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Lecturer(s)
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Brzezina Miroslav, doc. RNDr. CSc., dr. h. c.
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Černá Dana, doc. RNDr. Ph.D.
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Course content
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Lectures: 1. Numerical methods - numerical model, sources of error, numerical stability, speed of computation. Paralellelization of numerical computations - basic models of parallel programming, methods of parallelization, Amdahl's law. 2. Direct methods for solving linear systems - Gaussian elimination, Gaussian elimination for tridiagonal matrix, LU decomposition, Choleski decomposition. 3. Iterative methods for solving linear systems - Jacobi method, Gauss-Seidel method, successive over-relaxation, conjugate gradient method. 4. Solving rectangular linear systems - normal equations system, singular value decomposition, pseudoinverse matrix. 5. Solving nonlinear equations - fixed-point iteration, the secant method, Newton's method. 6. Interpolation - Lagrange and Hermite interpolation, splines. 7. Numerical integration - the rectangular rule, the trapezoidal rule, Simpson's rule. 8. Numerical solution of ordinary differential equations with initial value problems - the transformation of a n-th order differential equation into a system of n simultaneous equations of the first order. One-step methods - Euler methods, Runge-Kutta methods. Stiff differential equations. 9. Boundary value problems - finite difference method. 10. classification of second-order partial differential equations. Numerical solution of elliptic partial differential equations - finite difference method. 11. Numerical solution of parabolic partial differential equations - finite difference method, method of lines, Rothe method. 12. Numerical solution of hyperbolic partial differential equations - finite difference method, method of lines.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Written assignment presentation and defence
- 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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Metric and normed spaces, Banach fix-point theorem, numerical methods, boundary value problems for 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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Oral exam, Written exam
Credit: Working out a semestral work. Exam: Written.
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Recommended literature
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NEKVINDA, M., ŠRUBAŘ, J., VILD, J. Úvod do numerické matematiky. Praha, 1976.
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