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Lecturer(s)
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Pavlišta Martin, Ing. Ph.D.
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Janíček Petr, doc. RNDr. Ph.D.
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Course content
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1. týden: The propagation of errors during calculation. Systems of linear equations. Gauss elimination method. 2. týden: Method of factorization. inverse and determinant of a matrix. Iterative methods. 3. týden: Finding roots of one non-linear equation. 4. týden: Finding roots of a system of non-linear equations. Newton-Raphson method. Conversion to optimization problem. 5. týden: Interpolation, numerical differentiation and integration. Newton-Cotes quadrature formulae. 6. týden: 1st test on PC. 7. týden:Richardson's extrapolation, Gauss integration. 8. týden: Fitting of experimental data. Linear regression. 9. týden: Fitting of experimental data. Non-linear regression. 10. týden: Ordinary differential equation. Runge-Kutta methods. 11. týden: Numerical integration of ODEs. Multistep methods. 12. týden: Boundary values problem. Finite difference method. Introduction to finite element method. 13. týden: 2nd test on PC.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Skills training
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Learning outcomes
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The course provides students with basic knowledge of numerical methods such as approximation of functions (Lagrange's interpolation polynomial), splines, numerical differentiation, numerical integration, numerical methods of linear algebra, methods of solving nonlinear equations and systems, numerical methods for ordinary differential equations, and difference schemes for partial differential equations. Theoretical fundamentals are explained and practical applications are exercised on personal computers using standard software (MS Excel and MATLAB).
The student will be ready to use the numerical methods in solving practical problems.
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Prerequisites
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Basic knowledge of linear algebra, differential and integral calculus of one and several variables.
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Assessment methods and criteria
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Oral examination, Written examination
Two tests - solving problems on PC. Oral examination.
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Recommended literature
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Billo, E. Joseph. Excel for scientists and engineers : numerical methods. Hoboken: John Wiley & Sons, 2007. ISBN 978-0-471-38734-3.
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Epperson, James F. An introduction to numerical methods and analysis. New York: John Wiley & Sons, 2002. ISBN 0-471-31647-4.
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Sauer T. Numerical Analysis. Pearson Addison Wesley, 2006.
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