This preview shows pages 1–3. Sign up to view the full content.
AE202
Problem Set 2: MATLAB
DUE: 23 February 2011
Spring 2011
Include a printout of your MATLAB code with your homework
solutions.
Email electronic copies of your MATLAB functions to
cmartin6@illinois.edu
. In a
single
zip (or rar) file named
LastName_FirstName_AE202HW2.zip .
Please include
AE202
Homework 2
in the subject line of the email.
1.
In MATLAB polynomials are stored as a vector of their coefficients. i.e.
1
1
1
0
( )
...
nn
p x
a x
a
x
a x
a
is stored as a vector
p=[a
n
, a
n1
, … , a
1
, a
0
]
a.
Write a MATLAB function that computes the coefficients of the polynomial that is
formed by multiplying 2 other polynomials. Function should be of the form:
CombinedPolyCoeff = polyMultiply ( polyCoeffA, polyCoeffB)
You cannot use the inbuilt MATLAB function
conv
function
CombinedPolyCoeff = polyMultiply(polyCoeffA,polyCoeffB)
% Finds the product of 2 polynomials.
% All of the input and output polynomials are stored as a vector of their
% coefficients. P=a_n*x^n+…+a_1*x+a_0 =>[a_n,…,a_1,a_0]
% subsequent calculations assume polyCoeffA and PolyCoeffB are column
% vectors. Make sure they are.
[mA nA]=size(polyCoeffA);
[mB nB]=size(polyCoeffB);
if
mA<nA
polyCoeffA=polyCoeffA';
end
if
mB<nB
polyCoeffB=polyCoeffB';
end
% compute the degree of both input polynomials
nA=length(polyCoeffA)1;
nB=length(polyCoeffB)1;
% create a matrix that has the coefficients of polyA in each column
% offset by one in each subsequent column
A=reshape([repmat([polyCoeffA;zeros(nB+1,1)],nB,1);polyCoeffA],[],nB+1);
% compute each term in the product polynomial
% each row corresponds to a certain x exponent
C=A*polyCoeffB;
% sum the rows to get the product polynomial
CombinedPolyCoeff=sum(C,2);
% ensure output is correct orientation
if
mA<nA
CombinedPolyCoeff=CombinedPolyCoeff';
end
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Documentb.
Write a MATLAB function that computes the coefficients of the polynomial that is the
derivative of the input polynomial. Function should be of the form:
diffPolyCoeff = polyDerivative ( polyCoeff)
You cannot use the inbuilt MATLAB function
polyder
function
diffPolyCoeff = polyDerivative (polyCoeff)
% Finds the derivative of the input polynomial given by vector polyCoeff.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 Martin

Click to edit the document details