06713: Homework 2
Due September 17
Required Problems
1. (a) In class, we derived the socalled normal equations for the least squares fit of a
data set to a straight line. But what if we want to fit to the function y=a+bt+cet, to a
collection of m experi
06713: Homework 5
Due Oct. 22
1. (a) Find the general solution to the equation 2 xy
dy
y2 = x2 .
dx
dy
= y + y.
dx
dy
(c) Solve the following initial value problem:
= xy + x + y + 1, y(0)=0. State the
dx
values of x for which the solution is valid.
(b)
06713: Homework 4
Due Oct. 10
1. (a) One famous event in National Football League History was the perfect season
played by the Miami Dolphins in 1972. In that year, the Dolphin won all 17 games
they played. In this problem, you will examine how unusual t
06713: Homework 1
Due September 5 in class
Homework Guidelines
You are encouraged to collaborate with your classmates on homework problems, with
two caveats. First, it is a very good idea for you to make a serious attempt at each
problem before you cons
06713: Homework 3
Due Sept. 26
1 2 1
1. The matrix C = 2 3 0 is symmetric. Show by direct calculation that the
1 0 1
eigenvalues of C are real and that the eigenvectors form an orthogonal set. Also show
how the vectors (1,0,0)T, (0,1,0) T, and (0,0,1)
.
LL

at = A+
~3
tt)
? \
b
LLL

y43 = y x
J
TI'
x b i d j 14i6; A x = f 3 ~ > + ~ ~ ) ~ X
i
Prb
4
yt L
in(22].=
( * Soluti~nto Problem 3 in A.eigpment
1

06713
*)
( * Pram Ax=b we have to Solve for x *)
A = ( ( 1 , 5, 1 , 4 ) s ( 1 , 0 , 1, 1 ) s
06713: Homework 7
Due Monday November 26
1. (a) In class, we discussed a model for a chromatography column. Solve this model
using the Freundlich adsorption isotherm, = KC n (with n > 1) with the following
initial/boundary conditions:
C = C exp( ax) for
06713: Homework 8
Due Monday December 3
Please take a few minutes to fill out the course evaluation form available at
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Information from these course evaluations is valuable for improving courses
for future students. The comments entered in
06713: Homework 6
Due October 31
1. Many experimental devices (for example, quartz crystal microbalances) involve
components that are forced oscillators. If a forced oscillator has no damping, it is
described by
d2x
+ kx = F cos( wt ),
dt 2
where m, k, F