| TANA55 | Numerical Methods, 7,5 ECTS credits. /Numeriska metoder med Matlab/ |
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Prel. scheduled
hours: 66 |
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Area of Education: Science Subject area: Mathematics |
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| Advancement level
(A-D): B
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| 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. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) Calculus, Linear Algebra and Introduction to Programming Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding. |
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| Supplementary courses: TANA50 Numerical Methods II, TANA70 Fortran |
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| Organisation: Lectures, exercises and laborations. |
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| Course contents: 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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| Course literature: L Eldén, L Wittmeyer-Koch: Numeriska beräkningar- analys och illustrationer med Matlab. Studentlitteratur. T Elfving, J Eriksson, U Ouchterlony, I Skoglund: Numeriska beräkningar - en exempelsamling. Studentlitteratur. From the department: Formulary, computer assignments etc. |
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| Examination: | |||
| Written examination Computer exercises |
3 p 2 p |
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Course language is Swedish. Department offering the course: MAI. Director of Studies: Tommy Elving Examiner: Ingegerd Skoglund Link to the course homepage at the department Course Syllabus in Swedish |
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