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FP-NUMAcad. year: 2022/2023
Students will become familiar with the analysis of basic problems of numerical mathematics and suitable algorithms for their solution. The introductory part of the course is intended for familiarization with algorithm designs, data abstraction and their implementation so that students think about the use of computing resources algorithmically and thus be able to effectively use program resources for data processing in the future.Subsequently, the student will be introduced to some numerical methods (approximation of functions, solution of nonlinear equations, approximate determination of derivative and integral, solution of differential equations) suitable for modeling various problems of economic practice.
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Number of ECTS credits
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Learning outcomes of the course unit
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Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Credit requirements:Preparation and submission of a seminar paper, which will be graded at least "E". Assignment of the seminar work will be published in the news and on e-learning.
The exam is written and lasts 1 hour. If the student does not achieve at least 60% of the total number of attainable points, the written part and the entire exam are graded "F".
Individual study plan:Credit requirements:Preparation and submission of a seminar paper, which will be graded at least "E". Assignment of the seminar paper will be published in the news and on e-learning.
Course curriculum
An overview of the general principles and types of calculation methods used in applications of differential and integral calculus, linear algebra and differential equations with an emphasis on the issue of their errors, convergence and stability of calculations:
The concept of an algorithm and the complexity of an algorithm (algorithm, basic properties, flow diagram, cycles with a constant number of repetitions, with a condition at the beginning and end of the cycle)Characterization of calculation methods, errors and their classification, convergence and stability, repetition of the course of the function,Solving nonlinear equationsSolving linear systemsRoots of polynomials, use of Horner's scheme, interpolationApproximation of functionsNumerical integration and derivationNumerical solution of differential equationsGraph theory I (introduction – undirected, directed and graded graphs)Graph Theory II (Dijkstra's shortest path algorithm, Kruskal's algorithm)Differential equationMonte Carlo methodsFinal summary
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Participation in exercises is controlled.
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Basic literature
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Elearning
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Lecture
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Syllabus
1. The concept of an algorithm and the complexity of an algorithm (algorithm, basic properties, flowchart, cycles with a constant number of repetitions, with a condition at the beginning and end of the cycle)2. Graphs (undirected, directed and graded, Dijkstra's shortest path algorithm, Kruskal's algorithm)3. Characterization of calculation methods, errors and their classification, convergence and stability4. Solving nonlinear equations5. Roots of polynomials, use of Horner's scheme6. Solving linear systems7. Interpolation8. Approximation of functions9. Numerical integration and derivation10. Numerical solution of differential equations11. Differential equation12. Monte Carlo methods.13. Final summary
Exercise