontal axis) if the dice are fair. What is the probability that the 5th roll is the r
HW#8 Prob 2 Fit the distribution of X to a normal distribution pdf when n =100, 1,000 and 10,000 N=100
20
15
10
5
0
0
10
20
30
40
50 N
60
70
80
90
100
N=1,000
300 250 200 150 100 50 0 400
420
440
460
480
500 N=1000
520
540
560
580
600
N=10,000
3500 3000 2
ChBE 521
Homework 7
due Wednesday, November 11
1. How would you use nite dierences to solve the boundary value problem in spherical coordinates d dr r2 dc(r) dr = kc(r)
subject to the boundary conditions c(1) = 1, Solve the problem using N = 100. 2. Using
Partial Dierential Equations (cont.)
ChBE 521 Applied Mathematics
November 19, 2008
Time dependence
Last time, recall that we solved the one-dimensional steady-state problem (Poisson equation), Lu = f, where L = d2 , dx2
using both nite dierences and coll