5. Solve Au=0, r>1, 0 < θ < 2π, u(1.0) = cos θ, 0 < θ < 2π. 5. Solve Au=0, r>1, 0
5. Solve Au=0, r>1, 0 < θ < 2π, a(1,0) cos θ, 0 < θ < 2π. 5. Solve Au=0, r>1, 0
All of them please if you can 6. Solve the Dirichlet problem 0<r<3 la(3.0) = 1-cos0+ 2 sin 20. θ < 2π 0 7. Solve the Dirichlet problem lu(3,0) = 3-2 sin θ + cos 20, θ 0 2π 8. Solve the Dirichlet problem a(3,0) 2 + sin 20, 0 θ<2π 6. Solve the Dirichlet problem 0
5. Solve u(a,8) = 0. Answer: u(r,θ)-2(d-r) 5. Solve u(a,8) = 0. Answer: u(r,θ)-2(d-r)
23. What values for θ(0 2π) satisfy the equation? θ 2 sin θ cos θ + cos θ 0
Problem 6. Describe the surface r(u, u)-R cos u x + R sin u ý + uz where 0 < u < 2π and 0 < u-H. and R and H are positive constants. What is the surface element and what is the total surface area? Show that Or/au, or/àv are continuous across the "cut at 2T coS W T
a) Use the d'Alembert solution to solve au au - <r< ,t> 0, at2 48,2 ux,0) = cos 3x, u(,0) = 21 b) Consider the heat equation диди 0<x<1, t > 0, at ax? with boundary conditions uz (0,t) = 0, uz(1,t) = 0, > 0, and initial conditions u(x,0) = { 0, 2.0, 0<r < 0.5, 0.5 <<1. Use the method of separation of variables to solve the equation.
Solve 2cos0+4 = -6cOs 6 on the interval 0<θ< Σπ. π π. 2π 0, π. 2π π3Τ 2 4
Use trigonometric identities to solve the equation 2sin(2θ)-2cos(θ)=0 exactly for 0≤θ≤2π. A.) What is 2sin(2θ) in terms of sin(θ)and cos(θ)? B.) After making the substitution from part 1, what is the common factor for the left side of the expression 2sin(2θ)-2cos(θ)=0 ? C.) Choose the correctly factored expression from below. a.) b.) c.) d.) We were unable to transcribe this imageAsin(e) cos(O) = 2cos(e) We were unable to transcribe this imageWe were unable to transcribe this image
Solve the equation for the interval [0, 2π). cos^2x + 2 cos x + 1 = 0 2 sin^2x = sin x cos x = sin x sec^2x - 2 = tan^2x
8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.