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Main menu for Browse IS/STAG
Course info
KMA / SDP
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Course description
Department/Unit / Abbreviation
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KMA
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SDP
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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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Seminar on Differential Calculus
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Form of course completion
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Pre-Exam Credit
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Form of course completion
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Pre-Exam Credit
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Accredited / Credits
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Yes,
2
Cred.
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Type of completion
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-
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Type of completion
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-
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Time requirements
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Tutorial
2
[Hours/Week]
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Course credit prior to examination
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No
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Course credit prior to examination
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No
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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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NO
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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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0 / -
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0 / -
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0 / -
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Included in study average
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NO
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Winter semester
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125 / -
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24 / -
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206 / -
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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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Winter + Summer
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Semester taught
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Winter + Summer
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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 |
S|N |
Periodicity |
každý rok
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Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
Yes
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Fundamental theoretical course |
No
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Evaluation scale |
S|N |
Substituted course
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None
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Preclusive courses
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KMA/SMA1
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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 the course is to introduce students to the concepts of higher mathematical analysis, such as:
Fundamentals of set theory, real numbers. Sequences, limits of sequences, series of real numbers, partial sum of a series, sum of a series, convergence and absolute convergence of a series, alternating series. Real functions of one real variable, derivatives, differential functions; basic theorems of differential calculus, investigation of the graph of a function of one real variable; Taylor's formula and higher order derivatives, graph of a function; basics of integral calculus.
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Requirements on student
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It is necessary to obtain at least 50% points from the assignments given lecturer.
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Content
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Fundamentals of set theory, real numbers. Sequences, limits of sequences, series of real numbers, partial sum of a series, sum of a series, convergence and absolute convergence of a series, alternating series. Real functions of one real variable, derivatives, differential functions; basic theorems of differential calculus, investigation of the graph of a function of one real variable; Taylor's formula and higher order derivatives, graph of a function; basics of integral calculus.
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Activities
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Fields of study
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Guarantors and lecturers
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Guarantors:
RNDr. Petr Tomiczek, CSc. (100%),
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Tutorial lecturer:
Ing. Jan Čepička, Ph.D. (100%),
Ing. Jiří Egermaier, Ph.D. (100%),
Mgr. Alexej Moskovka (100%),
Ing. Petr Nečesal, Ph.D. (100%),
Doc. RNDr. Petr Stehlík, Ph.D. (100%),
RNDr. Vladimír Švígler, Ph.D. (100%),
Ing. Eva Turnerová, 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 comprehensive test (10-40)
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26
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Contact hours
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26
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Total
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52
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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: |
identifikovat kvadratickou, exponenciální, logaritmickou a goniometrickou rovnici |
klasifikovat obory čísel |
popsat pravidla úprav početních a algebraických výrazů |
popsat základní funkce (polynomy, goniometrické funkce, exponenciální, logaritmické funkce) |
rozpoznat aritmetickou a geometrickou posloupnost |
rozpoznat úlohy na přímou a nepřímou úměru |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
načrtnout grafy základních funkcí |
spočítat částečný součet aritmetické a geometrické posloupnosti |
upravit početní a algebraické výrazy |
vyřešit kvadratickou, exponenciální, logaritmickou a goniometrickou rovnici |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
formulovat Taylorovu větu |
popsat derivaci a integrál funkce jedné reálné proměnné |
popsat posloupnost a řadu reálných čísel |
popsat spojitou a inverzní funkci |
rozpoznat logické symboly, výroky a kvantifikátory |
Skills - skills resulting from the course: |
derivovat a integrovat funkce jedné reálné proměnné |
nakreslit graf inverzní funkce; algebraické, goniometrické, exponenciální a hyperbolické |
rozhodnout o konvergenci a divergenci posloupnosti, řady a nevlastního integrálu |
řešit optimalizační úlohy pro funkce jedné reálné proměnné |
spočítat maximum, minimum, supremum a infimum číselné množiny |
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: |
Test |
Skills - skills achieved by taking this course are verified by the following means: |
Test |
Competences - competence achieved by taking this course are verified by the following means: |
Test |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Seminar |
Skills - the following training methods are used to achieve the required skills: |
Seminar |
Competences - the following training methods are used to achieve the required competences: |
Seminar |
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