Foolproof: A Sampling
of Mathematical Folk
Humor
Paul Renteln and Alan Dundes
I
n the discipline known as folkloristics [D1] (the
study of folklore), a folk is defined as any
group whatsoever that shares at least one
common linking factor. The factor coul
Math 674
Assignment #12
Due November 28, 2012
Reading: 3.4, 3.5 [Skipping 3.3]
1. Use a perturbation series x = a0 + a1 + a2
2
+ O( 3 ) to solve the equation
x3 (4 + )x + 2 = 0
= 103 .
to order 2. Estimate the error for
2. What is the expression for a dip
Math 674
Assignment #9
Due October 31, 2012
Reading: 2.5, 2.6
1. 2.4.1.a
2. 2.4.1.b [Warning: I found some typos in the problem in my printing of the book.]
3. 2.4.2. Recall that the principal moments of inertia A, B , C are the eigenvalues of the tensor
Math 674
Assignment #8
Due October 24, 2012
Reading: No new reading.
1. 2.3.3.a
2. 2.3.3.b. For simplicity, only consider the case where n is even.
3. 2.3.5
4. Legendres dierential equation is
(1 x2 )y 2xy + n(n + 1)y = 0.
Use the method of Frobenius to s
Math 674
Assignment #7
Due October 17, 2012
Reading: As assigned in class.
Dont forget the older problems- Question 3 from Homework 5 is still due!
1. 2.3.2
Math 674
Assignment #6
Due October 10, 2012
Read: 2.3 (Pages 74-82.)
1. Use conformal mappings to solve the problem
and u = 1 on x = 0.
u=1
u = 0 in the rst quadrant, with u = 0 on y = 0
u=0
u=0
Hint: Consider = ln z .
2. Use conformal mappings to solve t
Math 674
Assignment #5
Due October 3, 2012
Read: 2.1 and 2.2 (Pages 61-71.)
1. Prove that the operator u u in Rn is rotationally symmetric, that is if A is an n n
orthogonal matrix and if y = Ax, then
2
2
2 + + y 2
y1
n
u=
2
2
2 + + x2
x1
n
u
2. Prove tha
Math 674
Assignment #4
Due September 26, 2012
Read: 1.6 and 1.7 (Pages 44-58.)
1. 1.5.1
2. 1.5.2
3. 1.5.6.a
4. 1.5.6.b
5. 1.5.6.c [Equation (1.5.56) contains a typographical error, at least in my copy of the text.]
6. 1.5.6.d
Math 674
Assignment #2
Due September 12, 2012
Read: 1.5 (You can skip 1.5.3 if you did not take Integral Transforms last semester). pp. 32-44.
1. 1.4.3.a
2. 1.4.3.b
Hint:
What would happen if you showed that 1.4.54b satised 1.4.55(a-c)?
Integrate by par
Math 674
Assignment #2
Due September 12, 2012
Read: 1.4 (1.4.1 - 1.4.7). Pages 16-28.
1. 1.2.2 (p. 12). Provide a graph of your solution.
2. 1.3.2 a (p. 16)
3. 1.3.2 b (p. 16)
4. 1.3.3 (p. 16)
Math 674
Assignment #1
Due September 12, 2012
Read: 1.1, 1.2, (1.2.1, 1.2.2), 1.3. Pages 1-15.
1. Let Lu = u with boundary conditions u(0) = u(1) = 0. Find the eigenvalues and eigenfunctions for this operator. In particular, is an eigenvalue and u is a co
MATH 674
Applied Partial Differential Equations
Class Policies
Mike OLeary
Ofce: YR 307A
Ofce Phone: 410-704-4757
Email:[email protected]
Fall 2012
Class: W 5:30-8:10
Room: YR 121
Section: 101
Ofce Hours: Tu 1-2 and by appointment
Prerequisites: Prerequi