x(t+2) = x(t+1) . x(t) , t >=0
Solve a transformed version of the difference equation....
x(t+2) = x(t+1) . x(t) , t >=0
Solve a transformed version of the difference equation. Think of
a transformation that takes multiplication to addition, apply this
transformation to above ewn, and solve the transformed system.
We are given x(0) = 1 and x(1) = 1
Choose C so that y(t) = −1/(t + C) is a solution to the initial
value...
Choose C so that y(t) = −1/(t + C) is a solution to the initial
value problem
y' = y2 y(2) = 3.
Verify that the given formula is a solution to the initial value
problem.
x′ = −y, y′ = x, x(0) = 1, y(0) = 0: x(t) = cost, y(t) = sin
t
Consider the recurrence relation T(1) = 0, T(n) = 25T(n/5) +
5n.
(a) Use the Master...
Consider the recurrence relation T(1) = 0, T(n) = 25T(n/5) +
5n.
(a) Use the Master Theorem to find the order of magnitude of
T(n)
(b) Use any of the various tools from class to find a closed-form
formula for T(n), i.e. exactly solve the recurrence.
(c) Verify your solution for n = 5 and n = 25.
Find the (real-valued) general solution to the system of ODEs
given by:
X’=[{-1,-1},{2,-3}]X (X is a...
Find the (real-valued) general solution to the system of ODEs
given by:
X’=[{-1,-1},{2,-3}]X (X is a vector)
-1,-1, is the 1st row of the matrix
2,-3, is the 2nd row of the matrix.
Then, determine whether the equilibrium solution x1(t) = 0,
x2(t) = 0 is stable, a saddle, or unstable.
Solve the following initial/boundary value problem:
∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π,
u(t,0)=u(t,π)=0 for t>0,
u(0,x)=sin^2x...
Solve the following initial/boundary value problem:
∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π,
u(t,0)=u(t,π)=0 for t>0,
u(0,x)=sin^2x for 0≤x≤ π.
if you like, you can use/cite the solution of Fourier sine
series of sin^2(x) on [0,pi] = 1/4-(1/4)cos(2x)
please show all steps and work clearly so I can follow your
logic and learn to solve similar ones myself.
Consider the wave function at t = 0, ψ(x, 0) = C sin(3πx/2)
cos(πx/2) on the...
Consider the wave function at t = 0, ψ(x, 0) = C sin(3πx/2)
cos(πx/2) on the interval 0 ≤ x ≤ 1.
(1) What is the normalization constant, C?
(2) Express ψ(x,0) as a linear combination of the eigenstates of
the infinite square well on the interval, 0 < x < 1. (You
will only need two terms.)
(3) The energies of the eigenstates are En =
h̄2π2n2/(2m) for a = 1. What is
ψ(x, t)?
(4) Compute the expectation...
Find the absolute extrema of the function on the closed
interval
f(x)= 1 - | t...
Find the absolute extrema of the function on the closed
interval
f(x)= 1 - | t -1|, [-7, 4]
minimum =
maximim =
f(x)= x^3 - (3/2)x^2, [-3, 2]
minimim =
maximim =
f(x)= 7-x, [-5, 5]
minimim =
maximim =
Determine how the following lines interact.
(x, y, z) = (-2, 1, 3) + t(1, -1,...
Determine how the following lines interact.
(x, y, z) = (-2, 1, 3) + t(1, -1, 5) ; (x, y, z) =
(-3, 0, 2) + s(-1, 2, -3)
(x, y, z) = (1, 2, 0) + t(1, 1, -1) ; (x, y, z) =
(3, 4, -1) + s(2, 2, -2)
x = 2 + t, y = -1 + 2t, z = -1 – t ; x = -1 - 2s,
y = -1 -1s, z = 1...