University of Pardubice
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for academic year 2025/2026
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Course: Applied Mathematics I.

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Course title Applied Mathematics I.
Course code KID/XDM11
Organizational form of instruction Lecture
Level of course Doctoral
Year of study 1
Semester Winter
Number of ECTS credits 0
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Kulička Jiří, Mgr. Ph.D.
  • Půlpán Zdeněk, prof. PhDr. RNDr. CSc.
Course content
The numerical spaces (sentences, konvergence, complete spaces, open and concludet interval (spaces), continuous mapping, compactness). Vector spaces and the linear operators (basic, dimension, the normed space, space with the scalar product. The linear operators as well vectors. Matrix and representation of linear operators with help matrix, norm of matrix, principle of fix point.Mistakes by the numerical calculation (mistakes of arithmetical operations, rounding, approach with help probability. Decision procedure of equations (diference, linear diference equations, iterations method, Newton's Method of bisector). System of linear equations, Gauss-elimination, L-V break up, Gauss-Jordan elimination. Methods of iteration, inverse matrix. Aproximation and interpolation. Method of least squares, the orthogonal system of functions. Lagrange, Newton and Hermite polynoms, mistakes of interpolation. Equidistant progression of nodes. Splayns and numerical derivation, the numerical integration; Methods of Newton-Cotes, method of trapezoid, formula of Simpson. The Fourier transformation and their numerical ways. The numerical solving of diferential equations, formulation of problems, method of gradual approximation, Euler's method, method of Runge-Kutta, convergency of one node methods). Frontier property. Sets and binar relation (function, tolerance, equivalence, characteristics). The algebraic structures (semigroups and monoids, isomorphism, homomorphism of polygroups, groups, circle, universal algebras). Units (ordering, joint, break, distributive units, booleas algebra, logic, algebras of logic nets).

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Demonstration, Skills training
  • Term paper - 36 hours per semester
  • Term paper - 36 hours per semester
  • Term paper - 36 hours per semester
Learning outcomes
Create groundwork use it system MATLAB for numerical analysis.
Proposition mathematical model processing quantitative quantities.
Prerequisites
unspecified

Assessment methods and criteria
Oral examination, Written examination

The knowledge of the basic numerical proceedings for using the program's tools (MATLAB, MATHEMATICA, ...)
Recommended literature
  • Koucký, J. Elementární metody řešení obyčejných diferenciálních rovnic. Praha: NČSAV, 1953.
  • Prágerová, A. Diferenční rovnice. Praha: Státní nakladatelství technické literatury, 1971.
  • Přikryl, Petr. Numerické metody matematické analýzy. Praha: Státní nakladatelství technické literatury, 1985.
  • Ralston, Anthony. Základy numerické matematiky. Praha: Academia, 1973.
  • Rektorys, K. a kol. Přehled užité matematiky. Praha: Prometheus, 2000.
  • Schwarz, Š. Základy náuky o riešení rovnic. Praha: NČSAV, 1958.
  • Vitásek, Emil. Numerické metody. Praha: Státní nakladatelství technické literatury, 1987.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
University of Pardubice, date of update: 16.03.2026 23:51. Data created for academic year 2025/2026