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
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 t
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
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
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. Als
.
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
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 fol
06713: Homework 8
Due Monday December 3
Please take a few minutes to fill out the course evaluation form available at
www.cmu.edu/uca
Information from these course evaluations is valuable for improvi
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