| Course title | Applied Mathematics I. |
|---|---|
| Course code | KID/PAM11 |
| Organizational form of instruction | Lecture |
| Level of course | Doctoral |
| Year of study | not specified |
| 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) |
|---|
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| 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), Skills training |
| 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 |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Transport Engineering | Study plan (Version): Transport Means and Infrastructure: Electrical Engineering (2013) | Category: Transportation and communications | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Transport Engineering | Study plan (Version): Transport Means and Infrastructure: Transport Means (2013) | Category: Transportation and communications | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Transport Engineering | Study plan (Version): Transport Means and Infrastructure: Transport Infrastructure (2013) | Category: Transportation and communications | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Transport Engineering | Study plan (Version): Transport Means and Infrastructure: Transport Means (2013) | Category: Transportation and communications | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Transport Engineering | Study plan (Version): Transport Means and Infrastructure: Electrical Engineering (2013) | Category: Transportation and communications | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Transport Engineering | Study plan (Version): Transport Means and Infrastructure: Transport Infrastructure (2013) | Category: Transportation and communications | 1 | Recommended year of study:1, Recommended semester: Winter |