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Course info
KMA / MMM2
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Course description
Department/Unit / Abbreviation
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KMA
/
MMM2
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Mathematical Modelling Methods 2
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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-
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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-
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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KMT/MMM2
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The aim of this course is to provide the students basic mathematical tools for the description and modeling of laws and quantities of nature and to learn them to solve basic problems from application fields. Last but not least, we try to provide the future teachers of mathematics, physics, biology, chemistry, geography the necessary mathematical background for a modern analysis of problems from the above stated areas.
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Requirements on student
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Tests during the term;
written and oral exam
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Content
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1. Sequence as a model of a discrete system - recurrence and difference equation. Sequence as a mathematical object - algebra and properties, convergence and divergence. Sequence of partial sums - infinite sums. Sequences in finance, biology and social sciences.
2. Function as a model of a continuous system - basic functions, graphs, diagrams. Function operations, continuity, composed function. Local properties. Function as a tool of description of natural and economic quantities and dependences.
3. Fundaments of differential calculus - difference, differential, derivative. Methods of differentiation. Modeling of changes in natural sciences, economy and social sciences.
4. Methods of differential calculus - basic optimization, formulation of basic natural laws. Primitive function and methods of solving simple differential equations. Potential.
5. Definite integral as a model of a balance principle. Properties and methods of calculations. Integral sum - geometric and physical interpretation.
6. Local polynomial approximation of a function - Taylor formula, derivatives and differentials of higher orders, simple approximate calculations.
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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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65
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Preparation for comprehensive test (10-40)
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25
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Preparation for formative assessments (2-20)
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20
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Preparation for an examination (30-60)
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30
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Total
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140
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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: |
There is no prerequisite for this course. Students should be familiar with a high school algebra and trigonometry. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
The student is able to understand and to describe the basic laws in nature sciences by mathematical tools. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Test |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Multimedia supported teaching |
Task-based study method |
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