MU01104 Mathematical Analysis IV

Mathematical Institute in Opava
Summer 2018
Extent and Intensity
3/0/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Vladimír Averbuch, DrSc. (lecturer)
Guaranteed by
Vladimír Averbuch, DrSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU01904 Mathematical Analysis IV - Exe
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
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).
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
English
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2019, Summer 2020, Summer 2021.
  • Enrolment Statistics (Summer 2018, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2018/MU01104