| TANA61 | Scientific Computing part 1, ECTS-points /Tekniska beräkningar del 1/ Advancement level: B | |
| Aim: The course provides basic knowledge about numerical methods for solving mathematical problems, with applications in technology and science. Special attention is paid to matters concerning accuracy and efficiency. The course also gives practical familarity with numerical computations on calculators and computers.Prerequisites: TATM 06 Calculus. TATM 18 Linear Algebra. TSRT01 Introduction to MATLAB.Supplementary courses: TANA 70 Fortran. TANA 50 Numerical Methods II. TANA 60 Numerical solution of partial differential equations. TANA 77 Programmering av parallelldatorer, tekniska beräkningar.Course organization: The theory is presented in the lectures. The exercises exemplifies the theory. The computer exercises investigates important numerical properties of algorithms and software.Course content: Error analysis: Sources of errors and error propagation. Cancellation. Floating point arithmetic. The machine constant. Linear Algebra: Gaussian elimination with applications. The LR-factorization. Special matrices. Norms, perturbation theory and condition numbers. The least squares method. The normalequations. The QR factorization. Interpolation by polynomials with error analysis. Interpolation by cubic splines. Approximation by Bezier polynomials.Course literature: Eldén, L., Wittmeyer-Koch, L.: Numerisk analys en introduktion (med formelsamling). Studentlitteratur. The English edition.: Eldén, L., Wittmeyer-Koch, L.: Numerical Analysis an Introduction. Department of Mathematics, 1995. Elfving, T., Eriksson, J., Ouchterlony, U., Skoglund, I.: Numerisk analys en exempelsamling. Studentlitteratur. From the deaprtment: Instruction for the computer exercises. | ||
| LAB1 | Computer exercises, 1,5 p. | |