Course objectives:
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The aim of the course is to make the students familiar with the following topics: The way from a mathematical model to computer program, problems connected with the implementation of numerical algorithms on computer, computational environment and its effect on mathematical software (MS). Properties of computer arithmetic and their consequences for the quality of MS, examples of computational difficulties. Well- and ill-conditioned numerical problems, stable and unstable algorithms, examples. Searching for MS on the Internet, sources of quality MS.
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Requirements on student
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Term project: computational solution of a set of
numerical problems using given MS, evaluation of the results obtained.
Credit
Most homework assigned C at least, a preliminary protocol of the term project shown, participance at the written exam.
Examination
The written part will take place in the first half of the examination period (max. 2 hours). At the end of the period an oral exam that will be oriented to the general knowledge. No practical computations during the oral exam but the term project will be discussed to some detail. The classification will depend on the student's homework, the test written, and the quality of the term project as well.
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Content
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Approximate time schedule: first third of the term - general properties of the mathematical software (MS) and the basic features of its use, the condition of a numerical problem, properties of a finite precision arithmetics; second third - computational environment and its influence on MS, the properties of the machine arithmetics and its effect on MS, reliability and credibility of MS; the final third - properties of quality MS, a more detailed analysis of the topics of the course on the example of MS for automatic quadrature or for automatic solution of ordinary differential equations. During the term the students will be given information on quality MS on the Internet and on other resources that may be useful in the field of MS and scientific computing.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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52
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Graduate study programme term essay (40-50)
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40
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Preparation for an examination (30-60)
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45
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Total
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137
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
Knowledge of the fundamentals of numerical analysis and algebra,
undergraduate calculus, working knowledge of Matlab or ability to use a
high-level programming language (Fortran, C). |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
Upon the completion of the course the student will:
- know the fundamental mathematical software and be able to use it
- be able to discuss the condition of the numerical problems and stability of computational algorithms
- know the properties of the finite precision arithmetics
- be able to judge the credibility of the results obtained |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
Written exam |
Test |
Seminar work |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Lecture supplemented with a discussion |
Interactive lecture |
Practicum |
Textual studies |
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