e0 cno DUc vA DAo TAo .a DAI HOC HUE Ho vd, ten thi sinh: 56 b6o danh: srNH sAU D4r HOC NAM 2OO7 thi: To5.n cho Vat li (dd,nh cho Cao hqc) g'ian ld,m bd,i,: 180 phrit KY ) THI TUYEN M6n Thdi CAU I. 1. XAc dinh c6c he s6 Lame trong hO toa d6 tru (p,g, r). Tri d6, divA'trong hO toa d6 tru (p,g, r). 2. Tinh luu s6 cria hb,m vecto: F - @ili + (br)i @,b 1d, hX,ng sd) doc theo dulng trbn b6,n kinh ft nXm trong mit phH,ng rOa, c6 tAm trtng vdi g6c toa d6. Nghiem lai dinh ly Stokes. ,\ 1 .J , t t ) trm bleu tnuc cua CAu II. GiAi Uai toan ' I t r1l, t>0, t)0, )r sin1z. 0<r<( (. CAu III. Mot thanh dbng chd,t, d6,t doc theo truc Or, c6 do ddi (., m1t chung quanh c6,ch nhiet, cA hai mrit tr:0,r - (. cria thanh duoc giu & nhiet d6 kh6ng. Bi6t phAn b6 nhi6t ban dhu cria thanh ducvc cho bdi u(r,o) : t"(na; "1, o ( n 1(. (c Id hing sd). Tim phAn b6 nhiet trong thanh. CAu IV. Tim hbm u(r,y) dibu ho), trong hinh trbn 12 + y2 < 1 vd, thoA man dibu ki6n tren bien 12 + A2 : 1 cria hinh trbn (cho trong toa d6 cqc) "l _ sin2e, (0S pS2r). lr:1 CAu V. Chfng minh rXng hh,m oo f +2k a2k*r I u(r,a,z,t): t I Lkr(r,a,z)6il+ Ak r(r,a,z)ffi), k:O L thoA m6,n phucrng trinh truybn s6ng 'tltt:11r, * uaa *'ltrzz, (rrArz, t) e Ra (r,,a,z) e R3 utt : u(0, t) - a2rtrr*, o ( u(!., t) : 0, u(r,0) - 0, ut(r,0) : vh, c5,c dibu kien ban dhu I u(r,g, 2,0) - r(r,U,,z), 1 r, (r,a, 2,0) - u(r,a, z), Ap dung, gidi bbi to6n ( "" - u*, * uaa l'ttzzt \ u(",U,2,0) - 12 - A2 + 2r' , L rr (r,a,2,0) - a3 * zz l rz l r Ghi chir: Cdn bo coi, thi, kh6ng gi,d,i thi'ch gi th€m * 1, (r,a,z) e IR3 . DUc vA DAo TAo .a DAI HOC HUE Ho vd, ten thi sinh: 56 b6o danh: srNH sAU D4r HOC NAM 2OO7 thi: To5.n cho Vat li (dd,nh cho Cao hqc) g'ian ld,m bd,i,: 180 phrit KY ) THI. Ra (r,,a,z) e R3 utt : u(0, t) - a2rtrr*, o ( u(!., t) : 0, u(r,0) - 0, ut(r,0) : vh, c5,c dibu kien ban dhu I u(r,g, 2,0) - r(r,U,,z), 1 r, (r,a, 2,0) - u(r,a, z), Ap dung, gidi. z), Ap dung, gidi bbi to6n ( "" - u*, * uaa l'ttzzt u(",U,2,0) - 12 - A2 + 2r' , L rr (r,a,2,0) - a3 * zz l rz l r Ghi chir: Cdn bo coi,