| TANA25 | Numerical Methods II, 4,5 ECTS credits. /Numeriska metoder II/ |
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Area of Education: Subject area: |
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| Advancement level
(A-D): C
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| Aim: The student should be able to understand and apply modern techniques for solving important computational problems in Science and Technology. Another purpose is to give knowledge about the use of commercial software for scientific computations. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) Numerical Methods I / Numerical Algorithms. A Basic Programming course. 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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| Organisation: The course consists of lectures, lessons and computer exercises. |
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| Course contents: Linear Algebra: LU-factorization. Perturbation Theory. The Singular Value Decomposition and the Pseudoinverse. Orthogonal transformations using the Householder and the Given´s methods. The QR decomposition and the Least Squares Problem. The Eigenvalue Problem: Normal forms. Perturbation Theory and error estimates. The Rayleigh quotient. The Power method and Inverse Iteration. Transformation to Hessenberg and tridiagonal form. The QR-algorithm. Systems of nonlinear equations and nonlinear least squares problems. The Newton and Gauss-Newton methods. Ordinary Differential Equations: Runge-Kutta methods. Multistep methods. Errror estimates and step lenght control. Difference equations. Stability and Convergence. Methods for stiff systems. |
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| Course literature: G. Dahlquist and �.ke Björck: Numerical Methods and Scientific Computations, Volume 2. (manuscript from the Department of Mathematics) |
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| Examination: | |||
| Written examination Laboratory work |
2 p 1 p |
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Course language is English/swedish. Department offering the course: MAI. Director of Studies: Examiner: Tommy Elfving Course Syllabus in Swedish |
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