Alexander Clines
Assignment Homework5 due 11/04/2015 at 11:00pm CST
-(n pi)2 , sqrt(2 ) sin(n pi
1. (1 pt) Find the eigenvalues and eigenfunctions for y00 = y
on 0 x with BCs y(0) = 0 and y() = 0.
0
x) .
If in addition 0 = 0 is an eigenvalue with eigenfun
Alexander Clines
Assignment HW4 due 10/27/2015 at 12:00am CDT
f15jleem4354s001
1. (1 pt) Solve the BVP for the wave equation
3. (1 pt) Solve the BVP for the wave equation
2 u
2 u
(x,t) = 2 (x,t), 0 < x < , t > 0
2
t
x
2 u
2 u
(x,t) = 2 (x,t), 0 < x < , t
Alexander Clines
Assignment HW1 due 09/07/2015 at 11:00pm CDT
f15jleem4354s001
1
1
2
X1 = 6 , X2 = 2 e4t , X3 = 3 e3t
13
1
2
1. (1 pt) Write the system of first order equations in matrix
form.
dy
dx
= 4x + 5y,
= 5x + 7y
dt
dt
W (X1 , X2 , X3 ) =
d
dt
x
y
Alexander Clines
Assignment HW3 due 10/15/2015 at 11:00pm CDT
f15jleem4354s001
u(x,t) =
1. (1 pt) This problem is concerned with using separation of
variables to find product solutions. In particular you will substitute u(x,t) = X(x)T (t) into the given e
Alexander Clines
Assignment Homework5 due 11/06/2015 at 11:00pm CST
would enter
1. (1 pt) Find the eigenvalues and eigenfunctions for y00 = y
on 0 x with BCs y(0) = 0 and y() = 0.
-(n pi)2 , sqrt(2 ) sin(n pi
Note that any constant times an eigenfunction
Alexander Clines
Assignment HW2 due 09/25/2015 at 11:00pm CDT
f15jleem4354s001
Z b
f (x)g(x) dx =
1. (1 pt) Find the inner product of the given functions on the
interval, i.e., Find
h f , gi =
a
b
a
=
Z b
f (x)g(x) dx.
a
2. (1 pt) The functions f1 (x) = x
Alexander Clines
Assignment HW1 due 09/13/2015 at 11:00pm CDT
f15jleem4354s001
1. (1 pt) Write the system of first order equations in matrix
form.
dx
dy
= 4x + 5y,
= 5x + 7y
dt
dt
d
dt
x
y
=
x
y
4. (1 pt) Given that the vectors X1 , X2 , X3 are solutions
Alexander Clines
Assignment HW4 due 10/27/2015 at 11:30pm CDT
f15jleem4354s001
1. (1 pt) Solve the BVP for the wave equation
Correct Answers:
3*sin(t)*sin(x)-0.333333*sin(3*t)*sin(3*x)
2 u
2 u
(x,t) = 2 (x,t), 0 < x < , t > 0
2
t
x
3. (1 pt) Solve the BV
Alexander Clines
Assignment HW3 due 10/12/2015 at 11:00pm CDT
f15jleem4354s001
u(x,t) =
1. (1 pt) This problem is concerned with using separation of
variables to find product solutions. In particular you will substitute u(x,t) = X(x)T (t) into the given e
Alexander Clines
Assignment HW2 due 09/29/2015 at 11:00pm CDT
f15jleem4354s001
Z b
f (x)g(x) dx =
1. (1 pt) Find the inner product of the given functions on the
interval, i.e., Find
h f , gi =
a
b
a
=
Z b
f (x)g(x) dx.
a
Correct Answers:
First find an ant
Chase Martin
Assignment Homework 1 due 09/05/2016 at 11:00pm CDT
f16jleem4354s001
1. (1 point) Write the system of first order equations in matrix form.
dy
dx
= 5x + 4y,
= 3x + 7y
dt
dt
d
dt
x
y
=
x
y
-5
5. (1 point) Find the eigenvalues of C = -12
-8
Ent