tailieunhanh - Ebook Advanced engineering mathematics (2nd edition): Part 1

Equally as effective as either a textbook or reference manual, it approaches mathematical concepts from an engineering perspective, making physical applications more vivid and substantial. Its comprehensive instructional framework supports a conversational, down-to-earth narrative style, offering easy accessibility and frequent opportunities for application and reinforcement. | SECOND EDITION ADVANCED ENGINEERING MATHEMATICS Michael D. Greenberg SELECTED FORMULAS FIRST-ORDER LINEAR y p x y q x . General solution If y a b. p o b LEGENDRE EQUATION 1 - x2 y - 2xy Xy 0 Bounded solutions p x on 1 X 1 if A n n 1 Il 0 1 2 . BESSEL EQUATION x 2y xy x2 - id2 y 0 General solution y x AJ x BY x CH x DHi x MODIFIED BESSEL EQUATION x2y xy1 -X2 - I 2 y 0 General solution y i AI x BKịẶx REDUCIBLE TO A BESSEL EQUATION -ị- I x Ệ- bxcy 0 ax dx J Solution where Zi yi i denotes J c a 2 Ị and Ạ ị if b 0. and and Kị ị if b 0 L -c 1 a - a 2 MATRICES A 1 ự adịA. AB - B- A 1 ATp1 A 1 T detA CARTESIAN COORDINATES Il u x y V i .ri t- yj t k R xi t j ck. i R dxi rf j dzk f dy dz constant- surface dxdz constant- surface . dV dx dy dz dx dy constant-. surface d - d d A du du- du v 4 -Ĩ7C k4f 11 44 GGi GTk ƠX Jy Jz J Jx Jy JZ d2u 2U 2 u V u -f- 4- dx Uy- z 4 ậl ậG dx Oy z . l íXl cQ . V i A ƠI dip . A . V X V -X 1 1 i ---Z- ------- k dy dz j dx z dx dy J AB i d dĩ -Zi r B 1 A1 j k 0 Ỡ dy dz CYLINDRICAL COORDINATES u u r 0 z V v .êr voê vzè. X r cos y r sin 0 z z R rèr - - zêz f R drèr rdOèg dzêz r do dz constant-r surface dA dr dz constant-ớ surface dV r dr do dz 1 r dr do constant-2 surface dêr dô dêỹ _ fiio êr du V U dr 1 di r r dt 1. du . zfio J dz d2u fi u XX dr2 1 du r dr 1 fill d 2u fid fi fi2 1 d lỡ d V v 0Z rL r z 3 v ãT v- r dr r do dz i1 dvz dvn . dvr dvz 1 í d ri ị dvr V X V r do dz er - -tF ẻơ 1 1 az ar J r dr do J SPHERICAL COORDINATES u tt p p 0 V Vpèp Uệêộ V èg X psin p cos ớ y psin ọLsinớ z pcosip R pèp iZR dpef - 1- pdộêộ psmfi dQêo p1 sill p d b do IA p sin dpdO pdp d b constant-p surface constant- surface dV p2 sin dp d. p dỡ constant-ỡ surface 2Ĩ 0. Ỡp ẼỀỈ 0 Ỡp - ỡêp i i 27 77 sin ệ èo dip do dè Ị dêrỊ 777 77 cosạ êfl dip do fi 0. Ỡp dè0 n dèo 77 0 77 - sin e cos e dd do _ du . 1 du 1 d u V u 7 ep 7T7 e b . 77 . 777 eơ dp p dip pstn do 1 r d du 1 di. du V u p 77- .7 777 sin p- dp dp J sin dip dtp 1 fill sin p do2 1 d A t 1 V V p2 Up . r - p- up

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