tailieunhanh - Handbook of mathematics for engineers and scienteists part 171

Handbook of mathematics for engineers and scienteists part 171. 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. | 1158 Integral Transforms No. Original function f x f Laplace transform f p e px f x dx Jo 18 xmf n x m n - f 19 j- xm f x m n dxn L J dm -1 mp - f P dpm 20 r f t dt Jo f P P 21 1 x - t f t dt Jo 2 f P pl 22 f x - t v f t dt v -1 Jo r v 1 p-v-17 p 23 f e-a t dt Jo f p p a 24 f sinh a x -1 f t dt Jo af p p2 - a2 25 sin a x - t f t dt Jo af p p2 a2 26 1 fl t fz x -1 dt Jo 71 p 2 p 27 r i Jo fdt 1 f ST - f q dq p J p 28 1 Z tf t dt 1 fp - f q dq p J o 29 1 sin 2y xt f t dt Jo Vt f 1 pVp p 30 1 f cos 2 xt f t dt Vx J o Vf p 31 f 1 t2 expi-y f t dt Jo y m V 4x Vp7 vp 32 r x- t t2 f . t dt f Vp 33 f x - a i f Vx2 -t2 J1 at dt Jo f p2 a2 34 f x a i f Vx2 -12 i at dt Jo Z Vp2 - a2 . Tables of Laplace Transforms 1159 . Expressions with Power-Law Functions No. 1 Original function f x 1 A OO Laplace transform f p e px f x dx Jo 1 p 2 0 if 0 x a 1 if a x b I 0 if b x 1 e-ap - e-bp p 7 3 x _1_ p2 4 1 x a - eap Ei -ap 5 xn n 1 2 . n pn 1 6 xn-1 2 n 1 2 . 1 X 3 X . X 2n 1 n 2npn 1 2 7 1 y x a neap erfc aP 8 jx x a - Kyjaeap erfc ap 9 x a 3 2 2arx 2 - 2 np 1 2eap erfc ap 10 x1 2 x a -1 n p 1 2 - nal 2eap erfc ap 11 x 1 2 x a -1 na 1 2eap erfc ap 12 xv V -1 T v 1 p v 1 13 x a v v -1 e-apr v 1 ap 14 xv x a -1 v -1 keapr -v ap k avT v 1 15 x2 2ax 1 2 x a aeap K1 ap . Expressions with Exponential Functions No. Original function f x AO Laplace transform f p e px f x dx 70 1 -ax e p a -1 2 -ax xe p ay2 3 xv-1e-ax v 0 T v p a -v 4 1 -ax -bx x e -e ln p b - ln p a 5 x 1 - e 2 p 2a ln p 2a p ln p - 2 p a ln p a 6 exp -ax2 a 0 nb 1 2 exp bp2 erfc pvb a 4- 7 xexp -ax2 2b - 2n1 2b3 2p erfc pVb a 4b 1160 Integral Transforms No. Original function f x - Laplace transform f p e px f x dx 70 8 exp -a x a 0 2y pK 2ựap 9 y x exp -a x a 0 2 vn p3 1 2ựap exp -2ựap 10 L exp -a x a 0 yjx n p exp -2ựap 11 - exp -a x a 0 Xy x ựn a exp -2ựap 12 xv exp -a x a 0 2 a p v Kv 2-ựâp 13 exp -2yfax p1 In. 1 2p3 2ea p erfc a p 14 - exp -2 ựãx n p 1 2eaap erfc a p . Expressions with .