Math 31401
Takehome portion to midterm exam 2
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1. Let u(x, t) be the temperat
Math 3150 Practice Final Exam
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Write your answer in the space provided. Show work for full credit.
1. Suppose the ux law determining mass transport on the real line is J = 5u(x, t), where
u is a mass density, and there is an initial mass dens
Quiz
2
P
PDE for engineering students (3150)
Name and Unid:
1. Let C([1, 1]) be the space of continuous functions on [1, 1] equipped with the inner
product:
1
<f, g
>=
f
f(x) g(x) dx,
Vf,g e C([1, 1]).
We consider the subspace P
2 of all polynomials of de
Math 3150 Spring 2016 Homework 10
Due Friday April 8
April 4, 2016
1. Solve the initial value problem
2
2u
2 u
=
c
t2
x2
u(0, t) = 0 u(L, t) = 0 u(0, x) = sin
20
x
L
u
(0, x) = 8 sin
t
4
x
L
using the general solution from class.
2. (15.4.1) Consider a st
Math 3150 Spring 2016 Homework 9
Due Friday April 1
March 28, 2016
1. (15.2.1) Consider a taught string 0 x L with constant density and constant tension T
whose vertical displacement u(x, t) satisfies
2u
2u
= T 2 + Q
2
t
x
u(0, t) = 0
u(L, t) = 0
where Q(
Math 3150 Spring 2016 Homework 8
Due Wednesday March 23
March 17, 2016
1. For each of the following function determine if it is even, odd, or neither:
(a) f (x) = x4 3x2 + 7
(b) f (x) = x5 3x3 + 7
(c) f (x) =
x2 +4
x3 x
(d) f (x) = (cos(5x)2
2. Sketch the
Math 3150 Spring 2016 Homework 7
Due Friday March 4
February 26, 2016
1. (13.5.10) Using the maximum principles of Laplaces equation, prove that the solution of Poissons equation, u = g(x), subject to u(x, 0) = f (x) on the boundary, is unique.
2. (13.5.1
Math 3150 Spring 2016 Homework 6
Due Friday February 26
February 23, 2016
1. (13.3.3) Solve the initial value problem
2u
u
= K 2,
t
x
u(0, t) = 0,
u(L, t) = 0,
if the temperature is initially
(
0, if 0 < x L/2
u(x, 0) =
5, if L/2 < x L.
using the general
MATH 3150 SPRING 2016 HOMEWORK 1
DUE FRIDAY JANUARY 22
(1) (4.6.24) Given mutually orthogonal vectors v1 , v2 , . . . , vk in Rk show that
v1 + v2 + + vk 2 = v1 2 + v2 2 + + vk 2
(2) (6.1.20) Determine the eigenvalues and eigenvectors of the matri
Math 3150 Spring 2016 Homework 2
Due Friday January 29
January 22, 2016
1.
a) If u(x, t) is the temperature in a metal rod with variable crosssectional area A(x) and uniform thermal properties, give an expression for the total thermal energy in the rod, x
Math 3150 Spring 2016 Homework 3
Due Friday February 5
January 29, 2016
1. On Friday (section 12.4), example 2, we found that
Z L
0
x2
c + x + c2
2
!
Z L
cf (x) dx.
dx =
0
Find c2 .
2. (12.4.1) Determine the equilibrium temperature distribution for a rod
CS/ECE 3700
Spring 2016
Myers
Homework #4
HOMEWORK #4: Flipflops, Registers, and Counters
This homework is due at midnight in the ECE locker for CS/ECE 3700 on Friday, March 11, 2016. Be sure
to show all work for full credit.
Read Chapter 5, and complete
Math 3150 Spring 2016 Homework 5
Due Friday February 19
February 12, 2016
1. (13.3.1) Separate the variables in the following partial dierential equations to obtain systems
of ordinary dierential equations.
(a)
u
k
= 2
t
r r
2 u
r
.
r
(b)
2u 2u
+ 2 = 0.
Math 3150 Fall 2016 Homework 6
Due Friday October 7
1. (13.3.3) Solve the initial value problem
2u
u
= K 2,
t
x
u(0, t) = 0,
u(L, t) = 0,
if the temperature is initially
(
0, if 0 < x L/2
u(x, 0) =
5, if L/2 < x L.
using the general solution from lecture.
Math 3150 Fall 2016 Homework 10
Due Friday Nov. 11
1. Solve the initial value problem
2
2u
2 u
=
c
t2
x2
u(0, t) = 0 u(L, t) = 0 u(x, 0) = sin
20
x
L
u
(x, 0) = 8 sin
t
4
x
L
using the general solution from class.
Solution: The general solution is
u(x, t)
Fall 2016
Math 3150  Practice Exam 1
Section 001
Laplacian in polar coordinates:
1
u=
r r
2
u
1 2u
r
+ 2 2
r
r
General solution to the heat equation on a bar of length L with zero temperature ends:
u(x, t) =
X
Bn sin
n=1
n
n 2
x ek( L ) t
L
Gener
I
I
(5

_7:_
17

7
.4k
._
_1
7z.4

z
c
7
1
1
I
I
N
2

.L
,i
N
\
1
I
I
a
_
_

It
e
13
5
(14.3.18) For continuous functions,
(a) Under what conditions does f(x) equal its Fourier series for all x, L < x < L?
(b) Under what conditions does f(x) eq
Math 3150 Fall 2016 Homework 9
Due Friday November 4
1. (15.2.1) Consider a taught string 0 x L with constant density and constant tension T
whose vertical displacement u(x, t) satisfies
2u
2u
=
T
+ Q
t2
x2
where Q(x, t) = g is constant.
u(0, t) = 0
u(L,
Fall 2016
Math 3150  Final Exam
Section 001
General solution to the heat equation on a bar of length L with zero temperature ends:
u(x, t) =
X
Bn sin
n=1
n
n 2
x ek( L ) t
L
General solution to the heat equation on a bar of length L with insulated (i