| TANA43 | Numerical Algoritms, ECTS-points /Numeriska algoritmer för D/ 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 computer implementation of algorithms, especially implementation of mathematical functions. The course also gives practical familarity with numerical computations on calculators and computers.Prerequisites: TATM 03 Calculus, TATM 18 Linear Algebra, TDDB 92 Computer ProgrammingCourse organization: The course consists of lectures, lessons and computer exercises. The theory is mainly presented in the lectures. The lessons emphasize problem solving with calculators. In the computer exercises attention is concentrated on how to analyse results and to study implementation issues in order to obtain both good accuracy and efficiency.Course content: Error Analysis: Sources of Error and Error Propagation. Cancellation. Floating Point Arithmetic. IEEE Arithmetic. Numerical Remainder Term Estimates for Series. Computation of Elementary Functions. Non-linear Equations: The Bisection Method. Newton-Raphson's Method. The Secant Method. Error Estimation. Convergence Criteria and Rate of Convergence in Fixed Point Iteration. Interpolation: Newton's Interpolating Polynomial. Spline Interpolation. Numerical Differentiation. Difference Approximation of Derivatives. Richardson Extrapolation. Numerical Integration: The Trapezoidal rule and Romberg's Method. Generalized Integrals. Linear Algebra: Gaussian Elimination with Applications. LU-Decomposition. Perturbation Theory. Overdetermined Linear Systems and the Least Squares Method. Initial Value Problems: Euler's Method and Runge-Kutta Methods. Boundary Value Problems: The Finite Difference Method. 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. . Academic Press, 1990. Elfving, T., Eriksson, J., Ouchterlony, U., Skoglund, I.: Numerisk analys en exempelsamling. Studentlitteratur. From the department: Instructions for the computer exercises | ||
| TEN1 | , 3 p. | |
| LAB1 | , 0,5 p. | |