Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
First Quiz (solutions)
Due: 30 Sep 2013
Note: You are not required to simplify algebraic or numeric expressions.
1. Find the general solutions of the following rst order linear dierential equati
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Twelfth Quiz (take-home)
Due 4 Dec 2013
1. Consider the following boundary value problem for the heat equation (representing a
half innite rod):
2u
u
,
x > 0, t > 0
=
2
x
t
u(0, t) = 1,
t>0
x
u
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Seventh Quiz (solutions)
Due 11 Oct 2013
Instructions: Please write your nal answers on this sheet and as much of your work as you can t.
Additional work may be written on additional sheets stap
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Ninth Quiz (solutions)
Due 30 Oct 2013
Instructions: Please write your nal answers on this sheet and as much of your work as
you can t. Additional work may be written on additional sheets staple
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Eleventh Quiz (solutions)
Due 25 Nov 2013
1. Apply the Laplace transform in the t variable to convert the following to an ordinary
dierential equation, with boundary conditions, for U (the Lapla
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Tenth Quiz (solutions)
13 Nov 2013
1. Consider the equations below in polar coordinates. Use separation of variables to obtain
dierential equations for the indicated functions (with parameter ).
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Fifth Quiz (solutions)
Due 23 Sep 2013
Note: please show your work on this sheet.
1. (a) Find the inner product of x and x3 2x on the interval [1, 1].
1
x5 2x3
x(x 2x) dx =
Ans: (x, x 2x) =
5
3
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Third Quiz (solutions)
Due 11 Sep 2013
1. For each of the following Cauchy-Euler equations, write down the general solution for
the interval (0, ).
(a) x2 y + 2xy 2y = 0
Ans: m(m 1) + 2m 2 = 0 h
MATH 3423 Advanced Applied Math
NAME:
(Please print clearly)
Final Exam (solutions)
16 Dec 2013
1. Find the general solution of the following Cauchy-Euler equations on the interval (0, ):
(a) x2 y + xy 4y = 0.
Ans: m(m 1) + m 4 = m2 4 = 0 has two roots m
MATH 3423 Advanced Applied Math
NAME:
(Please print clearly)
Third Exam (solutions)
11 Dec 2013
1. The following boundary value problem represents steady state heat distribution in a
quarter disk. Solve it for u(r, ) in the form of an innite sum with term
MATH 3423 Advanced Applied Math
NAME:
(Please print clearly)
Second Exam (solutions)
4 Nov 2013
1. For the following Sturm-Liouville problem: y + y = 0, y (0) = 0, y (3) = 0, nd
the eigenvalues and eigenfunctions. Note: there are no negative eigenvalues;
MATH 3423 Advanced Applied Math
NAME:
(Please print clearly)
First Exam
30 Sep 2013
1. Find the general solution of the following Cauchy-Euler equations on the interval (0, ):
(a) 4x2 y + y = 0.
Ans: 4m(m 1) + 1 = 4m2 4m + 1 = 0 has a double root m = 1/2.
Math 3423 Advanced Applied Math
NAME:
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Eighth Quiz (solutions)
Due 23 Oct 2013
1. Using separation of variables, nd all product solutions u of the partial dierential equation below. Note: The ODEs you get should be rst order and ther
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Sixth Quiz (solutions)
Due 27 Sep 2013
Note: please show your work on this sheet.
1. For each of the following functions, simply write whether it is even or odd or neither (no
need to show any w
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Second Quiz (solutions)
06 Sep 2013
Note: You are not required to simplify algebraic or numeric expressions.
1. For the initial value problem y + xy + 2y = 0, y (0) = 2, y (0) = 1, answer the
fo
Math 3423 Advanced Applied Math
NAME:
(Please print clearly)
Fourth Quiz (solutions)
16 Sep 2013
1. For the following dierential equation: x2 y + (x 2)y = 0, assume a solution of the
form y =
cn xn+r (i.e., use the Frobenius method) and do the following
n