Course: Mathematical Modelling Methods 2

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Course title Mathematical Modelling Methods 2
Course code KMA/MMM2
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Čepička Jan, Ing. Ph.D.
  • Holubová Gabriela, Doc. Ing. Ph.D.
  • Looseová Iveta, Ing.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
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.

Learning activities and teaching methods
Multimedia supported teaching, Task-based study method, Lecture, Practicum
  • Contact hours - 65 hours per semester
  • Preparation for an examination (30-60) - 30 hours per semester
  • Preparation for formative assessments (2-20) - 20 hours per semester
  • Preparation for comprehensive test (10-40) - 25 hours per semester
prerequisite
professional knowledge
There is no prerequisite for this course. Students should be familiar with a high school algebra and trigonometry.
learning outcomes
The student is able to understand and to describe the basic laws in nature sciences by mathematical tools.
teaching methods
Lecture
Practicum
Multimedia supported teaching
Task-based study method
assessment methods
Combined exam
Test
Recommended literature
  • Drábek, Pavel; Míka, Stanislav. Matematická analýza I. 1. vyd. Plzeň : Západočeská univerzita, 1995. ISBN 80-7082-217-1.
  • Gillman, Leonard; McDowell, Robert H. Matematická analýza. 1. vyd. Praha : SNTL, 1980.
  • Míka, S. Speciální učební texty. Systém TRIAL, KMA ZCU.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Education - (16) Pedagogy, teacher training and social care 1 Summer
Faculty of Education Physics in Education (14) Physics courses 1 Summer
Faculty of Education Information Technologies in Education (14) Informatics courses 1 Summer
Faculty of Education Biology in Education (13) Biology courses 1 Summer
Faculty of Education Studies in Mathematics (16) Mathematics courses 1 Summer
Faculty of Education Information Technologies in Education (16) Informatics courses 1 Summer
Faculty of Education Chemistry in Education (15) Chemistry courses 1 Summer
Faculty of Education Geography in Education (13) Pedagogy, teacher training and social care 1 Summer
Faculty of Education Physical Education in Education (17) Physical education and sport 1 Summer
Faculty of Education Biology in Education (16) Biology courses 1 Summer
Faculty of Education Physics in Education (16) Physics courses 1 Summer
Faculty of Education Geography in Education (16) Pedagogy, teacher training and social care 1 Summer
Faculty of Education Information Technologies in Education (15) Informatics courses 1 Summer
Faculty of Education Geography in Education (14) Pedagogy, teacher training and social care 1 Summer
Faculty of Education Information Technologies in Education (13) Informatics courses 1 Summer
Faculty of Education Studies in Mathematics (14) Mathematics courses 1 Summer
Faculty of Education Information Technologies in Education (17) Informatics courses 1 Summer
Faculty of Education Chemistry in Education (13) Chemistry courses 1 Summer
Faculty of Education Geography in Education (1) Pedagogy, teacher training and social care 1 Summer
Faculty of Education Studies in Mathematics (1) Mathematics courses 1 Summer
Faculty of Education Biology in Education (17) Biology courses 1 Summer
Faculty of Education Physics in Education (15) Physics courses 1 Summer
Faculty of Education Physics in Education (13) Physics courses 1 Summer
Faculty of Education Chemistry in Education (17) Chemistry courses 1 Summer
Faculty of Education Geography in Education (17) Pedagogy, teacher training and social care 1 Summer
Faculty of Education Chemistry in Education (14) Chemistry courses 1 Summer
Faculty of Education Biology in Education (14) Biology courses 1 Summer
Faculty of Education Geography in Education (15) Pedagogy, teacher training and social care 1 Summer
Faculty of Education Studies in Mathematics (15) Mathematics courses 1 Summer
Faculty of Education Physical Education in Education (1) Physical education and sport 1 Summer
Faculty of Education - (17) Pedagogy, teacher training and social care 1 Summer
Faculty of Education Chemistry in Education (16) Chemistry courses 1 Summer
Faculty of Education Studies in Mathematics (13) Mathematics courses 1 Summer
Faculty of Education Physics in Education (17) Physics courses 1 Summer
Faculty of Education Studies in Mathematics (17) Mathematics courses 1 Summer
Faculty of Education Biology in Education (15) Biology courses 1 Summer