| studiehandbok@lith | |
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| TANA55 | Numerical Methods, 5 p (sw) /Numeriska metoder med Matlab/ 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: Calculus, Linear Algebra and Introduction to ProgrammingSupplementary courses: TANA 50 Numerical Methods II, TANA 70 FortranCourse content: Error Analysis: Sources of Error and Error Propagation.Cancellation. Floating Point 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. | ||
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