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Course info
KMA / MA1
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Course description
Department/Unit / Abbreviation
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KMA
/
MA1
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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 Analysis 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,
6
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
4
[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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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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227 / -
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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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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 |
No
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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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None
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Preclusive courses
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KMA/MA1-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 a basic introduction and active understanding of the fundamental concepts of mathematical analysis such as:
- infinite sequences and series of real numbers;
- functions of one real variable;
- differential and integral calculus.
Most students are advised to take KMA/SMA1 concurrently, in order to pass the exam successfully.
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Requirements on student
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Demonstrate knowledge of the definitions, fundamental theorems and their proofs concerning sequences, series, and functions of one real variable. Use rigorous arguments in calculus and ability to apply them in solving problems on the topics in the syllabus.
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Content
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Week 1: Sets and elementary operations; subsets of real numbers; absolute value; maximum, minimum, least upper bound, and greatest lower bound of a subset of real numbers;
Week 2: Sequences of real numbers; subsequences; bounded and monotone sequences; recursively defined sequences; convergent and divergent sequences;
Week 3: Algebra of limits and fundamental theorems concerning the properties of a limit;
Week 4: Conditions ensuring the convergence of infinite sequences and series;
Week 5: Absolute and relative convergence, alternating series;
Week 6: Functions of one real variable; graphical representation; inverse functions; composition of functions;
Week 7: Local and global behaviour of a function; limits; one-sided limits; algebra of limits;
Week 8: Continuity of a function at a point; points of discontinuity; continuity in a closed interval;
Week 9: Derivative and differential of a function - definition and both the geometrical and the physical meaning; differentiability and continuity of a function;
Week 10: Differentiation from first principles, product rule and chain rule, Rolle's theorem, Langrange's and Cauchy's mean value theorems; stationary points of a function; l'Hospital's rule;
Week 11: Indefinite integral; fundamental theorem of calculus; integration by parts and integration by substitution;
Week 12: Definite integral and its applications; mean value theorem inequalities for integrals;
Week 13: Improper integrals; higher order derivatives and differentials; Taylor's theorem;
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Activities
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Fields of study
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Studentům je k dispozici kurz v Moodle se všemi podstatnými informacemi a materiály.
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Guarantors and lecturers
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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:
http://home.zcu.cz/~tomiczek
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Recommended:
Pultr, Aleš. Matematická analýza I. Praha : Matfyzpress, 1995. ISBN 80-8586-3-09-X.
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Recommended:
Canuto, Claudio. Mathematical analysis I. New York : Springer, 2008. ISBN 978-88-470-0875-5.
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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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Recommended:
trial.kma.zcu.cz
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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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78
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Preparation for an examination (30-60)
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56
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Preparation for comprehensive test (10-40)
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24
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Total
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158
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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 mathematics |
explain basic methods of solving simple mathematical problems |
understand a simple mathematical text |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
solve linear and quadratic equations and inequalities as well as their systems |
work with absolute values, powers and simplify mathematical expressions |
sketch the graphs of elementary functions and their simple modifications |
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: |
demonstrate knowledge of the definitions and the elementary properties of sequences, series, and differentiable functions of one real variable |
be able to read and understand mathematical text |
use logical constructions in formulating basic definitions and theorems |
Skills - skills resulting from the course: |
use the calculus rules to differentiate functions |
sketch the graph of a function using critical points, the derivative tests for monotonicity and concavity properties |
set up max/min problems and use differentiation techniques to solve them |
evaluate integrals using techniques of integration, such as substitution and integration by parts |
to work with sequences and series of real numbers |
use developed theory in solving problems on physical systems |
use l'Hospital's rule |
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: |
Oral exam |
Written exam |
Test |
Skills - skills achieved by taking this course are verified by the following means: |
Oral exam |
Written exam |
Test |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
Written 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 supplemented with a discussion |
Interactive lecture |
Task-based study method |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
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