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Math ยท Advanced Math
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Solve one of the following problems. CIRCLE the letter of the problem you want to grade. A. Use Fourier transform methods to find a solution to ๐’–๐’™๐’™+๐’–๐’š๐’š= ๐ŸŽ ๐’‡๐’๐’“ -โˆž<๐’™<โˆž ,๐ŸŽ<๐’š<โˆž, Which satisfies ๐’–(๐’™,๐ŸŽ)={๐Ÿ ๐’Š๐’‡ |๐’™|<๐Ÿ๐ŸŽ ๐’๐’•๐’‰๐’†๐’“๐’˜๐’Š๐’”๐’† and ๐ฅ๐ข๐ฆ๐’šโ†’โˆž๐’–(๐’™,๐’š)=๐ŸŽ ๐’‡๐’๐’“ ๐’†๐’‚๐’„๐’‰ ๐’™ ๐’Š๐’ (โˆ’โˆž,โˆž). B. Use Fourier transform methods to find a formula for the solution to: ๐’–๐’•โˆ’๐’–๐’™๐’™= ๐’‡(๐’™,๐’•) ๐’Š๐’‡ -โˆž<๐’™<โˆž ,๐ŸŽ<๐’•<โˆž. ๐’–(๐’™,๐ŸŽ)=โˆ…(๐’™) ๐’Š๐’‡ -โˆž<๐’™<โˆž

Question 7 (20 marks) Solve one of the following problems. CIRCLE the letter of the problem you want to grade. A. Use Fourier transform methods to find a solution to uxx + uyy-0 for-oo < x < oo ,0 < u(x, 0)- i1 0 Which satisfies otherwise and lim u(x,y) - 0 for each x in (-0, 0o). B. Use Fourier transform methods to find a formula for the solution to: ut-uxx = f(x, t) if- o < x < 0 ,0 < t < 0.

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