Math 316 Assignment 1
Due Friday Jan 16 in class
Problem 1. Find the solution to the initial value problem for the ODE
dy
1+y
=
dx
1+x
for each of the initial conditions
(a) y(0) = 1,
(b) y(0) = 1,
(c) y(0) = 2
Problem 2. Find the general solutions to:
(a
Math 316 Assignment 2
Due Friday Jan 23 in class
Problem 1. Find the rst six non-zero terms in the power series y = an (x x0 )n of
n=0
the general solution of the following second-order, linear, homogeneous ODEs, centred at
the indicated point x0 :
a)
y +
Math 316 Assignment 4
Due Friday Feb. 6 in class
1. Consider the heat conduction problem:
u
2u
= 5 2,
t
x
0 < x < 3, t > 0,
with homogeneous boundary conditions
u(0, t) = u(3, t) = 0.
Find the solution for each of the initial conditions (using formulas fr
Math 316 Assignment 4 Solutions
1. Consider the heat conduction problem:
u
2u
= 5 2,
t
x
with homogeneous boundary conditions
0 < x < 3, t > 0,
u(0, t) = u(3, t) = 0.
Find the solution for each of the initial conditions (using formulas from class/notes/te
Math 316 Assignment 5
Due Monday Feb. 23 in class
1. For the sawtooth function
f (x) =
x
0x1
2x 1x2
dened on [0, 2], compute its
(a) compute its Fourier sine series
(b) computes its Fourier cosine series
(c) by evaluating f (1), use each of your results f