MU:MU01104 Mathematical Analysis IV - Course Information
MU01104 Mathematical Analysis IV
Mathematical Institute in OpavaSummer 2021
- Extent and Intensity
- 3/0/0. 5 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- RNDr. Petr Blaschke, Ph.D. (lecturer)
- Guaranteed by
- doc. RNDr. Michal Málek, Ph.D.
Mathematical Institute in Opava - Timetable
- Tue 8:05–10:30 RZ
- Prerequisites (in Czech)
- NOW( MU01904 Mathematical Analysis IV - Exe ) && ! MU01004 Mathematical Analysis IV && !NOW( MU01004 Mathematical Analysis IV ) && TYP_STUDIA(N)
- Course Enrolment Limitations
- The course is only offered to the students of the study fields the course is directly associated with.
- fields of study / plans the course is directly associated with
- Theoretical Physics (programme FPF, N1701 Fyz)
- Theoretical Physics (programme FPF, N1701 Fyz)
- Syllabus
- 1. Riemann integral (divisions, null sets, oscillation, Lebesgue theorem, Fubini's theorem, partition of unity, change of variable in the integral).
2. Differential forms (tensors, anti-symmetric tensors, differential forms, exterior differentiation).
3. Stokes theorem (chains, integral over a chain, Stokes theorem for chains, manifolds, tangent space, orientation, Stokes theorem for manifolds, theorems on rotation and divergence).
4. Basics of complex analysis (functions of one complex variable, derivatives and integrals in the complex domain, Cauchy's residue theorem and its consequences).
5. Ordinary differential equations (theorem on existence and uniqueness, solution methods, linear equations).
- 1. Riemann integral (divisions, null sets, oscillation, Lebesgue theorem, Fubini's theorem, partition of unity, change of variable in the integral).
- Literature
- recommended literature
- V. I. Averbuch, M. Málek. Matematická analýza III, IV. MÚ SU, Opava, 2003. URL info
- D. Krupka. Úvod do analýzy na varietách. SPN, Praha, 1986. info
- M. Spivak. Matematičeskij analiz na mnogoobrazijach. Mir, Moskva, 1968. info
- V. Jarník. Integrální počet I. ČSAV, Praha, 1963. info
- V. Jarník. Integrální počet II. ČSAV, Praha, 1963. info
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course can also be completed outside the examination period.
- Enrolment Statistics (recent)
- Permalink: https://is.slu.cz/course/sumu/summer2021/MU01104