Differential Equations Lecture Work Solutions 127

# Differential Equations Lecture Work Solutions 127 - 2 u...

This preview shows page 1. Sign up to view the full content.

4.7 Laplace’s equation in a sphere Problems 1. Solve Laplace’s equation on the sphere u rr + 2 r u r + 1 r 2 u θθ + cot θ r 2 u θ + 1 r 2 sin 2 θ u ϕϕ = 0 , 0 r < a, 0 < θ < π, 0 < ϕ < 2 π, subject to the boundary condition u r ( a, θ, ϕ ) = f ( θ ) . 2. Solve Laplace’s equation on the half sphere u rr + 2 r u r + 1 r 2 u
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 u θθ + cot θ r 2 u θ + 1 r 2 sin 2 θ u ϕϕ = 0 , ≤ r < a, < θ < π, < ϕ < π, subject to the boundary conditions u ( a, θ, ϕ ) = f ( θ, ϕ ) , u ( r, θ, 0) = u ( r, θ, π ) = 0 . 127...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern