Silabusi



silabusi

|saswavlo kursis dasaxeleba |U maTematikuri fizikis gantolebebi |

|saswavlo kursis kodi | |

|saswavlo kursis statusi |kursi gaTvaliswinebulia maTematikis da fizikis mimarTulebis mesame an meore kursis studentebisaTvis. |

|saswavlo kursis xangrZlivoba |erTi semestri |

|ECTS-saswavlo kursi kreditebi |5 krediti |

| |60 sakontaqto saaTi (leqcia 30 saaTi, seminari 15 saaTi, praqtikuli 15 saaTi) 65 saaTi damoukidebeli |

| |muSaobisaTvis. |

|leqtori |Pprof. giorgi jaiani, Tsu zust da sabunebismetyvelo mecnierebaTa fakulteti, maTematikis mimarTuleba, |

| |telefoni: 303040(samsaxuri), 290470(bina), e.mail: jaiani@viam.sci.tsu.ge |

|saswavlo kursis mizani |Tanamedrove moTxovnebis pirobebSi farTo profiliT maTematikuri ganaTlebis mqone specialistebis momzadebis |

| |umTavres mizans warmoadgens maTTvis myari maTematikuri codnis micema bunebriv (fizikur) da |

| |socialur-ekonomikur procesebTan kavSirSi. ramdenadac aRniSnuli procesebi, umTavresad, aRiwereba |

| |diferencialuri gantolebebiT, maTematikosis CamoyalibebaSi RerZuli mniSvneloba eniWeba maTematikuri |

| |fizikis gantolebebis safuZvlian Seswavlas. kerZod, isini unda icnobdnen maTematikuri fizikis ZiriTad |

| |gantolebebs, unda icodnen maTi momcveli zogadi saxis kerZowarmoebuliani diferencialuri gantolebebis |

| |klasifikacia, amonaxsnebis Tvisebebi, Sesabamisi sawyisi da sasazRvro amocanebis koreqtulad dasma da maTi|

| |gamokvlevis ZiriTadi meTodebi. saswavlo kursis SinaarsSi miTiTebuli Temebis nawili studentebma |

| |damoukideblad unda moamzadon saseminaro muSaobisaTvis. |

|saswavlo kursis Seswavlis wina |students gavlili unda hqondes diferencialuri Dda integraluri aRricxvis (kalkulus) da Cveulebriv |

|pirobebi |diferencialur gantolebaTa kursebi. |

|saswavlo kursis formati |leqcia, seminari, praqtikuli |

|saswavlo kursis Sinaarsi |Temebi |

| | |

| |Sesavali (ix. [6], Sesavali. ZiriTadi hipoTezebi, $1.1) |

| | |

| |1. maTematikuri fizikis ZiriTadi gantolebebi |

| | |

| |1.1. simis rxevis gantoleba (ix.[3], $2,1). |

| |1.2.membranis rxevis gantoleba (ix.[3], $2,1). |

| |1.3.drekadi Reros rxevis gantoleba (ix.[6], $3.1). |

| | |

| |1.4. kirxhof-liavis da raisner-mindlinis gantolebebi (ix.[6], $$2.4, 2.5). |

| | |

| |1.5. wrfivi drekadobis Teoriis gantolebebi (ix.[1], $3 da [5], §§1.15, 1.16, 1.18). |

| | |

| |1.6. ierarqiuli modelebi (ix.[6], $2.6, §3.2). |

| | |

| |1.7. hidrogazodinamikis gantolebebi (ix.[1], $1 da [6], §1.23). |

| | |

| |1.8. difuziis gantolebebi (ix.[1], $5 da [3] $2,2). |

| | |

| |1.9. gadatanis gantolebebi (ix.[1], $5 da [3], $2,4). |

| | |

| |1.10. maqsvelis gantolebebi (ix.[1], $4 da [3], $2,6). |

| | |

| |1.11. Sredingeris gantolebebi (ix.[1], $6 da [3], $2,7). |

| | |

| |1.12.klain-gordon-fokis da dirakis gantolebebi (ix.[3], $2,8). |

| | |

| |1.13. Capliginis gantoleba (ix.[4], Tavi I, $3, 3 da 4). |

| | |

| |2. kerZowarmoebuliani diferencialuri gantolebebis klasifikacia |

| | |

| |2.1. kerZowarmoebuliani diferencialuri gantolebis cneba (ix.[4], Tavi I, $1, 10 da [2], Tavi V, $1). |

| | |

| |2.2. tipebad dayofa. maxasiaTebeli zedapirebi (ix.[4], Tavi I, $1, 20). |

| | |

| |2.3. meore rigis wrfivi kerZowarmoebuliani diferencialuri gantolebebi (ix.[4], Tavi I, $1, 30). |

| | |

| |2.4. meore rigis wrfivi diferencialuri gantolebebi ori damoukidebeli cvladis SemTxvevaSi. maxasiaTebeli |

| |wirebi. kanonikuri saxe (ix. [4], Tavi I, $1, 50). |

| | |

| |2.5. meore rigis wrfiv kerZowarmoebulian diferencialur gantolebaTa sistemis klasifikacia (ix.[4], Tavi I,|

| |$1, 40). |

| | |

| |2.6. eqstremumisa da zaremba-Jiros principebi. |

| |2.7. ZiriTadi sasazRvro amocanebi elifsuri gantolebebisaTvis, maTi amoxsnadoba, erTaderToba, mdgradoba. |

| |koSi-kovalevskaias Teorema (ix. [2], Tavi V, $1, 5; [3], Tavi I, $4, 8 da [5], Tavi VII, $1). |

| | |

| |3. elifsuri gantolebebi |

| | |

| |3.1. harmoniuli funqciebis ZiriTadi Tvisebebi (ix. [1], Tavi II, $2, [5], Tavi I, $1 da [9], Tavi III). |

| | |

| |3.2. grinis funqcia da dirixles amocanis amoxsna birTvisa da naxevarsivrcisaTvis (ix. [5], Tavi I, $2; |

| |[2], Tavi VII, $5, 5.1 da [9], Tavi IV). |

| | |

| |3.3. potencialTa Teoria (ix. [5], Tavi I, $$3,4; [1], Tavi II, $$3-6 da [9], Tavi V). |

| | |

| |4. hiperboluri gantolebebi |

| | |

| |4.1. talRis gantoleba. koSis amocana (ix. [5], Tavi III, $$1,2 da [2], Tavi V, $2,3). |

| | |

| |4.2. gursas (maxasiaTeblebze monacemebiT) amocana kanonikuri saxis meore rigis zogadi hiperboluri |

| |gantolebisaTvis ori damoukidebeli cvladis SemTxvevaSi (ix. [5], Tavi III, $3, 40; $4,20). |

| | |

| |4.3. koSis amocana kanonikuri saxis meore rigis zogadi hiperboluri gantolebisaTvis ori damoukidebeli |

| |cvladis SemTxvevaSi (ix.[5], Tavi III, $4 da [2], Tavi V, $3, 2,7). |

| | |

| |paraboluri gantolebebi |

| |5.1. siTbogamtareblobis gantoleba. pirveli sasazRvro amocana (ix. [5], Tavi IV, $1 da [2], Tavi V, $2,4) |

| |koSi-dirixles amocana (ix. [5], Tavi IV, $2) |

| |kerZowarmoebuliani gantolebebis amonaxsnebis sigluvis Sesaxeb |

| |elifsuri gantolebebi |

| |paraboluri gantolebebi |

| |hiperboluri gantolebebi |

| |(ix. [5], Tavi IV, $3) |

| |gadagvarebuli gantolebebi |

| |trikomis gantoleba. trikomis amocana (ix. [4], Tavi IV, $1, 10, 20 da [7], Tavi X, §§1,2) |

| |keldiSis ganzogadoebuli Teorema (ix. [8]) |

| |maTematikuri fizikis gantolebebis gamokvlevis ZiriTadi meTodebi |

| |cvladTa gancalebis meTodi (ix. [5], Tavi VI, $1) |

| |integraluri gardaqmnebis meTodi (ix. [5], Tavi VI, §2 da [2], Tavi III) |

| |variaciuli meTodebi (ix. [5], Tavi VI, §4 da [2], Tavi VII, §1) |

| |ricxviTi meTodebi (ix. [5], Tavi VI, §3 da [7], Tavi XII, §1) |

| |laboratoriuli samuSaoebi (ix. [10]) |

| | |

| |1. analizuri amoxsnebi da maTi grafikuli ageba |

| |2. mimarTulebaTa veli da integraluri wirebi |

| |3. maTematikuri fizikis tipiuri gantolebebi |

| |LL |

| |literatura |

| | |

| |R.Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, |

| |Vol.1-Physical Origins and Potential Theory, Springer-Verlag, Berlin, Heidelberg, 1988 |

| |R.Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, |

| |Vol.2-Functional and Variational Methods, Springer-Verlag, Berlin, Heidelberg, 1988 |

| |В.С. Владимиров, Уравнения математической физики, Москва, ,, Наука”, 1981 |

| |А.В. Бицадзе, Некоторые классы уравнений в частных производных, Москва, ,,Наука”, 1981 |

| |А. Бицадзе, Уравнения математической физики, Москва, ,, Наука”, 1982 |

| |g. jaiani, uwyvet garemoTa meqanikis maTematikuri modelebi, Tbilisis universitetis gamomcemloba, Tbilisi,|

| |2004, 338 gv. |

| |R.Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol.4 –|

| |Integral Equations and Numerical Methods, Springer-Verlag, Berlin, Heidelberg, 1988 |

| |G. Jaiani, On a Generalization of the Keldysh Theorem, Georgian Mathematical Journal, Vol.3, 291-297, |

| |1995 |

| |a. gagniZe, maTemtikuri fizikis gantolebebi, Tbilisi, 2003, 221 gv. |

| |G. Hsiao. Differential Equations, Computing Lab, Newark, Delaware, 1994 |

|Sefaseba |kolokviumi (weriTi formiT, sami sakiTxi, TiToeuli swori pasuxi fasdeba 5 qulamde); |

| |saboloo gamocda oTxsakiTxiani bileTebiT. TiTeul sakiTxze pasuxi fasdeba 10 qulamde). |

| | |

| |daswreba |

| |10% |

| | |

| | |

| |praqtikuli mecadineoba (15%), laboratoriuli samuSoabei (5%) |

| |20% |

| | |

| | |

| |kolokviumi |

| |15% |

| | |

| | |

| |kolokviumi |

| |15% |

| | |

| | |

| |saboloo gamocda |

| |40% |

| | |

| | |

| |saboloo Sefaseba |

| |100% |

| | |

| |gamocdaze daSvebis winapiroba: aranakleb 30 qulisa 1-4 komponentebSi |

| |kreditis miniWebis aucilebebi piroba: aranakleb 21 qulisa saboloo gamocdaSi |

|savaldebulo literatura |R.Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, |

| |Vol.1-Physical Origins and Potential Theory, Springer-Verlag, Berlin, Heidelberg, 1988 |

| |R.Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, |

| |Vol.2-Functional and Variational Methods, Springer-Verlag, Berlin, Heidelberg, 1988 |

| |В.С. Владимиров, Уравнения математической физики, Москва, ,, Наука”, 1981 |

| |А.В. Бицадзе, Некоторые классы уравнений в частных производных, Москва, ,,Наука”, 1981 |

| |А. Бицадзе, Уравнения математической физики, Москва, ,, Наука”, 1982 |

| |g. jaiani, uwyvet garemoTa meqanikis maTematikuri modelebi, Tbilisis universitetis gamomcemloba, Tbilisi,|

| |2004, 338 gv. |

| |R.Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol.4 –|

| |Integral Equations and Numerical Methods, Springer-Verlag, Berlin, Heidelberg, 1988 |

| |G. Jaiani, On a Generalization of the Keldysh Theorem, Georgian Mathematical Journal, Vol.3, 291-297, |

| |1995 |

| |a. gagniZe, maTemtikuri fizikis gantolebebi, Tbilisi, 2003, 221 gv. |

| |G. Hsiao. Differential Equations, Computing Lab, Newark, Delaware, 1994 |

|damatebiTi literatura da sxva |R. Hекторис, Вариационные методы в математической физике, Москва, ,,Наука”,1981 |

|saswavlo masala |R. Temam, Navie-Stokes equations, AMS Chelsea, 2001 |

| |F. John, Partial Differential Equations, Springer-Verlag, Berlin, Heidelberg, New York, 1978 |

| |Б. М. Будак, А.А. Самарский, А.Н. Тихонов, Сборник задач по математической физике, Москва, ,,Наука”,1972|

| | |

| |А. В. Бицадзе, Д. Т. Калининченко, Сборник задач по уравнениям математической физики, Москва, ,,Наука”, |

| |1985 |

| |g. kvinikaZe, maTematikuri fizikis amocanaTa krebuli, naw. I, Tbilisis universitetis gamomcemloba, |

| |Tbilisi, 1997, 215 gv. |

| |g. kvinikaZe, maTematikuri fizikis amocanaTa krebuli, naw. II, Tbilisis universitetis gamomcemloba, |

| |Tbilisi, 2001, 360 gv. |

|swavlis Sedegi |kursis Seswavlis Semdeg students ecodineba maTematikuri fizikis ZiriTadi kerZowarmoebuliani |

| |diferencialuri gantolebebi, gamoumuSavda hiperboluri, paraboluri, elifsuri da gadagvarebuli |

| |gantolebebisaTvis sawyisi da sasazRvro amocanebis koreqtulad dasmis unar-Cvevebi, daeufleba maTi |

| |gamokvlevis ZiriTad funqcionalur-analizur da efeqtur meTodebs. |

SeniSvna: winamdebare silabusis Sesabamisi leqciebis kursis mopoveba SeiZleba Semdeg veb-gverdze: .

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