D ~ I HQC Q U ~ C GIA TPHCM

Dqi s6:

BE C u m G 6~ TAP TRU'&NG DqI HQC BACH KHOA

CHU'OFNG T ~ N H PFIEV

1. Phdp tinh ma t rb : Ma t r b vh chc phhep tinh tren ma t rb . Djnh thirc, Hgng c6a mot ma t rh , ma t r b nghich d b . He phuung trinh tuy&n tinh

2. Kh6ng gian vCctu, kh8ng gian vdcta con, tbng tqrc tikP clfa d c kh8ng gian vhectu con. He doc 14p tuy61-1 tinh, @p sinh, hmg cda mot he chc vtc tu. ~6 chi&, ca sir c h mot kh6ng gian vecta.

3. Anh xq tuy&n tinh, hnh, hgt nhh. Ma tr& c6a mot MI xq tuy&n tinh the0 cu sir Hwg c6a mot MI xg tuy6n tinh, d& thirc clfa mat ~I,I dbng chu. Kh6ng gian L(E,F), dqi sb L(E).

THI P& N G ~ H 2017 M ~ N : TOAN

1. Gih trj riCng, vdctu riCng, kh8ng gian riCng c6a mot ma t r b vu8ng v i c6a mot tg dbng cfru

2. Da thirc ctia mot tI,I dbng cdu hay ma tr@ w8ng, da thirc trigt ti&, Da thirc d@c trung.

3. Thu gQn (chCo h6a) chc ~I,I dbng d u v i chc ma tr$n vu6ng. Chc tiCu chuh chdo h6a duqc.

4. Tich v8 huhg, kh8ng gian c6 tich v8 h u h g (ti&n Hilbert), khdng gian Euclid, Tinh trgc giao. Cu s& tqrc giao, cu sir tqrc chub. Ty dbng cfru tqrc giao. Phdp chi& tqrc giao

5. Dwg song tuy&n tinh, dpng t o b phuung, bi&u thirc t~a-do c6a cClc dpng 66. 6. Thu gQn (chto h6a tqrc giao) chc ma t r b d6i xirng vh ~ I , I dbng chu dbi ximg. Djnh

19 cu b h v& chCo h6a tr(rc giao. Thu gQn dpng t o h phuung v& dpng chdo b h g chheo h6a tqrc giao.

Giiii tich:

1. Him vdctu n bi&n thgc: Gi5i hgn, su ii6n Qc, chc tinh chht, djnh 19 kep. 2. D p h h the0 huhg, DQO h h riCng, h h xq 16p C' tr&n mot t@p m&, vi p h h

clfa h h xq I@ c', ma tr4n Jacobi, djnh thirc Jacobi. 3. Anh xg c'-vi phai, Djnh 19 ctao ( h h nguqc) dja phuung, dho t o b cuc, h h h.

4. ~ n h xp 16p C?, CI;TC trj dia phumg, gih trj 1611 nhht hay b6 nhht cfia hhm nhi&u bi6n trbn t@p d6ng bj chi@.

5. Dwg vi p h h d h g (chinh xiic), dbng, djnh 19 Poincar6, Tich p h h d u h g ctia dwg vi phh .

6. Tich phfin kCp trbn t@p do duqc Jordan: Tinh chit* ,t, ngh'ia, vii chch tinh trong tga da Descartes, tga da cyc, ctjnh 19 Fubini.

7. Tich p h h bai ba: Tinh chh, c&h tinh trong @a @ Descartes, tga do tnp, t ~ a do chu.

8. Truhg vplc tu: Gradient, phi311 kf (Div), xohy (Rot), 9. Mat tham s8, y&u t6 dign tich m$t, tibp dign, t r u h g muc ti& phhp tuy&n. 10. Tich phiin mat, th6ng luqng, Iuu s6 cfia t r uhg vCc tu, c k djnh 19 cu b h : Green-

Riemann, Stokes, Gauss-Ostrogradskii vii img dwg 86 tinh luu s8, th8ng luqng.

Toiin 111:

1) Chu6i s8 thgc ho$c phirc: Chc ti8u chub hai tu (so shh , D'alambert, Cauchy, tich p h h , Leibnitz, Dirichlet, Abel), chu6i s8 hoi ty tuyet dbi, b h hai ty.

2) a) Dily h h , chu6i h i m mi& hai ty, hoi ty dibrn, hoi ty diu. b) Chu6i liiy thtra thgc, phirc: b h kinh hai ty, mi&n hoi ty, tinh t8ng . c) ~ h u 6 i Fourier: Khai tribn h h s8 t hbh chu6i Fourier.

3) DQO hiim ctia h h v6c tu mat bi6n thuc 4) H h khh tich (libn Qc timg khlic), djnh 19 hoi tu don dieu, hai tu bj ch$n.

Tich p h h suy rang. Tich p h h phu thuac tham s8 . 5) a) Phucmg trinh vi p h h chp 1: p h h ly, d h g chp, tuy&n tinh, Bernoulli, Vi

p h h t o b phdn, Largrange, Clairaut. b) Phuang tsinh vi phfin tuybn tinh chp 2. c) He phuong trinh vi p h h tuy&n tinh chp 1 he s6 hhg .

Xiic Suit ~ h h g kc:

1. Ph6p tha nggu nhibn v i c b khii nigm lien quan, Ciic ph6p tinh v& chc su kien, Xiic suit mat sy kign

2. Ciic m8 hinh xb suit the0 ciic quan bi&m &ng khh nhg , th6ng kb vii hinh h ~ c . He tibn d& xhc subt Kolmogorov

3. Ciic djnh 19 cu b h cDa phCp tinh xhc suht: Djnh 19 cong x b suit cho hai sg kien xung khkc, hai sg kign bht kkjl, t8ng quht cho n su kitn bht kf vii chc he quh. Xhc suit c6 di&u kien, djnh 1f nhiin xiic suht vii chc khai niem lien quan (su d$c lijp cfia hai hay nhi&u sy kien libn quan)

4. C6ng th.ixc xhc suht tohn p h h vii c8ng thirc Bayes

1. Khhi niem v& @i luqng nggu nhi&n. P h h ph6i x&c suht ctia dpi lugng ngau nhien. Diiy p h h ph6i xhc s d t ciia dpi luqng n d u nhien rbi rw. Day phdp thtr doc l@p Bernoulli vh p h h ph6i nhj thirc

2. Him qh? ph6i xic suh c h dpi lupng nggu nhi&n vh chc tinh chit ciia n6. HBm m& do p h h phoi xac suit ciia d ~ i luqng ngau &i&n l i h Qc vh chc tfnh chht

3. D~ Iugng nggu nhign nhi&u chi&. P h h ph6i xhc suht dbng thbi ciia d ~ i luqng n g b nhien nhi&u chi&u vh x6t cv th& chc t r u h g hqp p h h ph6i xhc suht dbng thlri ctia dqi lvqng nggu nhign hai chi& rbi qc, lien ~ c , d#c biet h b p h h ph6i v& m@t do p h h ph6i xhc s d t chub hai chi&.

4. Khhi niem dgc 14p ciia cic dpi luqng nggu nhidn. P h h ph6i xiic suht ciia hAm c b dpi luqng nggu nhien

C H U ~ G III. CAC DAC T R ~ G SO COA D ~ I LU'WG NGAU WN 1. Kjl vgng, Phucmg sai vh d c tinh chh. P h h ph6i xhc suit c6 &i&u kien vh kjl vgng c6 di&u kien. Chc dac trung s6 k h h ctia dgi luqng nggu nhien: hiep phucmg sai, he s6 tuung quan, trung vi.

2. Khho sit mot s6 dpi luqrng ng& nhih W n g dpng: Dpi luqng nggu nhien &@c trung cho s~ xuht hien mat s~ kien. Bpi luqng n g h nhien c6 p h h ph6i x b suh nhj thirc, p h h ~ h b i Poisson. Dpi luqng nggu nhien c6 phh ph6i x8c suit &u, p h h x h suht mil, p h h

chufin, vh khbo s6t Y chc tinh ch& ciia &i luqng nggu nhien c6 p h h ph6i chub.