TRTIONG DHSP TP.. Hdy tim c6c thenh phdn hiQp bii5n cria n6 trong h€ tga ctQ trU.. Biri 4: Dinh nghia mQt dai si5 Lie tr6n trudrng si5 thyc.. Ghi chli: - Sinh vi6n khdng tlugc sfr dgng t
Trang 1TRTIONG DHSP TP HCM
KHoA vAr rY
Kd'L
Hecphan,uil#
Hqc lcj' 2, ndm hgc 2006 - 2007
Lop Cft nh6n vqt lf
Thdi gian: 90 phirt
OC ttri ft'n 2
Bii 1: Ding kii5n thirc hinh hgc ve dulng vd mflt bQc Z,hdy gi6i thich tqi sao
trong thgc t6 nguoi ta ph6ng theo m{t paraboloid trdn xoay dO chiS tpo
Sngten thu ph6t s6ng thay vi ph6ng theo c6c m{t cong bdc2 kh6c
Biri 2:
he s6 Lame vi thOng sd vi phdn hang nh6t ctia h0 tqa dQ cong ndy
b) Tenxo hiQp bi6n c6 c6c thenh phdn xlz,Ut yz + zx,x+ y+ z trong hQ tga
dQ vu6ng g6c Hdy tim c6c thenh phdn hiQp bii5n cria n6 trong h€ tga
ctQ trU.
Bni 3: Tinh ma trQn exponent ' cta ma tr1n a=(o^ (o ll, b)' (c , =[o l) o) r,i r.et
qua niry suy ra dpi si5 Lie cria nhom Lie ma tran SO(2,R)
Biri 4: Dinh nghia mQt dai si5 Lie tr6n trudrng si5 thyc MO t6 dai sO Lie cria c6c nh6m Lie ma trfln GL(n, R) vd SL(n, R)
Ghi chli: - Sinh vi6n khdng tlugc sfr dgng tii li$u