Question

using the linearity property and a linear operator, justify if this PDE is linear or not.

u_{t}+u(u_{x})=0

Answer #1

(PDE)
WRITE down the solutions to the ff initial boundary problem for
wave equation in the form of Fourier series :
1. Utt = Uxx ; u( t,0) = u(t,phi) = 0 ; u(0,x)=1 , Ut( (0,x) =
0
2. Utt = 4Uxx ; u( t,0) = u(t,1) = 0 ; u(0,x)=x , Ut( (0,x) =
-x

Partial differential equations
Solve using the method of characteristics
ut +1/2 ux + 3/2 vx = 0 , u(x,0) =cos(2x)
vt + 3/2 ux + 1/2 vx = 0 , v(x,0) = sin(2x)

(PDE
Use the method of separation of variables and Fourier series to
solve where m is a real constant
And boundary value prob. Of Klein Gordon eqtn.
Given :
Utt - C^2 Uxx + m^2 U = 0 ,for 0 less than x less pi , t greater
than 0
U (0,t) = u (pi,t) =0 for t greater than 0
U (x,0) = f (x) , Ut (x,0)= g (x) for 0 less than x less than
pj

(PDE)
Solve the ff boundary value problems using Laplace Equationnon
the square , omega= { o<x<phi, 0< y <phi}:
u(x,0) =0, u(x,phi) = 0 ; u(0,y)= siny , u(phi,y) =0

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < pi,
t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sin2x - sin3x,
ut(x,0) = 0

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < pi,
t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinxcosx,
ut(x,0) = x(pi - x)

Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < L, t
> 0, u(0,t) = 0 = u(L,t), u(x,0) = x(L - x)2,
ut(x,0) = 0

Find the general solution of uxx − 3uxy +
2uyy = 0 using the the method of characteristics: let v
= y + 2x and w = y + x; define U(v, w) to be U(v, w) = U(y + 2x, y
+ x) = u(x, y); derive and solve a PDE for U(v, w); convert back to
u(x, y).

True or False. JUSTIFY YOUR ANSWER.
The 95% Confidence Interval is constructed using exclusively the
estimated parameter estimates of the Linear Regression Model.

Solving Systems of Linear Equations Using Linear
Transformations
In problems 2 and 5 find a basis for the solution set of the
homogeneous linear systems.
2. ?1 + ?2 + ?3 = 0
?1 − ?2 − ?3 = 0
5. ?1 + 2?2 − 2?3 + ?4 = 0
?1 − 2?2 + 2?3 + ?4 = 0.
So I'm in a Linear Algebra class at the moment, and the
professor wants us to work through our homework using...

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