Question 4 Consider the polar coordinates change of variables: -rcos,y= rsin 0 Consider u = u(x,y)....
The result of transforming the equation r2 = 8 rcos( 0) + 3 rsin( e) from polar to rectangular coordinates is: A. 2 2 = 8x + 3y Yx +y B. 2 X +y = 3x + 8y C. Vz? + y2 = 11 D. none of the preceding E. 2 x + y = 8x + 3y
14 points Consider the following equation : PDE: u+ 0 ,0<x <1, 0<y <1 BCs: u(0, y)= 0, u (1, y ) = 0 ,0<y <1 ICs: u (x,0)=0, u (x,1)=2 ,0<x <1 a) Using the PDE and the boundary conditions write the form of the solution u (x ,t) b) Now apply the initial condition to solve for the unknown coefficients in the solution from part (a)
14 points Consider the following equation : PDE: u+ 0 ,0
matlab code please
0 solutions submitted (max Unlimited) Problem2 A staircase of height h is modeled by the parametric equations: x = rcos(1) y = rsin(1) -=- trix where r=h[2 + 5 sin(1/8)]/10, n=4, and h 50m is the staircase height. Make a 3-D plot (shown) of the staircase. (Create a vector , for the domain 0 to 2π and use the pi1ot3 command.) so so nd ion Your Script em of 11% iength of vector t is 40e, use,...
13. Consider the random variables X and Y with the following expectations: E(X)= 2, E(Y)=1 E(X²)=15, E(Y2)=9, E(XY)=1. Let U = X + 2Y, V = 3X - Y and calculate the covariance of U and V.
Consider the nonlinear plane autonomous system satisfying the initial condition (x(0), y(0)) = (-2,0). (a) Change to polar coordinates and find the solution r(t) and θ(t) of the system. (b) As t goes to infinity (x(t),y(t)) will follow the circle trajectory. Find the radius and period of the circle trajectory. (limit behavior of the solution (a))
Consider the nonlinear plane autonomous system satisfying the initial condition (x(0), y(0)) = (-2,0). (a) Change to polar coordinates and find the solution r(t)...
My professor said " Hint: Use
change of variables formula u= xy, v= x^2 - y^2"
31. Consider the triple integral II w 2x dv, where W is the solid three-dimensional region bounded by the surfaces z = x2 + y2, z = 2(x2 + y2), and z = 1. Express it as an iterated integral in cylindrical coordinates. Do not evaluate it.
9. Consider the beam PDE for the transverse deflection u(x, t) of an elastic beam Utt + Kurz = 0 for 0 < x <L (30) where K > 0 is a constant. Suppose the boundary conditions are given by (31) u(0, t) = uz(0,t) = 0 Uwx (L, t) = Uzzz(L, t) = 0 (32) and the initial conditions are (33) u(x,0) = (x) u1(x,0) = V(x) (34) Use separation of variables to find the general solution to the...
Consider a real-valued function u(x, y), where x and y are real variables. For each way of defining u(x, y) below, determine whether there exists a real-valued function v(x, y) such that f(z) = u(x, y) + iv(x, y) is a function analytic in some domain D C C. If such a v(x, y) exists, find one such and determine the domain of analyticity D for f(z). If such a v(x, y) does not exist, prove that it does not...
Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice for integrating over disks. Once we choose a coordinate system we must figure out the area form (dA) for that system. For example, when switching from rectangular to polar coordinates we must change the form of the area element from drdy to rdrd0. To determine that rdrde is the correct formula how the edges of...
# 1: Consider the following curves in R la) 1822-32 x y + 37 U2 100. l ) 2x2 + 6 x y + 2 y-100. 1c) x2 + 4 x y + 4 y2-10:0. Write them in normal form. Give the change of variables that does this. For example, in 1a) the orthonormal basis of eigenvectors are λί 5,V1 (2,1)'/V5 and λ2 = St ( 100. ) . That is, 45, ½ = (1,-2)t/V5.S ( 1/V 5-2/v/5 ) (V6,...