Course: Mathematical Analysis IV

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Course title Mathematical Analysis IV
Course code MU/01004
Organizational form of instruction Lecture
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 5
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
Course availability The course is available to visiting students
Lecturer(s)
  • AVERBUCH Vladimír, DrSc.
Course content
1. Riemann integral (divisions, null sets, oscillation, Lebesgue Theorem on Riemann integral, Fubini Theorem, partition of unity, change of variables in integral). 2. Differential forms (tensors, antisymmetric tensors, differential forms, exterior differential). 3. Stokes Theorem (chains, integral over a chain, Stokes Theorem for chains, manifolds, tangent space, orientation, Stokes Theorem for manifolds, theorems on rotor and on divergence). 4. Elements of comlex analysis (functions of one comlex variable, derivative and integral for such functions, Cauchy formula, residues). 5. Ordinary differential equations (Theorem on existence and uniqueness of the solution, methods of solutions, linear equations).

Learning activities and teaching methods
unspecified
Recommended literature
  • M. Spivak. Matematičeskij analiz na mnogoobrazijach. Mir, Moskva, 1968.
  • V. I. Averbuch, M. Málek. Matematická analýza III, IV. MÚ SU, Opava, 2003.
  • V. Jarník. Integrální počet I. ČSAV, Praha, 1963.
  • V. Jarník. Integrální počet II. ČSAV, Praha, 1963.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2014-IVT) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 2 Summer
Mathematical Institute in Opava Applied Mathematics (2014-F) Mathematics courses 2 Summer
Mathematical Institute in Opava Applied Mathematics (2014-IVT) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 2 Summer