51_phuong trinh toan ly

7/30/2019 51_Phuong Trinh Toan Ly

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I HC QUC GIA H NI

TRNG I HC KHOA HC T NHIN

---------- ----------

CNG MN HC

PHNG TRNH TON L

1. Thng tin v ging vin:

H v tn : Phan Huy Thin

Chc danh : Ging vin.

n v : B mn vt l l thuyt, Khoa Vt L, Trng i Hc Khoa Hc TNhin.

Thi gian a im lm vic: 334 Nguyn Tri, Thanh Xun, H Ni, Vit NamPhone: (84) 04-8584615/8581419Fax: (84) 04-8583061Email: [email protected];[email protected]

Cc hng nghin cu chnh : Nghin cu l thuyt v cu trc ht nhn.

2. Thng tin chung v mn hc

Tn mn hc: Phng trnh ton l

M mn hc:

S tn ch: 2

Gi tn ch i vi cc hot ng hc tp:

+ Gi nghe ging l thuyt trn lp: 22

+ Gi lm bi tp trn lp

+ Gi tho lun trn lp: 4

+ Gi thc hnh trong phng th nghim :

+ Gi thc t ngoi trng:

+ Gi t hc, t nghin cu: 4

n v ph trch mn hc:

+ B mn Vt L V Tuyn

+ Khoa Vt L

Mn hc Tin quyt: C l thuyt, in ng lc, C lng t, Gii tch, i

s, Hm phc, Phng trnh vi phn, cc mn hc c s ca ngnh Vt l

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mailto:[email protected]:[email protected]:[email protected]:[email protected]


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3. Mc tiu mn hc:

- Mc tiu v kin thc v k nng:

+ Sinh vin xy dng cc phng trnh ton hc: Hyperbolic, Para bolic,Eliptic.. t cc hin tng vt l c bn nh : Cc qu trnh truyn sng,

truyn nhit, cc hin tng in t, cc hin tng khuych tn chtlng v cht kh trong cc mi trng c dng hnh hc khc nhau phthuc vo cch chn cc h ta cong trc giao : H ta tr, h ta cu

+ Gii cc phng trnh o hm ring bng phng php tch binFourier, phng php Dalembert, phng php hm Green, phng

php sai phn hu hnTrong qu trnh gii cc phng trnh c knng tnh bng gii tch v t duy ton hc tt.

- Mc tiu v kin thc v k nng:

+ Sau khi tm c nghim ca cc phng trnh, nh gi c tin cyv ngha vt l ca nghim.

+ Sau mn hc c kh nng t c cc gio trnh vt l l l thuyt.

+ Xy dng c t duy trit hc cc qu trnh v hin tng vt l, bitnh gi ng v tr v vai tr ca cc phn mm my tnh trong vic trgip xy dng v gii cc bi ton o hm ring.

+ Xc nh c vai tr ca cc mn ton hc cho vt l.

4. Tm tt ni dung mn hc:Phng trnh ton l l mn hc nhm mc ch cung cp cho sinh vin cc

cng c ton hc gii cc phng trnh c xy dng t cc hin tng vy l c bnnht trong th gii xung quanh nh truyn sng (sng nc, sng m thanh, sng int, sng hp dn), truyn nhit hay khuch tn vt cht trong cc mi trng hu hnv v hn. T cc hin tng c bn nht ca cc hin tng vt l c m t bngngn ng ton hc theo c th dng gii thch theo cc hin tng vt l khctrong th gii vi m v v m nh khuych tn ntron trong l phn ng, nghin cucc tnh cht v cc qu trnh vt l xy ra bn trong vt rn hoc cc qu trnh xy ratrong v tr v cc thin h.

gii phng trnh c nhiu phng php khc nhau: phng php tch binFourier, phng php c trng, phng php hm Green, phng php biu din tch

phn, phng php sai phn hu hn...

Cc i lng vt l ph thuc vo nhiu bin. Trong ton hc, tm nghiml hm nhiu bin ca phng trnh vi phn c mt ngnh hc l phng trnh ohm ring. Trong gio trnh ny chng ti cng phn loi cc dng phng trnh cxy dng t cc hin tng vt l theo mn hc phng trnh o hm ring ph hpvi cch v phng php gii. C th l c ba loi phng trnh o hm ring c bn:

phng trnh hyperbolic c trng cho qu trnh truyn sng, phng trnh parabolic

c trng cho qu trnh truyn nhit hay khuch tn v phng trnh elliptic c trngcho vic nghin cu cc qu trnh truyn nhit hay truyn sng trong trng thi dng.

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Vi s pht trin ca my tnh v cc phn mm tnh ton, c th dng giicc phng trnh ton l chnh xc v nhanh hn cch gii bng gii tch thng thngda trn cch m phng cc hin tng vt l.

5. Ni dung chi tit mn hc

Chng I: M U

1. Phn loi phng trnh o hm ring cp

2. Gii phng trnh vi phn cp

3. Khi nim chui v tchphn Fourier

4. Cc h ta cong trc giao

Chng II : PHNG TRNH HYPERBOLIC

1. Khi nim v phng trnh sng

2. Phng trnh dao ng ca dy3. Gii phng trnh dao ng ca dy bng phng php tch bin

4. Dao ng xon ca mt thanh ng cht

5. Dao ng vi bin nh ca mt si ch treo mt u

6. Phng trnh khng thun nht

7. Sng m trong cht kh hoc cht lng

8. Sng in v t

9. Chuyn ng sng ca cht rn10. Phng trnh dao ng ca mng

11. Gii phng trnh dao ng ca mng ch nht

12. Dao ng ca mng trn

Chng III PHNG TRNH PARABOLIC

1. Phng trnh truyn nhit

2. Cc iu kin ban u v iu kin bin cho phng trnh truyn nhit

3. Phng trnh khuych tn4. Qu trnh truyn nhit trong thanh, phng trnh truyn nhit mt chiu

5. Phng php tch bin cho phng trnh truyn nhit trong thanh hu hn

6. Truyn nhit trong thanh c ngun nhit

7. Bi ton truyn nhit hn hp

8. Truyn nhit trong thanh di v hn

9. Khi nim v hm Green

10. Truyn nhit trong h ta tr11. Truyn nhit trong ta cu

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Chng IV PHNG TRNH ELLIPTIC

1. M u

2. L thuyt th

3. Phng trnh Helmholtz

4. Hm iu ha v cc tnh cht

5. Phng trnh Poisson trong min ch nht

6. Cng thc tch phn Poisson trong min trn

Chng V CC PHP BIN I TCH PHN

1. Hm bc Heaviside v hm delta Dirac

2. Php bin i Laplace

3. Php bin i Fourier

Chng VI HM GREEN

1. Khi nim

2. Tm hm Green bng php bin i Laplace

Chng VII CC HM C BIT

1. Cc hm trc giao

2. Cc h Sturm-Liouville

3. H Sturm-Liouville cho cc hm lng gic v hm m

4. Phng trnh v hm Bessel

5. Tnh trc giao ca hm Bessel

6. Khai trin mt hm ty vo cc hm Bessel

7. a thc Legendre

8. nh ngha hm cu

9. Tnh trc giao ca hm cu

10. V d v hm cu

11. a thc Hermite

12. a thc Laguerre

13. Cc hm trc giao c bit

Chng VIII GII BNG MY TNH

1. Cc phn mm Mathematica cho phng trnh o hm ring

2. Cc phn mm Mathlab cho phng trnh o hm ring

3. Gii thiu phn mm mu cho bi ton dao ng ca dy

4. Gii thiu phn mm mu cho bi ton dao ng ca mng

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5. Gii thiu phn mm mu cho bi ton truyn nhit

6. Gii thiu phn mm mu cho bi ton dng Elliptic

6. Hc liu

- Hc liu bt buc.1. Phan Huy Thin, Gio Trnh Phng Trnh Ton - L. NXBHQG H Ni

2007.

2. Phan Huy Thin, Bi Tp Phng Trnh Ton - L. NXBHQG H Ni (Sxut bn 2008)

3. Abramowitz, M. , Stegun, A. Handbook of Mathematical Functions, 10thedition, New York: Dover Publications, 1972

- Hc liu tham kho

4. Arfken G. (1985), Mathematical Methods for Physics, 3rd

edition, AcademicPress.

5. nh Thanh. Phng php Ton - L. NXBGD. H Ni 1996.

6. Haberman R. (1987), Elementary Applied Partial Differential Equations,Prentice-Hall.

7. Heckbert P. (2000), Partial Differential Equations, Computer ScienceDepartment, Carnegie Mellon University.

8. Koshlyakov, N. S., Smirnov, M.M., Gliner, E.B., Differential Equations ofMathematical Physics, Amsterdam: North-Holland Publishing Company, 1964.

9. Nguyn nh Tr v Nguyn Trng Thi (1971), Phng trnh vt l ton, NXBi hc v Trung hc chuyn nghip, H Ni.

10.Nguyn T Uyn (1997), Phng trnh ton l, Khoa Vt l, Trng i hcKhoa hc T nhin HQG H Ni.

11. Partial Differentiatial Equations and Fourier Analysis. Ka Kit Tung -University of Washington (2000).

12. Roach, G.F., Greens Functions, Second Edition, London: CambridgeUniversity Press, 1982.

13. Snieder R. (1994), A Guided Tour of Mathematical Physics, UtrechtUniversity.

14. Sobolev, S.L., Partial Differential Equations of Mathematical Physics, NewYork: Dover Publications, 1964.

15. Stakgolf, I. Greens Functions and Boundary Value Prolems, New York: JohnWiley & Sons, 1979.

16. Strauss, W.A., Partial Differential Equations An Introduction, New York: Johnand Sons, 1992.

17. Tikhonov A.N Samarski A.A. Equations of mathematical physics. Gosteizdat,1968 ( in Russian ).

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18. Trodden M. (1999), Methods of Mathematical Physics, Lecture Notes,Department of Physics, Case Western Reserve University.

7. Hnh thc t chc dy hc

Ni dung Hnh thc t chc dy hc mn hc TngLn lp Thc hnh,

th nghim,in d,

T hc,t nghin

cuL thuyt Bi tp Tho lun

Chng 1 3 3 2 5 13

Chng 2 5 3 2 5 15

Chng 3 5 3 2 5 15

Chng 4 5 3 2 5 15

Chng 5 5 3 2 5 15

Chng 6 5 3 2 5 15

Chng 7 5 3 2 5 15

Chng 8 5 3 2 5 15

7.2. Lch trnh t chc dy hc c th

Tun Ni dung Ti liu Hnh thc dy hc v yucu sinh vin chun b

1 Chng I: M U

1. Phn loi phng trnh o hm ring cp

2. Gii phng trnh vi phn cp

3. Khi nim chui v tchphn Fourier

4. Cc h ta cong trc giao

[1] - SV c v t lm cc bitp

- n li cc kin thc vgii tch vector, phngtrnh vi phn thng

1,2 Chng II : PHNG TRNHHYPERBOLIC

1. Khi nim v phng trnh sng

2. Phng trnh dao ng ca dy

3. Gii phng trnh dao ng ca dy bngphng php tch bin

4. Dao ng xon ca mt thanh ng cht

5. Dao ng vi bin nh ca mt si chtreo mt u

6. Phng trnh khng thun nht

7. Sng m trong cht kh hoc cht lng

[1],[2] - Ging trn lp v lm ccbi tp mu.

- Sinh vin t lm cc bitp nh.

- n li cc kin thc vdao ng v sng, cc nhlut c hc

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8. Sng in v t

9. Chuyn ng sng ca cht rn10. Phng trnh dao ng ca mng

11. Gii phng trnh dao ng ca mngch nht

12. Dao ng ca mng trn

13. Nghim D'Alembert ca phng trnhsng

Mt s bi gii mu

Bi tp chng II3,4 Chng III PHNG TRNH

PARABOLIC

1. Phng trnh truyn nhit

2. Cc iu kin ban u v iu kin bincho phng trnh truyn nhit

3. Phng trnh khuych tn

4. Qu trnh truyn nhit trong thanh,

phng trnh truyn nhit mt chiu5. Phng php tch bin cho phng trnhtruyn nhit trong thanh hu hn

6. Truyn nhit trong thanh c ngun nhit

7. Bi ton truyn nhit hn hp

8. Truyn nhit trong thanh di v hn

9. Khi nim v hm Green

10. Truyn nhit trong h ta tr11. Truyn nhit trong ta cu

Mt s bi gii mu

Bi tp chng III



5,6 Chng IV PHNG TRNH ELLIPTIC

1. M u

2. L thuyt th

3. Phng trnh Helmholtz4. Hm iu ha v cc tnh cht



- n li cc kin thc vnhit

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12. a thc Laguerre

13. Cc hm trc giao c bitBi tp chng VII

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Chng VIII GII BNG MY TNH1. Cc phn mm Mathematica cho phngtrnh o hm ring

2. Cc phn mm Mathlab cho phng trnho hm ring

3. Gii thiu phn mm mu cho bi tondao ng ca dy

4. Gii thiu phn mm mu cho bi ton

dao ng ca mng5. Gii thiu phn mm mu cho bi tontruyn nhit

6. Gii thiu phn mm mu cho bi tondng Elliptic

Bi tp chng VIII



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

Cch thc nh gi, s hin din trn lp, mc tch cc tham gia cc hot ng trn

lp, cc qui nh v thi hn, cht lng cc bi tp, bi kim tra.

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

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

- im tiu lun v trnh by : 20%

- im kim tra gia k : 30%

- im kim tra cui k : 50%

9.2. Lch thi, kim tra.

- Thi gia k : tun th 9

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- Thi cui k : sau tun th 15

- Thi li : sau khi thi gia k 4 n 5 tun

9.3. Tiu ch nh gi cc loi bi tp v cc nhim v m ging vin giao chosinh vin.

- i vi bi tiu lun: ni dung c kh nng h thng ho cc ti liu truy cp, thamkho, c trnh by ngn gn, logic, sinh vin phi hiu ni dung vit ra, th hin khnng lm vic c lp, xut c cc kin hp l t ra c o su suy ngh vsng to.

- Vi bi kim tra cui k: khng kim tra s hc thuc lng m yu cu s hiubit bn cht hoc kh nng vn dng vo cc bi ton, vn thc t

DUYT CA TRNG P.CH NHIM KHOA GING VIN

KT. HIU TRNG H KHTNPH HIU TRNG

PGS.TS. Bi Duy Cam GS.TS. Nguyn Quang Bu Phan Huy Thin

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51_phuong trinh toan ly

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