{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# WS07 - APPM 4/5350 Worksheet Week 7 Figure 1 www.xkcd.com 1...

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

APPM 4/5350 Worksheet Week 7 Figure 1: www.xkcd.com 1. What are the requirements to differentiate a Fourier sine series on [0 , L ] term by term? 2. What are the requirements to differentiate a Fourier series on [ - L, L ] term by term? 3. Draw a function that satisfies 2 u = 0 on [0 , a ] when u (0) = 0 and u ( a ) = 8 . 4. Draw a function that does not satisfy 2 u = 0 on [0 , a ] but does satisfy u (0) = 0 and u ( a ) = 8 . 5. What is the solution to 2 u = 0 in a circle of radius R with f ( R, θ ) = 0 ? 6. Draw the Fourier cosine and sine series, and their periodic extensions, of f ( x ) = x 2 on [0 , L ] 7. Prove that the solution to Laplace’s equation with f ( r, θ ) = g ( θ ) on the boundary is unique. 8. Explain why f ( x ) = g ( y ) x, y implies f ( x ) = c and g ( y ) = c where c is a constant. 9. Write down the coefficients that solve f ( x ) = n =0 a n φ n ( x ) if the set { φ n ( x ) } n =0 form an orthogonal basis for the space that contains f ( x ) . 10. Where would you need boundary conditions to solve 2 u = 0 inside the domain r [0 , R ] and θ [ π 4 , 7 π 4 ] 11. Where would you need boundary conditions to solve δu δt = k 2 u inside the domain x [0 , b ] and y [0 , ) 12. What is L ( c 1 u 1 + c 2 u 2 ) , given that L
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online