VŠTE:BSA_ZMM Basics of mathematical modelin - Course Information

BSA_ZMM Basics of mathematical modeling

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/A3: Sat 13. 4. 14:50–16:20 D415, 16:30–18:00 D415, Sun 21. 4. 9:40–11:10 D415, 11:25–12:55 D415, 13:05–14:35 D415, Sun 19. 5. 9:40–11:10 D415, 11:25–12:55 D415, 13:05–14:35 D415, Z. Dušek
BSA_ZMM/P01: Mon 9:40–11:10 E4, Z. Dušek
BSA_ZMM/S01: Tue 13:05–14:35 N010, 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

• Kalman, D.: Elementary Mathematical Models, MAA, 1997
• Dušek, Z.: Základy matematického modelováni, VŠTE, studijní opora

Forms of Teaching

Lecture
Seminar
Tutorial

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.

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.

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