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Course info
KMA / M1E
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Course description
Department/Unit / Abbreviation
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KMA
/
M1E
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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 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
3
[Hours/Week]
Tutorial
3
[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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|
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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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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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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 |
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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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: basic work with vectors, matrices, systems of linear equations, analytic geometry, sequences; differential and integral calculus.
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Requirements on student
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During semester, students have to write three assignments (5-th week - 15 points, 9-th week - 15 points, 12-th week - 15 points) - it is necessary to obtain at least 23 points from these assignments.
The final examination is in the form of a written exam (18-20 points - grade 1,
14-17 points - grade 2, 10-13 points - grade 3, 0 - 9 points - grade 4) which is supplemented by an oral examination. All assessment tasks will assess the learning outcomes, especially, the ability to provide logical and coherent proofs of theoretical results and to analyze problems from the written part.
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Content
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Vectors, matrices, determinants, eigenvalues, eigenvectors. Systems of linear equations. Analytic geometry. Sequences. Functions of one real variable. Limits and continuity of function. Monotonic functions. Derivatives, concave down (up), extremes of functions. Behaviour of functions. Taylor's theorem. Indefinite and definite integral.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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-
Recommended:
Drábek, Pavel; Míka, Stanislav. Matematická analýza I. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-558-8.
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Recommended:
Matematická analýza 1
(Tomiczek Petr)
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Recommended:
Dolanský, Petr; Tuchanová, Milena. Matematika pro ekonomy 1 : pro distanční studium. Plzeň : ZČU, 1995. ISBN 80-7082-183-3.
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Recommended:
Dolanský, Petr; Tuchanová, Milena. Příklady z matematiky pro ekonomy I : distanční studium. 1. vyd. Plzeň : ZČU, 1995. ISBN 80-7082-184-1.
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Recommended:
Tesková, Libuše. Sbírka příkladů z lineární algebry. 5. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7043-263-2.
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Recommended:
Čížek, Jiří; Kubr, Milan; Míková, Marta. Sbírka příkladů z matematické analýzy I. 1. vyd. Plzeň : ZČU, 1995. ISBN 80-7082-216-3.
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Recommended:
Jirásek, František; Kriegelstein, Eduard; Tichý, Zdeněk. Sbírka řešených příkladů z matematiky : logika a množiny, lineární a vektorová algebra, analytická geometrie, posloupnosti a řady, diferenciální a integrální počet funkcí jedné proměnné. 2. nezměn. vyd. Praha : SNTL, 1981.
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Recommended:
Mašek, Josef. Základy matematiky I : cvičení. 1. vyd. Plzeň : Západočeská univerzita, 1999. ISBN 80-7082-567-7.
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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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Preparation for formative assessments (2-20)
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12
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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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45
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Preparation for comprehensive test (10-40)
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24
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Total
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159
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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: |
A good knowledge of basic functions - polynomial functions, goniometric function, exponetial function etc.. Basic knowledge of analytic geometry - equation of the straight line.
Skills in computing with algebraic terms, fractions, linear, qudratic equations and in solving linear systems of equations. |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
On completion of this module the student will be able to:
- understand to terms: convergent sequence, geometric series, vector, matrix, the rank of matrix, the inverse of matrix, eigenvalue and eigenvector, function, derivative of function, graph of function;
- know what the convergence sequence is;
- be able to prove elementary theorems concerning sequences;
- perform vectors and matrix calculations including reduction to echelon form;
- solve general systems of linear equations;
- differentiate function of a single real variable;
- solve extremal problems;
- describe the curve of function and sketch its graph;
- compute indefinite and difinite integral. |
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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 |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Practicum |
Multimedia supported teaching |
Interactive lecture |
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