F10hw09

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Unformatted text preview: 1 Problem 5.13 ƒt—rting with equ—tion SFQP in t—™ksonX  I d rH ~ @~A a  ~ @~A Ar jr R V j~ ~Hj H rr I 0 3  0 a R  2 'H =0 0 1 ¢ d ! ~ H e ~ | {z r } H = 1 cos  !rH sin H 'H ^ I` ˆˆ a R !a `=0 m= ` I r< ` ` P` C I r > a  !a +1 ` R r< ` ` P` C I r > Y m£  H ; 'H Y`m ; ' +1 ` @ A @ 3 A  2 1 @™os HAd'HrH  Y m£  H ; 'H Y`m ; ' @ ` cos  H = 1  2  1 @ A Y`;m ; ' 'H =0 `=0 m= A H cos  = 1 A sin H'Hd@™os HAd'H ” @ Y`m£  H ; 'H @ A sin H'Hd@™os HAd'H ” @IA ƒin™e 'H a sin 'Hx C ™os 'HyD the integr—l ˜e™omesX ” ” ”  2 'H =0  1 cos  H = 1 Y`m£  H ; 'H @  r H2 d `=0 m= 'H =0 +1 I` ˆˆ 3 0  ` R r< ` ` P` C I r > 3 2 I` ˆˆ A @ sin H sin 'Hx C sin H ™os 'HyA d@™os HAd'H ” ”   q ¢ £ ‡e know th—t sin H sin 'H a sin  ei' e i' a i  Y @H; 'HA Y @H; 'HA —nd sin H ™os 'H a i  q¢ £ i' e i' sin  e a  Y @H; 'HA C Y @H; 'HA F fy exploiting orthogon—lityD the integr—l ˜e™omesX r ¡ ¡£ ¢ P    Y`m£ @ H ; 'H A i Y l @ H ; 'H A C Y @ H ; 'H A x C Y l @ H ; 'H A C Y @ H ; 'H A y ” ” Q 'H H d@™os  H Ad'H r ¡ ¡...
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