## "Babes-Bolyai" University of Cluj-Napoca Faculty of Mathematics and Computer Science

 Numerical analysis (1)
 Code Semes-ter Hours: C+S+L Credits Type Section MC001 5 2+2+2 6 compulsory Matematică MC001 5 2+1+2 6 compulsory Informatică MC001 5 2+2+2 5 compulsory Matematică-Informatică MC001 5 2+2+2 6 compulsory Matematica Economica
 Teaching Staff in Charge
 Assoc.Prof. CHIOREAN Ioana Rodica, Ph.D., ioana@cs.ubbcluj.roAssoc.Prof. TRÎMBITAS Radu Tiberiu, Ph.D., tradu@cs.ubbcluj.roAsist. SOMOGYI Ildiko Mihaela, ilkovacs@math.ubbcluj.roLect. LISEI Hannelore-Inge, Ph.D., hanne@math.ubbcluj.ro
 Aims Basic course in numerical analysis.
 Content 1. Error theory: approximation, types of errors, semnificative digits, relations among different types of errors, the propagation of errors in calculus, approximation with a given error. 2. Finite and divided differences: definitions, properties, divided differences on multiple nodes. 3. Functions approximation: general notions, polinomyal interpolation (Lagrange, Hermite, Birkhoff, spline polynomial). Uniform approximation. Bernstein polynomial. Linear and positive operators. 4. Approximation of linear functionals: introduction, numerical derivation and integration of functions. Cuadrature formulae of Newton-Cotes type. Cuadratures of Gauss and Cebasev types. 5. Numerical solutions of some classes of operatorial equations: direct and iterative methods for solving systems of linear equations (Gauss, Jacobi, Gauss-Seidel, multigrid). 6. Solving numericaly some equations on R using Newton-Raphson method, secant method, combined methods. Methods for solving nonlinear equations on Rn and methods for solving differential equations. 7. The application of the presented methods at concrete problems derived from Phisics, Biology, etc.
 References 1. Gh. Coman, Analiza numerica, Ed. Libris, Cluj-Napoca, 1995. 2. D.D. Stancu, Analiza numerica, curs si culegere de probleme, Univ. Babes-Bolyai Cluj-Napoca, 1977 (lito). 3. O. Agratini, I.Chiorean, Gh.Coman, R.Trambitas,Analiza numerica si teoria aproximarii(vol.III), Presa Univ.Clujeana, 2002 4. P. Blaga, Gh. Coman, R. Trambitas, D. Vasaru, S. Pop, Analiza numerica, lucrari de laborator, Univ. Babes-Bolyai Cluj-Napoca, 1995 (lito). 5. A.O. Gelfand, Calculul cu diferente finite, Ed. Tehnica Bucuresti 1956. 6. B.P. Demidovici, A. Macon, Elements de calcul numerique, Ed. Mir, Moscou, 1979.
 Assessment Exam.