{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chem Differential Eq HW Solutions Fall 2011 52

# Chem Differential Eq HW Solutions Fall 2011 52 - 52 Chapter...

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

52 Chapter 3 Partial Differential Equations in Rectangular Coordinates Solutions to Exercises 3.10 1. We use a combination of solutions from (2) and (3) and try a solution of the form u ( x, y ) = n =1 sin mx A m cosh m (1 - y ) + B m sinh my . (If you have tried a different form of the solution, you can still do the prob- lem, but your answer may look different from the one derived here. The reason for our choice is to simplify the computations that follow.) The boundary conditions on the vertical sides are clearly satisfied. We now determine A m and B m so as to satisfy the conditions on the other sides. Starting with u (1 , 0) = 100, we find that 100 = m =1 A m cosh m sin mx. Thus A m cosh m is the sine Fourier coefficient of the function f ( x ) = 100. Hence A m cosh m = 2 π π 0 100 sin mx dx A m = 200 πm cosh m [1 - ( - 1) m ] . Using the boundary condition u y ( x, 1) = 0, we find 0 = m =1 sin
This is the end of the preview. Sign up to access the rest of the 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