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Lecturer(s)
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Černá Dana, doc. RNDr. Ph.D.
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Course content
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Lectures: 1. Numerical methods - basic concepts, speed of computation, parallelization. 2. Basic concept of numerical linear algebra, conditioning of matrices, Gaussian elimination - complexity, stability, pivotation, tridiagonal matrices. 3. LU decomposition and Cholesky decomposition. 4. Iterative methods - Jacobi method. 5. Gauss-Seidel method, successive over-relaxation. 6. Solving rectangular linear systems - normal equations system, singular value decomposition, pseudoinverse matrix. 7. Numerical solution of nonlinear equations - bisection method, the secant method, Newton's method. 8. Interpolation - Lagrange and Hermite interpolation. 9. Spline interpolation. 10. Numerical integration - the rectangular rule, the trapezoidal rule, Simpson's rule. 11. Numerical methods for computation of derivatives. 12. Numerical solution of initial value problems - basic concepts, the transformation of the n-th order differential equation into a system of n simultaneous equations of the first order. 13. One-step methods for initial value problems. 14. Reserve, revision.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 56 hours per semester
- Preparation for credit
- 15 hours per semester
- Semestral paper
- 20 hours per semester
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Learning outcomes
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Construction of the mathematical and numerical model. Basic approximate and numerical methods: Methods of linear algebra, interpolation, and quadrature, solution of nonlinear equations. Euler method for solving ordinary differential equations.
Knowlige of fundamentals of numerical mathematics.
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Prerequisites
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Passing of mathematical lectures of first four semestrs.
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Assessment methods and criteria
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Written exam
Exam: Written.
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Recommended literature
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Duintjer Tebbens E. J. ,Hnětynková I.,Plešinger M.,Strakoš Z.,Tichý P. Analýza metod pro maticové výpočty: Základní metody. Matfyzpress, 2012.
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Ueberhuber, Ch. W.:. Numerical Computation 1, 2.. Berlin, Springer-Verlag, 1997.
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Vitásek, E.:. Numerické metody.. Praha, SNTL, 1987.
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