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Course, academic year 2018/2019
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Introduction to Mathematical Methods of Physics - NUFY081
Title in English: Úvod do matematických metod fyziky
Guaranteed by: Department of Physics Education (32-KDF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2013 to 2018
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:0/3 C [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
Guarantor: doc. RNDr. Mgr. Vojtěch Žák, Ph.D.
prof. RNDr. Jiří Podolský, CSc., DSc.
RNDr. Marie Snětinová, Ph.D.
Classification: Teaching > Physics
Incompatibility : NUFY027
Interchangeability : NUFY027
Annotation -
Last update: T_KDF (23.05.2003)
Explanation and exercising of various mathematical methods used in the introductory physics course. Practical applications and solution of particular physical problems are emphasized. For the 1st year of the Bc study Physics aimed at Education (Physics-Mathematics).
Course completion requirements - Czech
Last update: RNDr. Marie Snětinová, Ph.D. (12.10.2017)

Podmínky k získání zápočtu pro studenty prezenčního studia:

  • Alespoň 75% účast na výuce;
  • dále je podmínkou zápočtu vypracování dvou úkolů, které studenti musejí odevzdat v předem stanoveném termínu.


Podmínky k získání zápočtu pro studenty kombinovaného studia a kurzu CŽV:

  • Podmínkou zápočtu je vypracování dvou úkolů, které studenti musejí odevzdat v předem stanoveném termínu.


Charakter podmínek pro získání zápočtu vylučuje opakování.

Literature -
Last update: T_KDF (12.05.2015)

Kvasnica J.: Matematický aparát fyziky, Academia, Praha, 1989.

Musilová J. & Musilová P.: Matematika pro porozumění a praxi I, VUTIUM, Brno, 2006.

Syllabus -
Last update: T_KDF (12.05.2015)

SYLABUS EN:

Coordinate systems.
The most common coordinates in plane and space: Cartesian, polar, cylindrical and spherical. Definition and motivation: planetary motion ...

Function and its derivative.
Recalling functions and limits. Differentiation and elementary methods of calculus. Physical applications, differential equations and examples (radioactive decay, discharging, harmonic oscillations). Three important generalizations: higher-order derivatives (Taylor expansion of functions), differentiation of functions of several variables (partial derivative), derivatives of vectors (velocity and acceleration in non-Cartesian coordinates).

Integration.
A primitive function (motivation: shape of water surface in a rotating glass), indefinite integral. Elementary rules and methods of calculus (per partes method, substitution, partial fractions). Definite integrals and their properties. Newton-Leibniz formula. Various physical and geometrical applications. Unbounded integrals: Euler-Poisson-Laplace integral and velocities of molecules.

 
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