Homework 5 Solution
1. We need to compute the regular Fourier series, the half-range Fourier
cosine series, and the half-range Fourier sine series for the given piecewise dened function.
(a) For the regular Fourier series, we assume the period length of t
MTHSC434, Section 1: Homework Assignment 5
More on Fourier series expansions
Due: Feb. 18, 2011
Total Point Value: 20 points
The purpose of this homework assignment is to help you
1. compute half-range Fourier series expansions;
2. notice minimization pro
MTHSC434, Section 1: Homework Assignment 4 Solution
2
= 1. Note also that
2
1. (a) The fundamental period is
f (x + p) = cos (2 (x + p)
= cos (2x + 2p)
which equals f (x) = cos (2x) when p = 1.
2
L
(b) The fundamental period is
=
.
4/L
2
(c) The fundament
MTHSC434, Section 1: Homework Assignment 4
Fourier Series expansions
Due: Feb. 11, 2011
Total Point Value: 20 points
The purpose of this homework assignment is to help you
1. recall properties of periodic and even/odd functions;
2. compute coecients assoc
MTHSC434, Section 1: Homework Assignment 3
Inner Products and Orthogonality
Due: Feb. 4, 2011
Total Point Value: 20 points
The purpose of this homework assignment is to help you
1. generalize the concept of inner products;
2. write arbitrary vectors in te
MTHSC 434, Section 1, Homework Assignment 2 Solution
1. (a)
x2 y1 (x) + 2xy1 (x) 6y1 (x) = x2 (2) + 2x(2x) 6x2
= 0.
(b) The dierential equation must be in standard form in order to use the reduction
of order technique given in the text. After dividing by
MTHSC 434, Section 1, Homework Assignment 2
Integration by parts and more ODEs
Due: 9:05am, Friday, Jan. 28, 2011
Point value: 20
The purpose of this homework assignment is to help you:
1. recall techniques for integration by parts;
2. resolve solutions t
MTHSC 434-001 Homework 1 Solution
1. (a) The characteristic equation is 2 4 + 5 = 0, and the roots are 1 = 2 + i,
2 = 2 i. Thus the general solution is
y (t) = e2t (c1 cos(t) + c2 sin(t) .
Note that y (t) = e2t (2c1 + c2 ) cos(t) + (2c2 c1 ) sin(t).
Thus
MTHSC434, Section 1: Numerical Solutions for Dierential
Equations
Total Point Value: 20 points
The purpose of this assignment is to help you
1. understand nite dierence approximations for the Poisson equation;
2. write code that solves computational probl