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Course info
KMA / MA1E
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Course description
Department/Unit / Abbreviation
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KMA
/
MA1E
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Academic Year
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2024/2025
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Academic Year
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2024/2025
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Title
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Mathematics 1
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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, English
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Occ/max
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|
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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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304 / -
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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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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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not determined
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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, English
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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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None
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Preclusive courses
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KMA/M1E
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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 a basic introduction to the fundamental concepts of mathematical analysis such as:
- infinite sequences and series of real numbers;
- functions of one real variable;
- differential calculus of functions of one variable;
- introduction to integral calculus of functions of one variable.
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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 test (required at least 60%)
Exam: witten and oral part.
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Content
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Week 1: Mathematical statements, sets and elementary operations.
Week 2: Sequences of real numbers, boundedness, monotonicity, supremum and infimum.
Week 3: Limit of a sequence. Methods of calculating a limit, properties of convergent sequences.
Week 4: Euler number. Series of real numbers, sum of series, geometric series, harmonic series.
Week 5: Functions of one real variable, their domain, restriction, equality of functions.
Week 6: Properties of functions. Inverse and composed functions.
Week 7: Limits of functions. Continuity of a function at a point.
Week 8: Points of discontinuity. Derivative of a function, their geometrical and the physical meaning. Rules of differentiation.
Week 9: Tangent and normal lines. Higher order derivatives. Extrema and optimization.
Week 10: l'Hospital's rule. Analysing graphs of functions. Solvability of nonlinear equations.
Week 11: Taylor's polynomial. Primitive function and indefinite integral.
Week 12: Integration by parts and integration by substitution. Definite integral.
Week 13: Improper integrals. Integrals with variable bounds.
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Activities
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Fields of study
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https://courseware.zcu.cz/portal/studium/courseware/kma/ma1e
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Guarantors and lecturers
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Guarantors:
RNDr. Vladimír Švígler, Ph.D. (100%),
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Lecturer:
Doc. RNDr. Jiří Benedikt, Ph.D. (100%),
RNDr. Vladimír Švígler, Ph.D. (100%),
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Tutorial lecturer:
Doc. RNDr. Jiří Benedikt, Ph.D. (100%),
Doc. Ing. Josef Daněk, Ph.D. (100%),
RNDr. Hana Formánková Levá (100%),
Doc. Ing. Gabriela Holubová, Ph.D. (100%),
RNDr. Vladimír Švígler, Ph.D. (100%),
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Literature
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Basic:
Drábek, Pavel; Míka, Stanislav. Matematická analýza I. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-558-8.
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Recommended:
Thomson, Bruckner, Bruckner. Elementary real analysis. 2008.
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Recommended:
Pultr, Aleš. Matematická analýza I. Praha : Matfyzpress, 1995. ISBN 80-8586-3-09-X.
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Recommended:
Zorich, Vladimir A. Mathematical Analysis I. Berlin, 2004. ISBN 3-540-40386-8.
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Recommended:
Polák, J. Přehled středoškolské matematiky.. Praha : Prometheus, 2008. ISBN 978-80-7196-356-1.
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Recommended:
Míková, Marta; Kubr, Milan; Čížek, Jiří. Sbírka příkladů z matematické analýzy I. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-568-5.
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Recommended:
Děmidovič, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. Havlíčkův Brod : Fragment, 2003. ISBN 80-7200-587-1.
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On-line library catalogues
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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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52
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Preparation for an examination (30-60)
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32
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Preparation for formative assessments (2-20)
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20
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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: |
be familiar with high school knowledges |
to explain basic methods of solving simple mathematical problems |
to understand a simple mathematical text |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
to solve linear and kvadratic equalities and inequalities and their systems |
to work with absolute values, powers and manipulate with mathematical expressions |
to sketch graphs of elementary functions |
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: |
understand logical constructions and to be able to read mathematical text |
use rigorous arguments in calculus and ability to apply them in solving problems on the topics in the syllabus |
demonstrate knowledge of the definitions and the elementary properties of sequences, series and continuous and differentiable functions of one real variable |
Skills - skills resulting from the course: |
use the rules of differentiation to differentiate functions |
sketch the graph of a function using critical points, and the derivative test for increasing/decreasing and concavity properties |
set up max/min problems and use differentiation to solve them |
use l'Hospital's rule |
evaluate integrals using techniques of integration, such as substitution and integration by parts |
use developed theory in solving problems on physical systems |
to work with sequences and series of real numbers |
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: |
Oral exam |
Written exam |
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 |
Task-based study method |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
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