{"id":53,"date":"2017-03-31T08:35:18","date_gmt":"2017-03-31T08:35:18","guid":{"rendered":"https:\/\/cmu-edu.eu\/traian-lalescu\/?page_id=53"},"modified":"2017-04-11T08:53:04","modified_gmt":"2017-04-11T08:53:04","slug":"sectiunea-c","status":"publish","type":"page","link":"https:\/\/cmu-edu.eu\/traian-lalescu\/sectiunea-c\/","title":{"rendered":"Sec\u021biunea C"},"content":{"rendered":"

Anul I – profil neelectric, Faculta\u021bi Tehnice<\/h2>\n

ANALIZ\u0102 MATEMATIC\u0102<\/strong><\/h3>\n
<\/div>\n

1. Mul\u021bimi de numere<\/h3>\n

Mul\u021bimea numerelor reale \u0219i elemente de topologie. Inegalita\u021bi remarcabile.<\/p>\n

2. \u0218iruri \u0219i serii de numere<\/h3>\n

\u0218iruri de numere. \u0218iruri definite prin recuren\u021be.\nSerii de numere. Criterii de convergen\u021ba pentru serii cu termeni pozitivi \u0219i oarecare.<\/p>\n

3. Func\u021bii continue<\/h3>\n

Limite de func\u021bii de una sau mai multe variabile. Puncte limita.\nFunc\u021bii elementare.\nProprietatea Darboux.\nContinuitate uniforma. Func\u021bii continue pe mul\u021bimi compacte.<\/p>\n

4. \u0218iruri \u0219i serii de func\u021bii<\/h3>\n

Convergen\u021ba punctuala \u0219i uniforma.\nTransmiterea proprieta\u021bilor de continuitate, derivabilitate \u0219i integrabilitate la limita \u0219irului\nsau suma seriei.\nSerii de puteri. Dezvoltarea func\u021biilor elementare \u00een serii de puteri.<\/p>\n

5. Calcul diferen\u021bial pentru func\u021bii de una \u0219i de mai multe variabile<\/h3>\n

Teoreme asupra func\u021biilor derivabile pe intervale: Fermat, Darboux, Cauchy, Lagrange.\nFormula lui Taylor pentru func\u021bii de o variabila reala cu restul Lagrange.\nDerivate par\u021biale. Derivata dupa direc\u021bie.\nDerivarea func\u021biilor compuse.\nDiferen\u021biala func\u021biilor de una \u0219i mai multe variabile. Formula lui Taylor pentru funcii de mai\nmulte variabile.\nExtreme de func\u021bii.<\/p>\n

6. Calcul integral<\/h3>\n

Integrala Riemann.\nIntegrale improprii \u0219i criterii de convergen\u021ba.\nIntegrale cu parametru. Continuitatea, derivabilitatea \u0219i integrabilitatea integralei cu\nparametru. Func\u021biile Beta \u0219i Gama ale lui Euler.<\/p><\/div>\n

ALGEBRA<\/strong><\/h3>\n
<\/div>\n

1. Matrice \u0219i determinan\u021bi<\/h3>\n

Determinan\u021bi.\nMatrice simetrice, antisimetrice, ortogonale.\nSisteme de ecua\u021bii liniare.<\/p>\n

2. Spa\u021bii vectoriale<\/h3>\n

Subspa\u021bii liniare. Subspa\u021biul generat. Opera\u021bii cu subspa\u021bii.\nBaza \u0219i dimensiune Matricea schimbarii de baze.<\/p>\n

3. Aplica\u021bii liniare<\/h3>\n

Nucleu \u0219i imagine. Matricele unei aplica\u021bii liniare.\nValori proprii \u0219i vectori proprii pentru endomorfisme \u0219i forma diagonala.\nPolinom caracteristic; teorema Cayley-Hamilton.\nForme liniare, biliniare \u0219i patratice. Forma canonica a unei forme patratice.<\/p>\n

4. Spa\u021bii euclidiene \u0219i normate<\/h3>\n

Produs scalar. Norma indusa. Distan\u021ba euclidiana.\nOrtogonalizare Gram-Schmidt.\nComplementul ortogonal al unui subspa\u021biu.\nMetoda transformarilor ortogonale pentru forma canonica a unei forme patratice.\nSpa\u021bii normate.<\/p>\n

GEOMETRIE<\/strong><\/h3>\n
<\/div>\n

1. Geometrie vectoriala<\/h3>\n

Spa\u021biul vectorial al vectorilor liberi. Vectori de pozi\u021bie.\nProduse cu vectori: scalar, vectorial, mixt.\nEcua\u021bii vectoriale pentru dreapta, plan, cerc, sfera.<\/p>\n

2. Geometrie analitica<\/h3>\n

Coordonate \u00een plan \u021bi spa\u021biu.\nDreapta \u00een spa\u021biu. Planul \u00een spa\u021biu. Perpendiculara comuna a doua drepte.\nConice \u0219i cuadrice. Reducerea la forma canonica a conicelor \u0219i cuadricelor.<\/p><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"

Anul I – profil neelectric, Faculta\u021bi Tehnice<\/p>\n","protected":false},"author":4,"featured_media":118,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-53","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/pages\/53","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/comments?post=53"}],"version-history":[{"count":5,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/pages\/53\/revisions"}],"predecessor-version":[{"id":120,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/pages\/53\/revisions\/120"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/media\/118"}],"wp:attachment":[{"href":"https:\/\/cmu-edu.eu\/traian-lalescu\/wp-json\/wp\/v2\/media?parent=53"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}