I HC QUC GIA H NI TRNG I HC KHOA HC T NHIN ---------- ----------

CNG MN HC

I S TUYN TNH & HNH HC GII TCH 21. Thng tin v ging vin: H v tn: Nguyn c t Chc danh, hc hm, hc v: PGS. TS.- Thi gian, a im lm vic: Cc ngy trong tun ti b mn i S - Hnh hc -T

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a ch lin h: B mn i S-Hnh hc-T p Email: datnd@vnu.edu.vn Cc hng nghin cu chnh: L thuyt dn 2. Thng tin v mn hc:-

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Tn mn hc: i s tuyn tnh v hnh hc gii tch 2 M mn hc: S tn ch: 04 Gi tn ch i vi cc hot ng hc tp: + Nghe ging l thuyt trn lp: 30 + Lm bi tp trn lp: 29 + T hc: 01

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n v ph trch mn hc: + B mn: i S-Hnh hc-T p + Khoa: Ton-C-Tin hc

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Mn hc tin quyt: i S tuyn tnh 1 Mn hc k tip: i S tuyn tnh 3 (i vi ngnh Ton hc), i s i cng (i vi ngnh Ton hc v Ton tin ng dng)

3. Mc tiu ca mn hc: - Mc tiu v kin thc: trang b cho sinh vin cc kin thc quan trng ca i s tuyn tnh. - Mc tiu v k nng: Thnh tho cc k thut gii h phng trnh tuyn tnh, tm gi tr ring, vect ring, cho ha ma trn, a ma trn trc giao v dng chnh tc, a dng ton phng v dng chnh tc, v phc tho c cc ng, mt bc hai.

- Cc mc tiu khc (thi hc tp) 4. Tm tt ni dung mn hc: Chng 3 l ni tip ca mn i s tuyn tnh 1, nghin cu cc phng php gii h phng trnh tuyn tnh v cu trc tp nghim ca n. Chng 4 gii thiu cc khi nim gi tr ring, vect ring phc v cho bi ton cho ha ma trn. Chng 5 xem xt khng gian vect Euclid, php bin i trc giao, php bin i i xng. Chng 6 nghin cu dng ton phng trn trng thc, nh l Sylvester v phn loi dng ton phng trn trng thc. Chng 7 nghin cu cc vn ca hnh hc gii tch, tp trung vo vic phn loi v v phc tho mt bc hai. 5. Ni dung chi tit mn hc: Chng 3. nh thc v h phng trnh tuyn tnh (tip theo) 3.1. H phng trnh tuyn tnh - Quy tc Cramer. 3.2. H phng trnh tuyn tnh - Phng php kh Gauss. 3.3. Cu trc nghim ca mt h phng trnh tuyn tnh. Chng 4. Cu trc ca t ng cu 4.1. Vc t ring v gi tr ring. 4.2. Khng gian con n nh ca cc t ng cu thc v phc. 4.3. T ng cu cho ha c. Chng 5. Khng gian vect Euclid 5.1. Khng gian vct Euclid. 5.2. Php bin i trc giao. 5.3. Php bin i i xng. Chng 6. Dng song tuyn tnh v dng ton phng 6.1. Khi nim dng song tuyn tnh v dng ton phng 6.2. a dng ton phng v dng chnh tc 6.3. Hng v hch ca dng ton phng 6.4. Ch s qun tnh 6.5. Dng ton phng xc nh du Chng 7. Hnh hc gii tch 7.1. Khng gian affine 7.2. Cc phng trong khng gian affine 7.3. nh x affine 7.4. Khng gian Euclid 7.5. Phng trong khng gian Euclid

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7.6. nh x trc giao 7.7. Phn loi cc ng bc hai trong mt phng 7.8. Mt bc hai trong khng gian ba chiu 7.9. Mt k bc hai 6. Hc liu: 6.1. Hc liu bt buc: 1. Nguyn Hu Vit Hng: i S Tuyn Tnh, NXB i Hc Quc Gia H Ni, ti bn ln 2, 2004. 6.2. Hc liu tham kho: 2. L Tun Hoa: i S Tuyn Tnh qua cc v d v bi tp, NXB i Hc Quc Gia H Ni, 2006. 3. I. V. Proskuryakov: Problem in Linear Algebra, Mir Publishers, Moscow 1978. Trang web http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring2005/CourseHome/index.htm ca mn hc "Linear algebra" ti MIT (c c bng ghi hnh bi ging ca Gilbert Strang). Chng trnh hc nhn mnh ng dng ca i s tuyn tnh cho cc ngnh k thut v khoa hc t nhin ni chung.4.

Trang web http://ocw.mit.edu/OcwWeb/Mathematics/18-700Fall2005/CourseHome/index.htm ca mn hc Linear algebra ti MIT. (Nhn mnh l thuyt v chng minh).5.

6. Gilbert Strang: Linear Algebra and its applications, , Brook/Cole, 3rd edition, 1988. (C bn pdf.) 7. Sheldon Axler: Linear Algebra Done Right, Springer, second edition, 1997. (C bn pdf.) 8. Carl D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2000. (C bn pdf.)9. 10.

W. H. Greub: Multilinear Algebra, Springer-Verlag, 1967. (C bn pdf.)

Hoffman, K., and R. Kunze. Linear Algebra. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 1971. (C bn djvu.) 7. Hnh thc t chc dy hc: 7.1. Lch trnh chung: Hnh thc t chc dy hc mn hc Ni dung L thuyt Chng 3 2 Ln lp Bi tp 2 Tho lun Thc hnh, th nghim, in d T hc, t nghin cu 0,2 Tng

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Chng 4 Chng 5 Chng 6 Chng 7 Tng

6 6 6 10 30

5 6 6 10 29

0,2 0,2 0,2 0,2 1

7.2. Lch trnh t chc dy hc c th: Ch thch: - V l thuyt th theo sch ca Gio s Nguyn Hu Vit Hng. - V bi tp: T tun 1 n tun 12 theo sch ca Gio s Nguyn Hu Vit Hng, Tun 13, 14, 15 theo sch ca Gio s L Tun Hoa. Tun Ni dung chnh Yu cu sinh Hnh thc t Ghi ch vin chun b chc dy hc 1 -L thuyt: Mc 3.7, 3.8, Chng minh Ln lp 3.9 quy tc -Bi tp: 34, , 46 (trang Cramer 164, 165, 166) -L thuyt: Mc 4.1, 4.2 -Bi tp: 1, ,4 (trang 197, 198), 6, 16, 17, 18, 20, 21, 36, 37 (trang 200, 202) inh ngha gi Ln lp tr ring, vect ring v cc v d tnh ton

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-L thuyt: Mc 4.3 nh l 3.7 Ln lp (trang 179) -Bi tp: 5,7,8,9,10,11,14,19,28,29, 43, 44, 45 (trang 198, 199, 200, 202, 203, 204, 205) -L thuyt: Mc 5.1 Mnh 1.5 Ln lp -Bi tp: 1, , 15 (trang (trang 209) 244, 245, 246) -L thuyt: Mc 5.2 H qu 2.21 Ln lp -Bi tp: 16, , 25 (trang (trang 230) v cc v d 246, 247, 248) -L thuyt: Mc 5.3 H qu 3.12 Ln lp -Bi tp: 35, , 45 (trang (trang 238) v cc v d 248 , , 251) -L thuyt: Mc 6.1, 6.2 V d trang Ln lp -Bi tp: 1, , 10 (trang 258

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Tun

Ni dung chnh 272, 273)

Yu cu sinh Hnh thc t Ghi ch vin chun b chc dy hc

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-L thuyt: Mc 6.3, 6.4 Mnh 3.4 Ln lp -Bi tp: 11, , 20 (trang trang 264 273, 274) -L thuyt: Mc 6.5 nh l 5.2 Ln lp -Bi tp: 21, , 30 (trang ca Sylvester 276) -L thuyt: Mc 7.1, 7.2 Mi lin h Ln lp -Bi tp: 31, 37 (trang gia phng trnh tham s 277) v phng trnh tng qut -L thuyt: Mc 7.3, 7.4 V d 3.13 -Bi tp: 38, , 46 (trang 278) -L thuyt: Mc 7.5, 7.6 nh l 6.5 -Bi tp: 33.1, , 33.12 (trang 224, 225, 226), 34.1, , 34.18 (trang 229, 230, 231) Ln lp

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11

12

Ln lp

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-L thuyt: Mc 7.8 V d v phn Ln lp -Bi tp: 35.1, , 35.23 loi mt bc hai (trang 234, , 238) -L thuyt: Mc 7.9 Cc v d v Ln lp -Bi tp: 36.1, , 36.22 mt k bc hai (trang 245, , 248) n tp

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8. Yu cu ca ging vin i vi mn hc: Yu cu ca ging vin v iu kin t chc ging dy mn hc: Ging ng rng ri thong mt, khng n, bng v phn tt, c microphone. Yu cu ca ging vin i vi sinh vin:- i hc ng gi, y (khng t hn 80% s bui), trong lp ch nghe ging,

tn trng ging vin, lm y cc bi tp v nh. 9. Phng php v hnh thc kim tra nh gi mn hc:

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9.1. Cc loi im kim tra v trng s ca tng loi im -

Phn t hc, t nghin cu, bi tp: 20% Thi gia k: 20% Thi cui k: 60% 9.2. Lch thi v kim tra Thi gia k vo tun th 8. Thi kt thc hc k vo hai tun sau khi hc xong.

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