MPBPOF01 Selected Chapters in Applied Mathematics I

Institute of physics in Opava
winter 2024
Extent and Intensity
1/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Jaroslav Vrba, Ph.D. (lecturer)
Mgr. Pavlína Jalůvková (seminar tutor)
RNDr. Jaroslav Vrba, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Jaroslav Vrba, Ph.D.
Institute of physics in Opava
Timetable
Wed 10:35–11:20 B4
  • Timetable of Seminar Groups:
MPBPOF01/A: Wed 11:25–13:00 B4, P. Jalůvková, J. Vrba
Prerequisites (in Czech)
(FAKULTA(FU) && TYP_STUDIA(B))
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course introduces students to the basic parts of mathematical analysis and algebra, which are necessary especially for the study of the basic physics course. Instruction emphasizes the solution of concrete problems and clarification of relevant basic definitions and theorems. - Mathematical Analysis III - Differential equations, division of differential equations, general and partial solutions of differential equations, geometric meaning of solutions; first order ordinary differential equations, method of separation of variables and variation of constant. - Algebra I - matrices, basic types of matrices, matrices in step form; equality, addition and multiplication of matrices; permutation of a set, determinant of a square matrix; basic properties and methods of calculating determinants; inverse matrices, methods of finding inverse matrices; system of linear equations and its solvability; Cramer's rule; equivalent modifications of a system of equations and Gaussian elimination method. - Algebra II - complex number, algebraic and goniometric form of complex number, representation of complex number; addition, multiplication and division of complex numbers, Moivre's theorem; polynomial of nth degree, root of polynomial, equality, sum, product and quotient of polynomials; algebraic equation of nth degree, solution of cubic, quartic and binomial equations; decomposition of polynomial in the domain of complex numbers.
Literature
    recommended literature
  • Kvasnica, J., Matematický aparát fyziky. Vyd. 2. opr. Praha: Academia, 1997. ISBN 80-200-0603-6.
  • Rektorys, K., Přehled užité matematiky. 7. vyd. Praha: Prometheus, 2000. Česká matice technická (Prometheus). ISBN 80-7196-181-7.
Language of instruction
Czech
Further Comments
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/fu/winter2024/MPBPOF01