| TANA62 | Scientific Computing part 2, ECTS-points /Tekniska beräkningar del 2/ 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. TANA61 Scientific Computing, part 1.Supplementary courses: TANA 70 Fortran. TANA50 Numerical Methods II. TANA60 Numerical solution of partial differential equations. TANA 77 Programmering av parallelldatorer, tekniska beräkningar.Course organization: The theory is presented in the lectures. The exercises exemplify the theory. The computer exercises investigate numerical properties of algorithms and software.Course content: Error analysis: Error propagation on computer arithmetic. Solution of nonlinear equations: The bisection method. Newton's method. The secant method. Error estimation. Theory of fixed point iteration. Numerical differentiation: Difference approximation of derivatives. Richardson extrapolation. Numerical integration: The trapezoidal rule and Romberg's method. Generalized integrals. The initial value problem: Euler's method and Runge Kutta methods. The boundary value problem: The finite difference method.Course literature: Eldén, Wittmeyer-Koch: Numerisk analys en introduktion (med formelsamling). Studentlitteratur. The English edition: Eldén, Wittmeyer-Koch: Numerical Analysis an Introduction. Department of Mathematics, 1995. Elfving, Eriksson, Ouchterlony, Skoglund: Numerisk analys en exempelsamling. Studentlitteratur. From the department: Instructions for the computer exercises. | ||
| TEN1 | Written examination, 2,5 p. | |
| LAB1 | Laboratory work, ,5 p. | |