1540470959-Boundary_Value_Problems_and_Partial_Differential_Equations__Powers

488 Answers to Odd-Numbered Exercises 25(ui+ 1 − 2 ui+ui− 1 )− 25 ui=−25,i= 1 , 2 , 3 , 4 ,5;u 0 =2,u 5 +(u 6 − u 4 )/( 2 / 5 ) ...

Chapter 7 489 i m 01 2 3 4 0 00 0 0 0 1 0 1110 2 0 3 / 22 3 / 2 0 3 0 25 / 22 0 4 0 9 / 43 9 / 4 0 .. . ∞ 0 3430 t= 321. Rememb ...

490 Answers to Odd-Numbered Exercises 5. i tm m 01 2 3 4 0001 /21 1/ 20 0.177 1 0 1 / 23 / 41 / 2 0 0.354 2 0 3 / 81 / 43 / 8 0 ...

Chapter 7 491 Coordinates and values of the correspondingui are:( 1 / 7 , 1 / 7 ),5α; ( 2 / 7 , 1 / 7 ),10α;( 3 / 7 , 1 / 7 ),1 ...

492 Answers to Odd-Numbered Exercises u 2 (m+ 1 )=^1 2 u 1 (m)+^1 4 u 5 (m)−u 2 (m− 1 ), u 5 (m+ 1 )=u 2 (m)−u 5 (m− 1 ). m 012 ...

Chapter 7 493 Chapter 7 Miscellaneous Exercises ui+^1 −( ^2 uxi) 2 +ui−^1 − √ 24 xiui=0,i= 0 , 1 ,2, u 1 −u− 1 2 x =1,u^3 = ...

494 Answers to Odd-Numbered Exercises First Problem Second Problem ii m 0123401234 0 0111001110 1 0 2 / 31 2 / 3 001 / 32 / 31 / ...

Index A acoustic vibrations, 235 aluminum nitride, oxygen removal from, 156 antenna vibrations, 226 approximation by Fourier ser ...

496 Index characteristic equation, 3, 10 characteristics, method of, 246 classifications of partial differential equations, 280– ...

Index 497 finite Fourier series, 91–94 first-order equations homogeneous, 1–2 nonhomogeneous, 20–21 Fisher’s equation, 252 Fitzh ...

498 Index higher-order equations, homogeneous, 9–11 homogeneous boundary conditions, as requirement, 282 homogeneous linear equa ...

Index 499 mean value property, 278 periodic functions, 61 membrane displacement, 255.See also potential equation method of chara ...

500 Index potential equation, 255–285 in disk, 275–279 limitations of product method, 280–282 Poisson equation, 268–269 polynomi ...

Index 501 generalizations on, 184–187 insulated ends (example), 157–161 semi-infinite rods, 184–187, 193–197 wave equation, 218, ...

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