. Consider a Bessel ODE of the form:
x^2y"+xy'+(x^2-1)y=0
What is the general solution to this ODE assuming that the
domain of the problem includes x=0? Why?
Find the solution to the heat equation on 0 < x < l,
with u(0, t) = 0, ux(l, t) = 0, and u(x, 0) =
phi(x).
This is sometimes called a "mixed" boundary condition.
Graph the production functions below. Q= 6L−1/4L2 , L ≥ 8
Q= 1/4L2 + 2L, 0 < L < 8
a. Graph the marginal product and average product curves.
b. Find the maximum attainable production. How much labor is used at that level?
c. Identify the ranges over which the marginal product is increasing and decreasing.
d. Identify the range over which the marginal product of labor is negative. e. Identify the ranges over which the average product of labor is...
1. Prove by contraction that
L = {0^x 1^y 0^x+y | x >= 1 and y
>=1} is not Regular.
Must use the Pumping Lemma.
[ HINT: Describe the language in English first. Use
example 3 from the lecture notes ]
a) Choose one S from L where
S is longer than N
(Describe S in
terms of N and M)
S = **??**
b) List all places v can be in
S: (i.e. all possible...
Consider the following first-order ODE dy/dx=x^2/y from x = 0 to
x = 2.4 with y(0) = 2. (a) solving with Euler’s explicit method
using h = 0.6 (b) solving with midpoint method using h = 0.6 (c)
solving with classical fourth-order Runge-Kutta method using h =
0.6. Plot the x-y curve according to your solution for both (a) and
(b).