tailieunhanh - Handbook of mathematics for engineers and scienteists part 172

Handbook of mathematics for engineers and scienteists part 172. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | . Tables of Inverse Laplace Transforms 1165 No. Laplace transform f p 14 f P p a 2 b2 15 -1 f P n 1 2 . pn 16 fl P f2 P 17 Vpf P 18 f 1 pVP p 19 pn T K p 20 73 73 I 21 p p 1 22 p f p p 4 v -o 23 f jp 24 f vp 25 ft jp 26 f Jp2 a2 27 f Jp2 - a2 28 f Jp2 a2 y p2 a2 29 f Jp2 - a2 y p2 - a2 30 f J p a 2 - b2 31 J ln p 32 1 J ln p p 33 f p - ia f p ia i2 -1 34 i f p - ia - f p ia i2 -1 1 A c io . Inverse transform f x - - epx f p dp ni J c-io i J e a x sin b x - t f t dt X x-t n- 1f t dt n- 1 Jo_ I f1 t f2 x-t dt Jo ro cos 2Vxt ----V- f t dt Jo yjnx f sin 2jxt f t dt Jo Vnt I x t V J2v iJTt f t dt Jo I Jo f t dt Jo Jo 2jxt-t2 f t dt Jo rx x v nt axt - at2 f t dt 0 oc t2 exp - 4XJf t dt oo 2 x t t2 7---OL2 exp Tf-------77 f t dt x -1 3 2 L 4 x -1 J f x - a f Vx2 -t2 Ji at dt Jo f x a f f Vx2 -t2 l1 at dt 0 x Jo aVx2 -t2 f t dt 0 Io ajx2 -12 f t dt Jo e ax f x be ax 1 f Vx2 -12 I1 bt dt Jo r - P 1 Jo W f t dt Jo r t fo xf Jo f t dt 2f x cos ax 2f x sin ax 1166 Integral Transforms No. 35 Laplace transform f p df p dp 1 c i Inverse transform f x - - epx f p dp 2ni J c-ioo - xf x 36 dn f p dpn -x nf x 37 n dmf p . p m n dpm -l T xmf x dxn L J 38 f . f q dq J p - f x x 39 1 f PT - f q dq p Jo i M dt Jx t 40 i r - f q dq p Jp 1 x ft dt Jo t . Expressions with Rational Functions No. 1 Laplace transform f p 1 p 1 c i Inverse transform f x - 7 epx f p dp 2ni J c-ioo 1 2 1 p a -ax e 3 1 p2 x 4 1 p p a 1 1 - e-ax a v 7 5 1 p a 2 -ax xe 6 p p a 2 1 - ax e-ax 7 1 p2 - a2 sinh ax a 8 p p2 - a2 cosh ax 9 1 p a p b 1 e bx e ax a - by 10 p p a p b -L- ae-ax - be-bx a - b v 11 1 p2 a2 sin ax a 12 p p2 a2 cos ax 13 1 p b 2 a2 e bx sin ax a 14 p p b 2 a2 e bx cos ax - sin ax L a J . Tables of Inverse Laplace Transforms 1167 No. 15 Laplace transform f p P3 1 c i . Inverse transform f x - - epx f p dp 2ni J c-i 1 2 2 X 16 1 p2 p a e ax ax - 1 a2 v 17 1 P P a p b hi h a b be ae ab a - b v 7 18 1 p p a 2 4 1 - e-ax - axe-ax a2 v 7 19 1 c - b e-ax a - c e-bx b -