| Course Unit Code | 310-3147/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| KUC14 | prof. RNDr. Radek Kučera, Ph.D. |
| Summary |
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| The aim of the course is to provide an overview of mathematical modeling using ordinary differential equations. The course is focused on the use of these models in practical engineering tasks. Students will acquire skills and competences that will enable them to understand the description of selected models and solve them using analytical or numerical methods. |
| Learning Outcomes of the Course Unit |
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| The course deals with mathematical modeling based on ordinary differential equations. Students will acquire advanced knowledge and skills of given parts of mathematics adapted to the needs of practical modeling in engineering practice. The course is focused on analytical and numerical solution of ordinary differential equations. |
| Course Contents |
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1. Introduction, basic terminology, motivational examples.
2. Systems of ordinary differential equations, Cauchy's problem.
3. Elimination method.
4. Euler method.
5. Method of constant variance.
6. Boundary value problems for ordinary differential equations.
7. Application examples for analytical methods.
8. One-step numerical methods.
9. Multi-step numerical methods.
10. Calculations with controlled accuracy.
11. Taylor series method.
12. Method of shooting.
13. Application examples for numerical methods.
14. Final summary, evaluation, reserve. |
| Recommended or Required Reading |
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| Required Reading: |
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| M.T.Heath: Scientific Computing. An Introductory Survey, McGraw-Hill, New York, 2002. M.T.Heath: Scientific Computing. An Introductory Survey, McGraw-Hill, New York, 2002. |
Krajc, B., Beremlijski, P.: Obyčejné diferenciálni rovnice. http://mi21.vsb.cz.
Kučera, R.: Numerická matematika pro Aplikované vědy a technologie. VŠB – TU Ostrava, skriptum, 2016.
Čermák, L.: Numerické metody pro řešení diferenciálních rovnic. VUT Brno, skriptum, 2020 . (https://math.fme.vutbr.cz/Home/cermakl/soubory-ke-stazeni)
Chapra, S., Canale, R.: Numerical Methods for Engineers. McGraw-Hill Education, 2009. |
| Recommended Reading: |
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| Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003. |
| M.T.Heath: Scientific Computing. An Introductory Survey, McGraw-Hill, New York, 2002. M.T.Heath: Scientific Computing. An Introductory Survey, McGraw-Hill, New York, 2002. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 20 | 5 |
| Examination | Examination | 80 | 51 |