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| TANA39 | Numerical Methods, 4 p (sw) /Numeriska metoder/ Advancement level: B | |
| Aim: The aim of the course is to give basic knowledge about numerical methods for solving mathematical problems, with applications in science and technology . The course also intends to give practical familarity with numerical computations on calculators and computers.Prerequisites: TATM 72 Calculus A. TATM 73 Calculus B. TATM 31 Linear Algebra. TDDB 18 Introduction to Programming in Ada.Supplementary courses: TANA 70 Fortran. TANA 25 Numerical Methods II. TANA 77 Programming of Parallel Computers, scientific computations.Course organization: The theory is mainly presented at the lectures. The lessons emphasize problem solving with calculators. The purpose of the computer exercises is to study numerical problem solving with computers. Attention is concentrated on how to analyze results and how to compare mathematically, but not numerically, equivalent methods with respect to 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. 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. Department of Mathematics, 1995. Elfving, T., Eriksson, J., Ouchterlony, U., Skoglund, I.: Numerisk analys en exempelsamling. Studentlitteratur. From the department: Instructions for the computer exercises. | ||
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