I am hoping with explanation to go with solving the problem, especially with regards to applying the boundary conditions correctly.
I am hoping with explanation to go with solving the problem, especially with regards to applying the boundary conditions...
Please give some insight on how to apply boundary conditions. This is really important for me to understand separation of variables and how/which terms are eliminated and why. Problem 2 Find the solution to V2 Y(r, e, ø) = 0 inside a sphere with the following boundary conditions: aw (1, e, ) sin20 cosp = ar Problem 2 Find the solution to V2 Y(r, e, ø) = 0 inside a sphere with the following boundary conditions: aw (1, e, )...
Find the solution to ∇2 Ψ(r, θ, φ) = 0 inside a sphere with the following boundary conditions: ∂Ψ (1,θ,φ)=sin2θcosφ.∂r Find the solution to V2(r, e, p) =0 inside a sphere with the following boundary conditions: ay (1, e, p) sin20 cosp. ar Find the solution to V2(r, e, p) =0 inside a sphere with the following boundary conditions: ay (1, e, p) sin20 cosp. ar
Find the solution to inside a sphere with the following boundary conditions applied to its three sides. Please give explanation. Find the solution to V24(r, e, ¢) = 0 inside a sphere with the following boundary conditions: (1, e, ) sin20 cosp ar
Do not worry about the plotting portion but I do want explanation throughout the problem in order for me to understand the methodology, especially in applying boundary conditions. Problem 1 grounded, but the end at r = a is held at The bottom and top of the of the wedge shown in the figure are V 5V. Usiing separation of variables find the potential everywhere inside the wedge by using separa- tion of variables, and plot it as a surface...
Question 3: BVP with periodic boundary conditions. Part I: Solve the following boundary value problem (BVP) where y(x,t) is defined for 0<x<. You must show all of your work (be sure to explore all possible eigenvalues). агу д?у 4 axat2 Subject to conditions: = y(x,0) = 4 sin 6x ayi at = 0 y(0) = 0 y(T) = 0 Solution: y(x, t) = Do your work on the next page. Part II: Follow up questions. You may answer these questions...
I having some trouble solving this boundary value problem. Thank you for your assistance. A thin wire coinciding with the x-axis on the interval [-L. L] is bent into the shape of a circle so that the ends x =-1 and x = L are joined. Under certain conditions, the temperature u(r, t) in the wire satisfies the boundary- value problem a au ot 11(-L. ) = u(Lt), t > 0 du ou .tso 11(x, 0) =fo), -L < x...
(4 points) This problem is concerned with solving an initial boundary value problem for the heat equation: u,(x, t)- uxx(x,), 0
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3) 0 Find the solution u using the expansion with the normalization conditions vn (0)-1, wn(0) 1 a. (3/10) Find the functionsw with index n1 b. (3/10) Find the functions vn with index n1 Un c. (4/10) Find the coefficients cn, with index n 1 Let u be...
Could you go through the steps in more detail? I am getting confused with the steps. Chapter 5. Function of Random Variables 14 Example 2. The probability density function of X is given by the Uniform distribution in (0, 1): 0 1 1 fx (x) otherwise Find the distribution of Y = eX Solution: Let Y = eX. Therefore, = P (e* < y) = P(X < logy) Fx(logy) Fy(y) P(Y logy logy = |x (r) dr - d logy...
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary conditions u(0,t1, t)- 0, and the initial condition 1--+ sin(z) u(z,0) = e solution u(z, t) by completing each of the following steps Find the equilibrium temperature distribution we r) Find th (b) Denote v, t)t) - ()Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x, t) Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary...