Course: Mathematical Analysis IV

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Course title Mathematical Analysis IV
Course code MU/01104
Organizational form of instruction Lecture
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • AVERBUCH Vladimír, DrSc.
Course content
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).

Learning activities and teaching methods
Recommended literature
  • D. Krupka. Úvod do analýzy na varietách. SPN, Praha, 1986.
  • 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
Faculty of Philosophy and Science in Opava Theoretical Physics (2) Physics courses - Summer