Exercise 4.3.2. Given the BVP-u' =f(x), u(0) = a, u'(1) = b 0 < x <...
4.3.2 Find the Fourier transforms (with f= 0 outside the ranges given) of (a) f(x)= 1 for 0 < x <L (b) f(x)= 1 for x < 0 (c) f(x)= So eikx dk (d) the finite wave train f(x)=sin x for 0<x< 107
4.3.2 The cumulative distribution func- tion of random variable X is 0 r<-1, Fx (x) = (z + 1)2-1 x < 1, r1 Find the PDF fx(a) of X
Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0 < t < oo 0 IC: u(z,0)= sin(nx)+x, 1 x by transforming it into homogeneous BCs and then solving the transformed problem Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0
p5:01 24% 10: 13.5K/s OUMNIAH Aransform the following BVP un = 4 Uxx 0<x<1, t>O u(0, t)=1 u(1, t)=2 into new one with homogeneous BCs produces 0<x<1, t> 0 a. wų = 4 Wxx -1, w(0, t) = 0 w(1, t)=0 0<x<1, t> 0 b. wy = 4 Wxx +x-1, w(0, t)=0 w(1, t)=0 0<x<1, t> 0 . C. Wy = 4 Wxx -x, w(0, t)=0 w(1, t)=0 d. W4 = 4 Wxx 0<x<1, t> p 5:01 -25%. OOK/S OUMNIAH...
Exercise 9. Solve the BVP a(0, t) = 0 u(r, t)-Uz(n, t) = 0 u(z, 0) = sin z 0<x<π, t>0, t >0 t > 0 (z,0) = 0 2
solve problem #1 depending on the given information Consider the following 1D second order elliptic equation with Dirichlet boundary conditions du(x) (c(x)du ) = f(x) (a $15 b), u(a) = ga, u(b) = gb dr: where u(x) is the unknown function, ga and gb are the Dirichlet boundary values, c(x) is a given coefficient function and f(x) is a given source function. See the theorem 10.1 in the textbook for the existence and uniqueness of the solution. 1.1 Weak Formulation...
= 0 over the domains 0<x<1 and t>0, where x is space and t is time at ax ди (1,1) = 0 ax Dirichlet and Neumann BCs are u(0, t)=80; Find the solution of the PDE that satisfies the given IC and BCs a. IC: u(x,0) 25sin (nx)
JO SUUS. 7.12. Solve the BVP y" = -2e-3y + 4(1+x)-3, 0<x<1, subject to y(0) = 0, y' (O) = 1, y(1) = In 2. Compare to the exact solution, y(x) = ln(1+x).
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
Using Integration Factor method to solve General b) Find Green's function for the BVP y(4) = -f, 0<x< 1, y(0) = y'(0) = y(1) = y'(1) = 0. u(n) = axu(k-1) +g(t) k=1 lo U(t) = U(0)U1(t) +Ư (0)U2(t) + ... +Un-1)(0)Un(t) +| Unt – TÌq(T)dx U (0) = 0 U (0) = 0 Tkk-2)(0) = 0 vlk-1)(0) = 1 - (0) = 0 Un-1)(0) = 0