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Course info
KMA / M2S
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Course description
Department/Unit / Abbreviation
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KMA
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M2S
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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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Mathematics 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,
4
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
2
[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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Czech
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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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287 / -
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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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Czech
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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 |
Yes
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Fundamental course |
Yes
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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KMA/ZME2
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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 an introduction to the concepts of advanced mathematical analysis such as:
- integral calculus of functions of one real variable;
- Taylor and Fourier series;
- differential equations of the 1st order and systems of differential equations of the 1st order;
- differential models of dynamical systems;
- functions of more variables;
- differential calculus of functions of more variables.
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Requirements on student
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Use rigorous arguments in calculus and be able to apply them in solving problems on the topics in the syllabus.
Credit: written tests during the term (required at least 60%)
Exam: witten and oral part.
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Content
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Week 1-2: Indefinite integral (recapitulation), definite integral; applications of integral calculus in solving physical problems.
Weeek 3: Taylor and Fourier expansion of a function.
Week 4-5: ODEs of the 1st order, nonlinear, linear. General and particular solutions, singular solutions. Formulation of the initial value problem. Methods of solving ODEs of the 1st order: direct integration, separation of variables, variation of parameters.
Week 6: Linear ODEs of higher orders - homogeneous, nonhomogeneous, with constant coefficients. Method of characteristic equation.
Week 7: Variation of parameters. Estimate of particular integral.
Week 8: Boundary value problems. Eigenvalue problems.
Week 9: Systems of ODEs of the 1st order.
Week 10-11. Functions of more variables and their properties.
Week 12: Introduction to differential calculus of functions of more variables. Partial derivatives, gradient.
Week 13: Recapitulation.
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Activities
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Fields of study
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Guarantors and lecturers
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Guarantors:
Ing. Jan Čepička, Ph.D. (100%),
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Lecturer:
Ing. Jan Čepička, Ph.D. (100%),
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Tutorial lecturer:
Doc. Ing. Radek Cibulka, Ph.D. (100%),
Ing. Jan Čepička, Ph.D. (100%),
RNDr. Milena Šebková (100%),
RNDr. Jonáš Volek, Ph.D. (100%),
Mgr. Radek Výrut (100%),
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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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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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32
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Contact hours
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52
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Total
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104
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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: |
rozpoznat logické symboly, výroky a kvantifikátory |
popsat posloupnost a řadu reálných čísel |
popsat spojitou a inverzní funkci |
popsat limitu funkce jedné reálné proměnné |
popsat derivaci funkce jedné reálné proměnné |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
nakreslit graf základních funkcí (algebraické, goniometrické, exponenciální a hyperbolické) |
vypočítat limitu funkce jedné reálné proměnné |
derivovat funkce jedné reálné proměnné |
vyřešit soustavu lineárních algebraických rovnic |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
definovat neurčitý integrál a primitivní funkci |
definovat určitý integrál a integrální součty |
formulovat Taylorovu a Fourierovu řadu |
formulovat počáteční úlohu pro obyčejnou diferenciální rovnici prvního řádu |
formulovat počáteční a okrajovou úlohu pro obyčejnou diferenciální rovnici druhého řádu |
definovat pojem funkce více proměnných |
definovat parciální derivace a gradient |
Skills - skills resulting from the course: |
metodami integrálního počtu (per partes, substituce, rozklad na parciální zlomky) najít primitivní funkci |
rozvinout jednoduché funkce v Taylorovu a Fourierovu řadu |
metodou separace proměnných vyřešit obyčejnou diferenciální rovnici prvního řádu |
řešit homogenní i nehomogenní lineární obyčejné diferenciální rovnice vyšších řádů s konstantními koeficienty |
aplikovat diferenciální rovnice a znalost jejich řešení na úlohy z praxe |
stanovit parciální derivace a gradient funkce více proměnných |
Competences - competences resulting from the course: |
N/A |
N/A |
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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 |
Skills demonstration during practicum |
Skills - skills achieved by taking this course are verified by the following means: |
Written exam |
Test |
Skills demonstration during practicum |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Lecture with visual aids |
One-to-One tutorial |
Task-based study method |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
Task-based study method |
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