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Main menu for Browse IS/STAG
Course info
KID / YAMAT
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Course description
Department/Unit / Abbreviation
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KID
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YAMAT
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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
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Form of course completion
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Examination
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Form of course completion
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Examination
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Accredited / Credits
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Yes,
7
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
22
[Hours/Semester]
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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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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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50 / -
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0 / -
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1 / -
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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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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
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Internship duration
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0
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No. of hours of on-premise lessons |
0
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Evaluation scale |
A|B|C|D|E|F |
Periodicity |
každý rok
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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 |
A|B|C|D|E|F |
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 objectives of the course are to familiarize students with basic knowledge of vector calculus in 3D, sequences and series, functions and their limits, differential and integral calculus, first order differential equations, numerical calculations and interpolation and approximation of functions.
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Requirements on student
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Requirements for exam
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Content
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1. Basics of vector calculus in three-dimensional Euclidean space
(3D coordinate system, distance of points in 3D, vectors basic concepts, linear dependence
and complanarity of vectors, linear combinations of vectors, basis vector space, scalar,
vector and mixed product of vectors)
2. Sequence and its limit
(Sequence, limit of sequence, computation of limit of sequences, monotonicity of sequences,
convergence and sum of a geometric series)
3. Function and its limit
(function, function defined in parts, continuity and limit of function, one-sided limits, rules
for calculating limits, calculating type limits of functions)
4. Differential calculus of functions of one real variable
(Definition of derivative, theorems on derivatives of powers, goniometric, logarithmic,
exponential and cyclometric functions, derivatives of compound functions, differential functions,
L'Hospital's rule for calculating limits of functions, tangents and normals)
5. The progression of a function
(monotony of a function, stationary points of a function, local and absolute extremes of a function, inflection
points of the function, convexity and concavity of the function, asymptotes of the graph of the function, optimization problems)
6. Indefinite integral of functions of one real variable
(primitive functions and the indefinite integral, methods of integration - direct, substitution and per partes)
7. The definite integral and its applications
(methods of calculating definite integrals, calculating the area under the graph of a function)
8. First order differential equations
(initial problem, method of separation of variables, method of variation of a constant, growth models
decrease and decrease, logistic model)
9. Differential and integral calculus of functions of two or more real variables
(functions of two or more variables, continuity and limit, partial derivatives, geometric meaning
of partial derivatives, extremes of functions, Reimann's multivariate integral, calculation of
multivariate integrals on a compact interval, application of double integrals)
10. Fundamentals of numerical calculations
(engineering calculations on a calculator, Taylor's polynomial, approximate calculations of function values
using differential equations, numerical solution of equations, simple iteration method, Newton's method,
Euler's method of solving differential equations)
11. Interpolation and approximation of functions
(Lagrange's and Newton's interpolation polynomial, Least Squares method)
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Activities
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Fields of study
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Dostupné na https://ct.upce.cz/mathjiku/m1.html
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Guarantors and lecturers
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Literature
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Basic:
Jehlička, Vladimír. Matematika 2 : multimediální studijní opora : (videozáznamy přednášek). Pardubice: Univerzita Pardubice, 2013. ISBN 978-80-7395-576-2.
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Recommended:
Cabrnochová,R. - Prachař,O. Průvodce předmětem MATEMATIKA I. ( třetí. část )- Úlohy z lineární algebry, analytické geometrie a z nekonečných řad.. Pardubice, 2008.
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Recommended:
Kolda,S.-Machačová ,L.-Prachař,O. Cvičebnice z Matematiky II.. Pardubice, 2007.
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Recommended:
Prachař, Otakar. Průvodce předmětem matematika II.. Pardubice: Univerzita Pardubice, 2003. ISBN 80-7194-557-9.
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Prerequisites - other information about course preconditions |
General knowledge of basic mathematics from previous studies |
Competences acquired |
Basic knowledge of - vector calculus in 3D, sequences and series, functions and their limits, differential and integral calculus, first order differential equations, numerical calculations and interpolation and approximation of functions. |
Teaching methods |
- Monologic (reading, lecture, briefing)
- Dialogic (discussion, interview, brainstorming)
- Work with text (with textbook, with book)
- Methods of individual activities
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Assessment methods |
- Oral examination
- Written examination
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