toan cao cap 3 - de cuong chinh thuc (hutech) 20jun12

cng chi tit Ton cao cp 3 1

TRNG I HC K THUT CNG NGH TP. HCM

KHOA CNG NGH THNG TIN

CNG HA X HI CH NGHA VIT NAM

c lp T do Hnh phc

CNG CHI TIT HC PHN (Chng trnh o to tn ch, t Kha 2011)

1. Thng tin chung v mn hc - Tn mn hc: Ton cao cp 3 - M mn hc: 321009 - S tn ch: 3 - Thuc chng trnh o to bc: i hc - Loi mn hc: Bt buc - Cc mn hc tin quyt: Ton cao cp 1, Ton cao cp 2 - Cc mn hc k tip: - Gi tn ch i vi cc hot ng:

Nghe ging l thuyt: 33 tit Lm bi tp trn lp: 12 tit T hc nh: 90 tit

- Khoa, b mn ph trch mn hc: Khoa Cng ngh Thng tin, b mn Ton.

2. Mc tiu ca mn hc

- Kin thc: Hiu cc khi nim tch phn tch phn ng, tch phn mt, tch phn suy rng, chui s, chui hm v cc bi ton v phng trnh o hm ring.

- K nng: Nm vng cc phng php tnh tch phn ng, tch phn mt, s hi t ca chui s, chui hm v hiu cch gii mt s phng trnh o hm ring .

- Thi hc tp: i hc y v lm cc bi tp v nh, m bo thi gian t hc nh.

3. Tm tt ni dung mn hc

Tch tch phn ng, tch phn mt, tch phn suy rng, l thuyt chui v phng trnh o hm ring.

4. Ti liu hc tp

4.1 Gio trnh chnh:

[1] Cng Khanh (ch bin), Nguyn Minh Hng, Ng Thu Lng, Gii tch hm nhiu bin v phng trnh vi phn, NXB H Quc Gia TpHCM, 2010.

[2] Cng Khanh (ch bin), Nguyn Minh Hng, Ng Thu Lng, Gii tch hm mt bin v l thuyt chui, NXB H Quc Gia TpHCM, 2010.

4.2 Gio trnh tham kho thm:

[1] Nguyn nh Tr (ch bin). Ton cao cp, tp 2, NXB GD, 2009.

[2] Nguyn nh Tr (ch bin). Ton cao cp, tp 3, NXB GD, 2009.

Khoa Cng ngh Thng tin - HUTECH 20-Jun-12


NI DUNG CC BI C CHNH

Chng 1. Tch phn ng (9 tit) 1.1 Tch phn ng loi mt 1.2 Tch phn ng loi hai 1.3 Cng thc Green 1.4 iu kin khng ph thuc ng ly tch phn 1.5 Tch phn ng loi hai trong khng gian

Chng 2. Tch phn mt (9 tit) 2.1 Tch phn mt loi mt 2.2 Tch phn mt loi hai 2.3 nh l Gauss-Ostrogratski 2.4 nh l Stokes 2.5* Gii thiu v trng vector

Chng 3. Tch phn suy rng v l thuyt chui (18 tit) 3.1 Tch phn suy rng loi mt 3.2 Tch phn suy rng loi hai 3.3 Chui s 3.4 Chui ly tha 3.5 Chui Taylor 3.6 Chui Fourier

Chng 4. Phng trnh o hm ring (9 tit ) 4.1 Khi nim chung v phng trnh o hm ring 4.2 Phng trnh truyn nhit, phng php tch bin 4.3 Phng trnh sng 4.4 Phng trnh Laplace

5. Cc phng php ging dy v hc tp ca mn hc

Ging vin thuyt trnh, dng bng vit kt hp vi dng my chiu.

6. Chnh sch i vi mn hc v cc yu cu khc ca ging vin i vi sinh vin

Yu cu sinh vin hin din y v tch cc tham gia cc hot ng trn lp; chun b bi trc khi ln lp; trau di k nng hc nhm; tun th cc qui nh v thi hn, cht lng cc bi tp, bi kim tra do ging vin a ra.

Khuyn khch sinh vin rn luyn k nng tm kim v x l thng tin ti th vin v trn Internet, dng cc chng trnh CAS trn my tnh h tr vic tnh ton.

7. Thang im nh gi

Ging vin nh gi theo thang im 10, Phng o to s quy i sang thang im ch v thang im 4 phc v cho vic xp loi trung bnh hc k, trung bnh tch ly v xt hc v.

8. Phng php, hnh thc kim tra - nh gi kt qu hc tp mn hc

8.1. Kim tra nh gi qu trnh: C trng s chung l 30%, bao gm cc im nh gi b phn nh sau (ging vin thng bo r cch tnh im b phn cho sinh vin khi bt u mn hc):



- im kim tra thng xuyn trong qu trnh hc tp. - im nh gi nhn thc v thi tham gia tho lun. - im chuyn cn. - im tiu lun. - im thi gia k. - im nh gi khi lng t hcca sinh vin (hon thnh tt ni dung, nhim v m ging

vin giao cho c nhn/tun; bi tp nhm/thng; bi tp c nhn/hc k,).

8.2. Kim tra - nh gi cui k: im thi kt thc hc phn c trng s 70%. Hnh thc thi trc nghim, mi sinh vin mt khc nhau. Thi lng 60 - 75 pht (20-25 cu hi). Sinh vin khng c tham kho ti liu khi thi. Cu trc thi v thi mu sinh vin s c ging vin cung cp trong qu trnh hc.

9. Ni dung chi tit mn hc v phn b thi gian c th

Hnh thc t chc dy hc

Ln lp Ni dung L

thuyt Bi tp

T hc

Tng

Chng 1. Tch phn ng (9 tit)

1.1 Tch phn ng loi mt - nh ngha, cc tnh cht. - Cng thc tnh (dng tham s, dng tng minh y=f(x), trong ta

cc) - ng dng tch phn ng loi mt: khi lng v trng tm cung.

2

1

6 9

1.2 Tch phn ng loi hai - nh ngha, tnh cht. - ngha c hc. - Cng thc tnh.

1.3 Cng thc Green

2 1 6 9

1.4 iu kin khng ph thuc ng ly tch phn - Bn mnh tng ng. - Cch tnh tch phn. - Mt cch gii phng trnh vi phn ton phn. 1.5 Tch phn ng loi hai trong khng gian.

2 1 6 9

Chng 2. Tch phn mt (9 tit)

2.1 Tch phn mt loi mt - nh ngha, tnh cht, cch tnh. - ng dng: Din tch mt. Khi lng, trng tm.

2 1 6 9



2.2 Tch phn mt loi hai - Mt nh hng v nh ngha tch phn mt loi hai. - Cch tnh.

2 1 6 9

2.3 nh l Gauss-Ostrogradski 2.4 nh l Stokes 2.5* Gii thiu v trng vector

- Hon lu, thng lng ca trng vector. - Dng vector ca cc cng thc Gauss-Ostrogradski, cng thc

Stokes. - Trng th, trng ng, trng in, trng iu ha.

2 1 6 9

Chng 3. Tch phn suy rng v l thuyt chui (18 tit)

3.1 Tch phn suy rng loi mt - nh ngha. - Tch phn hm khng m. Cc dnh l so snh. - Hi t tuyt i.

2 1 6 9

3.2 Tch phn suy rng loi hai - nh ngha. - Tch phn hm khng m. Cc nh l so snh. - Hi t tuyt i.

2 1 6 9

3.3 Chui s - nh ngha chui hi t. Cc tnh cht chui hi t. iu kin cn

hi t. - Chui s khng m. Cc tiu chun hi t. - Hi t tuyt i.

4 2 12 18

3.4. Chui ly tha - Khi qut v chui hm. - Chui ly tha. nh l Abel. - Bn knh hi t. - Cc tnh cht ca chui ly tha.

2 1 6 9

3.5. Chui Taylor - nh ngha chui Taylor. - iu kin khai trin hm s v chui Taylor. - Khai trin Maclaurin cc hm c bn.

3.6 Chui Fourier - Khai trin hm tun hon chu k 2 vo chui Fourier. - Khai trin Fourier trn cc on.

2 1 6 9



Chng 4. Phng trnh o hm ring (9 tit)

4.1 Khi nim chung v phng trnh o hm ring 4.2 Phng trnh truyn nhit, phng php tch bin

- Phng trnh thun nht, iu kin bin thun nht. - Phng trnh thun nht, iu kin bin khng thun nht. - Phng trnh thun nht, hai u khng trao i nhit. - Phng trnh khng thun nht, iu kin bin thun nht.

3 0 6 9

4.3 Phng trnh sng - Phng trnh thun nht, iu kin bin thun nht. - Phng trnh khng thun nht, iu kin bin thun nht. - Cng thc DAlembert.

3 0 6 9

4.4 Phng trnh Laplace - Bi ton Dirichlet trong hnh ch nht.

3 0 6 9

Tng cng 33 12 90 135

10. Ngy ph duyt: 22/06/2012

Ngi vit (K v ghi r h tn)

GS. TSKH. Cng Khanh

T trng B mn (K v ghi r h tn)

ThS. Nguyn Cao Tr

Trng khoa (K v ghi r h tn)

GS. TSKH. Cng Khanh


toan cao cap 3 - de cuong chinh thuc (hutech) 20jun12

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