This course is an introduction to "Numerical Analysis " oriented towards computational solution of problems in engineering and sciences. With relative mathematical rigor, it introduces the student to modeling certain typical problems and to the development of methods to solve them on the computer. Introduces the fundamentals of floating point computer calculations and their implications for the accuracy of the obtained solutions. It emphasizes the errors of the methods and their computational efficiency . Furthermore, the student is informed on the existence and use of Numerical Libraries (eg. LAPACK, EISPAC, MINPACK, ODEPACK, SLATEC, NAG, IMSL, MARTRAN), graphic libraries (eg. PGPLOT, MUESLI, DISLIN) and Algebraic Systems (eg. Octave, Scilab, Matlab) with the emphasis on Free and Open Source Software.
(1) modeling typical problems in engineering
(2) developing methods to solve these problems on a computer
(3) knowledge of floating point operations in and their impact on computer calculations
(4) knowledge of the errors committed by numerical methods
(5) knowledge of computational efficiency and effectiveness of numerical methods
(6) information on the existence and use of Numerical Libraries and other related tools
Course Content (Syllabus)
Errors, Root finding, Interpolation , Numerical integration, Numerical Linear Algebra and especially Solving Systems of Linear Equations with exact (direct) and iterative methods , Numerical Solution of Ordinary Differential Equations and Function Fitting by Least Squares and Householder Factorization.
Errors, Root finding, Interpolation, Numerical integration, Numerical Linear Algebra, Numerical Solution of Ordinary Differential Equations, Least Squares, Householder Factorization