VŠTE:BSA_ZMM Základy matem. modelov. - Course Information
BSA_ZMM Základy matematického modelování
Institute of Technology and Business in České Budějovicesummer 2022
- Extent and Intensity
- 2/2/0. 5 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Zdeněk Dušek, Ph.D. (seminar tutor)
- Guaranteed by
- doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice - Timetable of Seminar Groups
- BSA_ZMM/A1: Sun 6. 3. 13:05–14:35 E5, 14:50–16:20 E5, Sat 2. 4. 14:50–16:20 E5, 16:30–18:00 E5, Sat 14. 5. 14:50–16:20 E5, 16:30–18:00 E5, Sat 21. 5. 14:50–16:20 E5, 16:30–18:00 E5, Z. Dušek
BSA_ZMM/P01: Mon 8:00–9:30 B3, Z. Dušek
BSA_ZMM/S01: Mon 9:40–11:10 D515, Z. Dušek - Course Enrolment Limitations
- The course is offered to students of any study field.
- Course objectives supported by learning outcomes
- The student will gain theoretical knowledge and practical skills needed in related subjects. After completing the course, the student will independently solve basic problems from the subject matter and is able to apply them to practical problems.
- Learning outcomes
- Upon successful completion of the course, the student: 1. is able to analyze simple problems related to the topics discussed, 2. can independently design ways to solve basic problems, 3. manages to solve tasks related to the issue of sequences and series, 4. masters the basic principles of mathematical modeling using the apparatus of differential equations of type models, 5. is familiar with the issues of logistics modeling.
- Syllabus
- Lectures: 1. Arithmetic and geometric sequences, differential and functional equations of sequence. 2. Sequence of partial sums, sum of geometric series. 3. Applications of arithmetic sequences - models with linear growth. 4. Application of geometric sequences - models with exponential growth, resp. exponential decay. 5. Models with quadratic growth, finding the optimal point. 6. Logarithmic and exponential functions, logarithmic representation of data, logarithmic scales - examples. 7. Cleaning the tank by draining and filling, cleaning the pond with a continuous flow. 8. Mixed models - drug dosing during its simultaneous degradation, mortgage repayment. 9. Logistic models - population growth with limited resources. 10. Limits of validity of the logistics model. 11. Logistic model in the current catch, hunter-prey model. 12. General properties of logistic models with catch. 13. Chaos in logistics models. Seminars: 1. Arithmetic and geometric sequences, differential and functional equations of sequence. 2. Sequence of partial sums, sum of geometric series. 3. Applications of arithmetic sequences - models with linear growth. 4. Application of geometric sequences - models with exponential growth, resp. exponential decay. 5. Models with quadratic growth, finding the optimal point. 6. Logarithmic and exponential functions, logarithmic representation of data, logarithmic scales - examples. 7. Cleaning the tank by draining and filling, cleaning the pond with a continuous flow. 8. Mixed models - drug dosing during its simultaneous degradation, mortgage repayment. 9. Logistic models - population growth with limited resources. 10. Limits of validity of the logistics model. 11. Logistic model in the current catch, hunter-prey model. 12. General properties of logistic models with catch. 13. Chaos in logistics models.
- Literature
- required literature
- KALMAN, D., 1997. Elementary Mathematical Models, Order Aplenty and a Glimpse of Chaos. [s. l.]: Mathematical Association of America. ISBN 978-0-88385-707-6.
- VER, P. J. a Ch. SHAKIBAN, 2018. Applied Linear Algebra. [s. l.]: Springer. ISBN 978-3-319-91041-3.
- LAY, D. C., S. R. LAY a J. J. McDONALD, 2016. Linear Algebra and its Applications. [s. l.]: Pearson Education Limited. ISBN 978-1-292-09223-2.
- HUSAR, P., 2016. Maturitní otázky z matematiky, [s. l.]: Praha, Petr Husar - Zkoušky nanečisto. ISBN: 978-80-270-1981-6.
- recommended literature
- MEERSCHAERT, M., 2013. Mathematical Modeling. [s. l.]: Elsevier. ISBN 978-0-12-386912-8.
- DYM, C. L., 2004. Principles of Mathematical Modeling. [s. l.]: Elsevier. ISBN 0-12-226551-3.
- ODVÁRKO, O., 2008. Matematika pro gymnázia: posloupnosti a řady, [s. l.]: Praha, Prometheus, 2008, ISBN: 978-80-7196-391-2.
- HRUŠKA, M., 2012. Státní maturita z matematiky v testových úlohách včetně řešení, [s. l.]: Olomouc, Rubico. ISBN: 80-7346-149-2.
- Forms of Teaching
- Lecture
Seminar - Teaching Methods
- Frontal Teaching
Brainstorming
Critical Thinking
- Student Workload
Activities Number of Hours of Study Workload Daily Study Combined Study Preparation for the Mid-term Test 10 10 Preparation for Lectures 24 Preparation for Seminars, Exercises, Tutorial 24 84 Preparation for the Final Test 20 20 Attendance on Lectures 26 Attendance on Seminars/Exercises/Tutorial/Excursion 26 16 Total: 130 130 - Assessment Methods and Assesment Rate
- Test – mid-term 30 %
Test – final 70 % - Exam conditions
- To successfully complete the course, it is necessary to achieve a total of at least 70% of the ongoing and final evaluation under the conditions set out below. In the continuous evaluation, 30 points can be obtained, ie 30%. In the final evaluation, a total of 70 points can be obtained, ie 70%. Overall classification of the course, ie points for the final evaluation (70 - 0) + points from the continuous evaluation (30 - 0): A 100 - 90, B 89,99 - 84, C 83,99 - 77, D 76,99 - 73, E 72.99 - 70, FX 69.99 - 30, F 29.99 - 0. The student of the full-time form of study is obliged to fulfill the obligatory 70% attendance at the contact teaching, ie everything except lectures. If the participation is not met, the student will be automatically classified "F".
- Language of instruction
- Czech
- Teacher's information
- Attendance at classes in all forms is governed by a separate internal standard of VŠTE (Records of student attendance at VŠTE). For full-time students, 70% attendance is required for contact classes, ie everything except lectures.
- Enrolment Statistics (summer 2022, recent)
- Permalink: https://is.vstecb.cz/course/vste/summer2022/BSA_ZMM